From fa7ee4f89fa92a50a9891fe74834d0fb6345d31a Mon Sep 17 00:00:00 2001 From: Michael Dumelle Date: Thu, 20 Nov 2025 12:45:54 -0800 Subject: [PATCH 1/9] version update --- DESCRIPTION | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/DESCRIPTION b/DESCRIPTION index 8f203cb..18f3533 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,6 +1,6 @@ Package: spmodel Title: Spatial Statistical Modeling and Prediction -Version: 0.11.1 +Version: 0.12.0 Authors@R: c( person(given = "Michael", family = "Dumelle", From 09abe3e09201de98374936c7c267ea5727523dce Mon Sep 17 00:00:00 2001 From: Michael Dumelle Date: Thu, 20 Nov 2025 12:48:32 -0800 Subject: [PATCH 2/9] some bk improvements --- NEWS.md | 8 ++++++++ R/get_local_list.R | 15 ++++++++++++--- R/predict.R | 2 +- R/predict_block.R | 26 +++++++++++++++++++++++++- man/predict.spmodel.Rd | 2 +- 5 files changed, 47 insertions(+), 6 deletions(-) diff --git a/NEWS.md b/NEWS.md index 02cfd15..5ca8933 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,3 +1,11 @@ +# spmodel 0.12.0 + +## Minor Updates + +* Changed the default `size` argument to the local argument in `predict(..., block = TRUE)` and `augment(..., block = TRUE)` from 1000 to 4000. This enhances the block prediction (i.e., Kriging) approximation's accuracy but can slightly increase computational complexity. +* Enhanced efficiency of block prediction (i.e., Kriging) for large `newdata` objects. +* Minor documentation updates. + # spmodel 0.11.1 ## Minor Updates diff --git a/R/get_local_list.R b/R/get_local_list.R index 052e83b..fbd8578 100644 --- a/R/get_local_list.R +++ b/R/get_local_list.R @@ -168,7 +168,7 @@ get_local_list_prediction_block <- function(local) { if (is.logical(local)) { if (local) { - local <- list(method = "covariance", size = 1000) + local <- list(method = "covariance", size = 4000) } else { local <- list(method = "all") } @@ -190,10 +190,19 @@ get_local_list_prediction_block <- function(local) { } if (local$method %in% c("distance", "covariance") && !"size" %in% names_local) { - local$size <- 1000 + local$size <- 4000 } - # no parallel required + if (!"parallel" %in% names_local) { + local$parallel <- FALSE + local$ncores <- NULL + } + + if (local$parallel) { + if (!"ncores" %in% names_local) { + local$ncores <- parallel::detectCores() + } + } local } diff --git a/R/predict.R b/R/predict.R index d011a0c..fd1170b 100644 --- a/R/predict.R +++ b/R/predict.R @@ -73,7 +73,7 @@ #' If \code{block} is \code{TRUE}, \code{local} accepts \code{method} and \code{size}, #' and \code{method} takes values of \code{"all"}, \code{"covariance"}, #' and \code{"distance"}, similar as when \code{block} is \code{FALSE}. -#' The default \code{method} is \code{"distance"} with size \code{1000}. This default \code{size} is +#' The default \code{method} is \code{"covariance"} with size \code{4000}. This default \code{size} is #' much larger than when \code{block} is \code{FALSE}. This is because when \code{block} is \code{TRUE}, #' covariances and explanatory variables are averaged before prediction, which greatly #' reduces computational burden, only requiring the Cholesky decomposition diff --git a/R/predict_block.R b/R/predict_block.R index bf458f4..24c87cf 100644 --- a/R/predict_block.R +++ b/R/predict_block.R @@ -143,7 +143,11 @@ predict_block_splm <- function(object, newdata, se.fit, scale, df, interval, lev c0 <- colMeans(covmatrix(object, newdata = newdata, cov_type = "pred.obs")) Sig <- covmatrix(object) - s0 <- mean(covmatrix(object, newdata = newdata, cov_type = "pred.pred")) + if (NROW(newdata) > 1e4) { + s0 <- get_bk_var(object, newdata, local) + } else { + s0 <- mean(covmatrix(object, newdata = newdata, cov_type = "pred.pred")) + } Xmat <- model.matrix(object) if (local$method == "all") { @@ -234,3 +238,23 @@ predict_block_splm <- function(object, newdata, se.fit, scale, df, interval, lev stop("Interval must be none, confidence, or prediction") } } + +get_bk_var <- function(object, newdata, local) { + index <- seq(1, NROW(newdata)) + object$obdata <- newdata + if (local$parallel) { + cl <- parallel::makeCluster(local$ncores) + val <- parallel::parLapply(cl, index, get_each_bk_meancov, object, newdata) + cl <- parallel::stopCluster(cl) + } else { + val <- lapply(index, get_each_bk_meancov, object, newdata) + } + mean(unlist(val)) +} + +get_each_bk_meancov <- function(index, object, newdata) { + newdata <- newdata[index, , drop = FALSE] + val <- as.vector(spmodel::covmatrix(object, newdata = newdata, cov_type = "obs.pred")) + val[index] <- val[index] + object$coefficients$spcov[["ie"]] # this is to add ie variance to diagonal (which is omitted with newdata) + mean(val) +} diff --git a/man/predict.spmodel.Rd b/man/predict.spmodel.Rd index 72a4378..30a9d13 100644 --- a/man/predict.spmodel.Rd +++ b/man/predict.spmodel.Rd @@ -235,7 +235,7 @@ that \code{local} is transformed into If \code{block} is \code{TRUE}, \code{local} accepts \code{method} and \code{size}, and \code{method} takes values of \code{"all"}, \code{"covariance"}, and \code{"distance"}, similar as when \code{block} is \code{FALSE}. -The default \code{method} is \code{"distance"} with size \code{1000}. This default \code{size} is +The default \code{method} is \code{"covariance"} with size \code{4000}. This default \code{size} is much larger than when \code{block} is \code{FALSE}. This is because when \code{block} is \code{TRUE}, covariances and explanatory variables are averaged before prediction, which greatly reduces computational burden, only requiring the Cholesky decomposition From 5f130f1cfb00b6d1ad380ab845cf2e55e26979a8 Mon Sep 17 00:00:00 2001 From: Michael Dumelle Date: Fri, 21 Nov 2025 11:11:54 -0800 Subject: [PATCH 3/9] remove unncessary formula argument in get_esv_cloud() --- R/esv.R | 2 +- R/get_esv.R | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/R/esv.R b/R/esv.R index b392dd9..71a0306 100644 --- a/R/esv.R +++ b/R/esv.R @@ -170,7 +170,7 @@ esv <- function(formula, data, xcoord, ycoord, cloud = FALSE, robust = FALSE, bi residual_vector2 <- residual_vector^2 if (cloud) { - esv_out <- get_esv_cloud(residual_vector2, dist_vector, formula) + esv_out <- get_esv_cloud(residual_vector2, dist_vector) } else { if (robust) { residual_vector12 <- sqrt(residual_vector) diff --git a/R/get_esv.R b/R/get_esv.R index 6ad4f78..0933fd7 100644 --- a/R/get_esv.R +++ b/R/get_esv.R @@ -62,7 +62,7 @@ get_esv_robust <- function(residual_vector12, dist_vector, bins, cutoff, formula esv_out } -get_esv_cloud <- function(residual_vector2, dist_vector, formula) { +get_esv_cloud <- function(residual_vector2, dist_vector) { esv_out <- tibble::tibble(dist = dist_vector, gamma = residual_vector2 / 2) From da80d71a920d86e5478dc4b9bcf445d48ad8b2a6 Mon Sep 17 00:00:00 2001 From: Michael Dumelle Date: Fri, 21 Nov 2025 11:40:50 -0800 Subject: [PATCH 4/9] add eacf --- NAMESPACE | 2 + NEWS.md | 4 + R/eacf.R | 204 +++++++++++++++++++++++++++++++++++ R/get_eacf.R | 41 +++++++ R/get_eacf_dotlist.R | 68 ++++++++++++ man/eacf.Rd | 89 +++++++++++++++ tests/testthat/test-extras.R | 92 ++++++++++++++++ tests/testthat/test-spglm.R | 9 ++ tests/testthat/test-splm.R | 9 ++ 9 files changed, 518 insertions(+) create mode 100644 R/eacf.R create mode 100644 R/get_eacf.R create mode 100644 R/get_eacf_dotlist.R create mode 100644 man/eacf.Rd diff --git a/NAMESPACE b/NAMESPACE index be4ce1d..f504a1a 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -188,6 +188,7 @@ S3method(model.matrix,spautor) S3method(model.matrix,spgautor) S3method(model.matrix,spglm) S3method(model.matrix,splm) +S3method(plot,eacf) S3method(plot,esv) S3method(plot,spautor) S3method(plot,spgautor) @@ -359,6 +360,7 @@ export(augment) export(covmatrix) export(dispersion_initial) export(dispersion_params) +export(eacf) export(esv) export(glance) export(glances) diff --git a/NEWS.md b/NEWS.md index 5ca8933..0ff0240 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,5 +1,9 @@ # spmodel 0.12.0 +## Major Updates + +* Added `eacf()` to compute the empirical autocovariance function. + ## Minor Updates * Changed the default `size` argument to the local argument in `predict(..., block = TRUE)` and `augment(..., block = TRUE)` from 1000 to 4000. This enhances the block prediction (i.e., Kriging) approximation's accuracy but can slightly increase computational complexity. diff --git a/R/eacf.R b/R/eacf.R new file mode 100644 index 0000000..63c5ae6 --- /dev/null +++ b/R/eacf.R @@ -0,0 +1,204 @@ +#' Compute the empirical autocovariance +#' +#' @description Compute the empirical autocovariance (i.e., empirical covariance) +#' for varying bin sizes and cutoff values. +#' +#' @param formula A formula describing the fixed effect structure. +#' @param data A data frame or \code{sf} object containing the variables in \code{formula} +#' and geographic information. +#' @param xcoord Name of the variable in \code{data} representing the x-coordinate. +#' Can be quoted or unquoted. Not required if \code{data} is an \code{sf} object. +#' @param ycoord Name of the variable in \code{data} representing the y-coordinate. +#' Can be quoted or unquoted. Not required if \code{data} is an \code{sf} object. +#' @param cloud A logical indicating whether the empirical autocovariance should +#' be summarized by distance class or not. When \code{cloud = FALSE} (the default), pairwise autocovariances +#' are binned and averaged within distance classes. When \code{cloud} = TRUE, +#' all pairwise autocovariances and distances are returned (this is known as +#' the "cloud" autocovariance). +#' @param bins The number of equally spaced bins. The default is 15. Ignored if +#' \code{cloud = TRUE}. +#' @param cutoff The maximum distance considered. +#' The default is half the diagonal of the bounding box from the coordinates. +#' @param dist_matrix A distance matrix to be used instead of providing coordinate names. +#' @param partition_factor An optional formula specifying the partition factor. +#' If specified, autocovariances are only computed for observations sharing the +#' same level of the partition factor. +#' +#' @details The empirical autocovariance (i.e., empirical covariance) is a tool used to visualize and model +#' spatial dependence by estimating the semivariance of a process at varying distances. +#' For a constant-mean process, the +#' autocovariance at distance \eqn{h} is denoted \eqn{Cov(h)} and defined as +#' \eqn{Cov(z1, z2)}. Under second-order stationarity, +#' \eqn{Cov(h) = Cov(0) - \gamma(h)}, where \eqn{gamma(h)} is the semivariance function at distance \code{h}. Typically the residuals from an ordinary +#' least squares fit defined by \code{formula} are second-order stationary with +#' mean zero. These residuals are used to compute the empirical autocovariance +#' At a distance \code{h}, the empirical autocovariance is +#' \eqn{1/N(h) \sum (r1 \times r2)}, where \eqn{N(h)} is the number of (unique) +#' pairs in the set of observations whose distance separation is \code{h} and +#' \code{r1} and \code{r2} are residuals corresponding to observations whose +#' distance separation is \code{h}. In spmodel, these distance bins actually +#' contain observations whose distance separation is \code{h +- c}, +#' where \code{c} is a constant determined implicitly by \code{bins}. Typically, +#' only observations whose distance separation is below some cutoff are used +#' to compute the empirical semivariogram (this cutoff is determined by \code{cutoff}). +#' +#' @name eacf +#' +#' @return If \code{cloud = FALSE}, a tibble (data.frame) with distance bins +#' (\code{bins}), the average distance (\code{dist}), the average autocovariance (\code{acov}), and the +#' number of (unique) pairs (\code{np}). If \code{cloud = TRUE}, a tibble +#' (data.frame) with distance (\code{dist}) and autocovariance (\code{acov}) +#' for each unique pair. +#' +#' @export +#' +#' @examples +#' eacf(sulfate ~ 1, sulfate) +#' plot(eacf(sulfate ~ 1, sulfate)) +eacf <- function(formula, data, xcoord, ycoord, cloud = FALSE, bins = 15, cutoff, dist_matrix, partition_factor) { + + # filter out missing response values + na_index <- is.na(data[[all.vars(formula)[1]]]) + data <- data[!na_index, , drop = FALSE] + # finding model frame + data_model_frame <- model.frame(formula, data, drop.unused.levels = TRUE, na.action = na.pass) + # model matrix with potential NA + ob_predictors <- complete.cases(model.matrix(formula, data_model_frame)) + if (any(!ob_predictors)) { + stop("Cannot have NA values in predictors.", call. = FALSE) + } + + # covert sp to sf + attr_sp <- attr(class(data), "package") + if (!is.null(attr_sp) && length(attr_sp) == 1 && attr_sp == "sp") { + stop("sf objects must be used instead of sp objects. To convert your sp object into an sf object, run sf::st_as_sf().", call. = FALSE) + } + + ## convert sf to data frame (point geometry) (1d objects obsolete) + ### see if data has sf class + if (inherits(data, "sf")) { + data <- suppressWarnings(sf::st_centroid(data)) + data <- sf_to_df(data) + ### name xcoord ".xcoord" to be used later + xcoord <- ".xcoord" + ### name ycoord ".ycoord" to be used later + ycoord <- ".ycoord" + } + + # compute spatial distances + if (missing(dist_matrix)) { + # non standard evaluation for the x and y coordinates + xcoord <- substitute(xcoord) + ycoord <- substitute(ycoord) + + if (missing(xcoord)) { + stop("The xcoord argument must be specified.", call. = FALSE) + } + + if (!missing(xcoord)) { + if (!as.character(xcoord) %in% colnames(data)) { + stop("The xcoord argument must match the name of a variable in data.", call. = FALSE) + } + } + + if (missing(ycoord)) { + dist_matrix <- spdist(data, xcoord) + } else { + if (!as.character(ycoord) %in% colnames(data)) { + stop("The ycoord argument must match the name of a variable in data.", call. = FALSE) + } + dist_matrix <- spdist(data, xcoord, ycoord) + } + } + + + dist_matrix <- as.matrix(dist_matrix) + dist_matrix <- dist_matrix[upper.tri(dist_matrix)] + + if (any(dist_matrix == 0)) { + warning("Zero distances observed between at least one pair. Ignoring pairs. If using splm(), consider a different estimation method.", call. = FALSE) + } + + if (missing(partition_factor)) { + partition_factor <- NULL + } + + if (!is.null(partition_factor)) { + # partition_matrix_val <- triu(partition_matrix(partition_factor, data = data), k = 1) + partition_matrix_val <- as.matrix(partition_matrix(partition_factor, data = data)) + partition_matrix_val <- partition_matrix_val[upper.tri(partition_matrix_val)] + dist_matrix <- dist_matrix * partition_matrix_val + } + + if (missing(cutoff)) { + cutoff <- NULL + } + if (is.null(cutoff)) { + cutoff <- max(dist_matrix) / 2 + } + + dist_vector <- dist_matrix + if (any(dist_vector == 0)) { + dist_index <- dist_vector > 0 & dist_vector <= cutoff + } else { + dist_index <- dist_vector <= cutoff + } + + dist_vector <- dist_vector[dist_index] + + # compute squared differences in the residuals + lmod <- lm(formula = formula, data = data) + residuals <- residuals(lmod) + residual_matrix <- outer(residuals, residuals) # ybar is the fitted mean + residual_matrix <- residual_matrix[upper.tri(residual_matrix)] + if (!is.null(partition_factor)) { + residual_matrix <- residual_matrix * partition_matrix_val + } + + residual_vector <- residual_matrix + residual_vector <- residual_vector[dist_index] + residual_vector2 <- residual_vector # just to align with esv() names + + + if (cloud) { + eacf_out <- get_eacf_cloud(residual_vector2, dist_vector) + } else { + eacf_out <- get_eacf(residual_vector2, dist_vector, bins, cutoff) + } + + + + + # remove NA + # eacf_out <- na.omit(eacf_out) + eacf_out <- structure(eacf_out, class = c("eacf", class(eacf_out)), call = match.call(), cloud = cloud) + eacf_out +} + +#' @rdname eacf +#' @method plot eacf +#' @param x An object from \code{eacf()}. +#' @param ... Other arguments passed to other methods. +#' @export +plot.eacf <- function(x, ...) { + + cal <- attr(x, "call") + if (!is.na(m.f <- match("formula", names(cal)))) { + cal <- cal[c(1, m.f)] + names(cal)[2L] <- "" + } + cc <- deparse(cal, 80) + nc <- nchar(cc[1L], "c") + abbr <- length(cc) > 1 || nc > 75 + sub.caption <- if (abbr) { + paste(substr(cc[1L], 1L, min(75L, nc)), "...") + } else { + cc[1L] + } + + dotlist <- list(...) + dotlist <- get_eacf_dotlist_defaults(x, dotlist, cloud = attr(x, "cloud")) + + do.call("plot", c(list(x = x$dist, y = x$acov), dotlist)) + title(sub = sub.caption) +} diff --git a/R/get_eacf.R b/R/get_eacf.R new file mode 100644 index 0000000..e10bff8 --- /dev/null +++ b/R/get_eacf.R @@ -0,0 +1,41 @@ +get_eacf <- function(residual_vector2, dist_vector, bins, cutoff, formula) { + + # compute semivariogram classes + dist_classes <- cut(dist_vector, breaks = seq(0, cutoff, length.out = bins + 1)) + + # compute squared differences within each class + acov <- tapply(residual_vector2, dist_classes, function(x) mean(x)) + + # compute pairs within each class + np <- tapply(residual_vector2, dist_classes, length) + + # set as zero if necessary + np <- ifelse(is.na(np), 0, np) + + # compute average distance within each class + dist <- tapply(dist_vector, dist_classes, mean) + + # return output + eacf_out <- tibble::tibble( + bins = factor(levels(dist_classes), levels = levels(dist_classes)), + dist = as.numeric(dist), + acov = as.numeric(acov), + np = as.numeric(np) + ) + + # set row names to NULL + # row.names(eacf_out) <- NULL + + eacf_out +} + + +get_eacf_cloud <- function(residual_vector2, dist_vector) { + + eacf_out <- tibble::tibble(dist = dist_vector, acov = residual_vector2) + + # set row names to NULL + # row.names(eacf_out) <- NULL + + eacf_out +} diff --git a/R/get_eacf_dotlist.R b/R/get_eacf_dotlist.R new file mode 100644 index 0000000..6e051a9 --- /dev/null +++ b/R/get_eacf_dotlist.R @@ -0,0 +1,68 @@ +#' Get empirical autocovariance dotlist +#' +#' @param ... Additional arguments to \code{eacf()} +#' @param max_halfdist +#' +#' @return An eacf dotlist +#' +#' @noRd +get_eacf_dotlist <- function(..., max_halfdist) { + # storing dotlist and setting defaults for eacf + dotlist <- list(...) + + if (!("bins" %in% names(dotlist))) { + dotlist$bins <- 15 + } + + if (!("cutoff" %in% names(dotlist))) { + dotlist$cutoff <- max_halfdist + } + + # make dotlist eacf + dotlist_eacf <- list(bins = dotlist$bins, cutoff = dotlist$cutoff) +} + + +get_eacf_dotlist_defaults <- function(x, dotlist, cloud) { + + names_dotlist <- names(dotlist) + + # set defaults + if (!"main" %in% names_dotlist) { + dotlist$main <- "Empirical Autocovariance" + if (cloud) dotlist$main <- paste0(dotlist$main, " (Cloud)") + } + + if (!"xlab" %in% names_dotlist) { + dotlist$xlab <- "Distance" + } + + if (!"ylab" %in% names_dotlist) { + dotlist$ylab <- "Autocovariance" + } + + if (!cloud && !"pch" %in% names_dotlist) { + dotlist$pch <- 19 + } + + if (!cloud && !"cex" %in% names_dotlist) { + dotlist$cex <- (x$np - min(x$np)) / (max(x$np) - min(x$np)) * 2 + 1 + } + + if (!"ylim" %in% names_dotlist) { + + # include zero if not in limits + + ## all greater than zero (positive) + if (all(x$acov > 0)) { + dotlist$ylim <- c(0, 1.1 * max(x$acov)) + } + + ## all less than zero (negative) + if (all(x$acov < 0)) { + dotlist$ylim <- c(1.1 * min(x$acov), 0) + } + } + + dotlist +} diff --git a/man/eacf.Rd b/man/eacf.Rd new file mode 100644 index 0000000..c9cefe0 --- /dev/null +++ b/man/eacf.Rd @@ -0,0 +1,89 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/eacf.R +\name{eacf} +\alias{eacf} +\alias{plot.eacf} +\title{Compute the empirical autocovariance} +\usage{ +eacf( + formula, + data, + xcoord, + ycoord, + cloud = FALSE, + bins = 15, + cutoff, + dist_matrix, + partition_factor +) + +\method{plot}{eacf}(x, ...) +} +\arguments{ +\item{formula}{A formula describing the fixed effect structure.} + +\item{data}{A data frame or \code{sf} object containing the variables in \code{formula} +and geographic information.} + +\item{xcoord}{Name of the variable in \code{data} representing the x-coordinate. +Can be quoted or unquoted. Not required if \code{data} is an \code{sf} object.} + +\item{ycoord}{Name of the variable in \code{data} representing the y-coordinate. +Can be quoted or unquoted. Not required if \code{data} is an \code{sf} object.} + +\item{cloud}{A logical indicating whether the empirical autocovariance should +be summarized by distance class or not. When \code{cloud = FALSE} (the default), pairwise autocovariances +are binned and averaged within distance classes. When \code{cloud} = TRUE, +all pairwise autocovariances and distances are returned (this is known as +the "cloud" autocovariance).} + +\item{bins}{The number of equally spaced bins. The default is 15. Ignored if +\code{cloud = TRUE}.} + +\item{cutoff}{The maximum distance considered. +The default is half the diagonal of the bounding box from the coordinates.} + +\item{dist_matrix}{A distance matrix to be used instead of providing coordinate names.} + +\item{partition_factor}{An optional formula specifying the partition factor. +If specified, autocovariances are only computed for observations sharing the +same level of the partition factor.} + +\item{x}{An object from \code{eacf()}.} + +\item{...}{Other arguments passed to other methods.} +} +\value{ +If \code{cloud = FALSE}, a tibble (data.frame) with distance bins +(\code{bins}), the average distance (\code{dist}), the average autocovariance (\code{acov}), and the +number of (unique) pairs (\code{np}). If \code{cloud = TRUE}, a tibble +(data.frame) with distance (\code{dist}) and autocovariance (\code{acov}) +for each unique pair. +} +\description{ +Compute the empirical autocovariance (i.e., empirical covariance) +for varying bin sizes and cutoff values. +} +\details{ +The empirical autocovariance (i.e., empirical covariance) is a tool used to visualize and model +spatial dependence by estimating the semivariance of a process at varying distances. +For a constant-mean process, the +autocovariance at distance \eqn{h} is denoted \eqn{Cov(h)} and defined as +\eqn{Cov(z1, z2)}. Under second-order stationarity, +\eqn{Cov(h) = Cov(0) - \gamma(h)}, where \eqn{gamma(h)} is the semivariance function at distance \code{h}. Typically the residuals from an ordinary +least squares fit defined by \code{formula} are second-order stationary with +mean zero. These residuals are used to compute the empirical autocovariance +At a distance \code{h}, the empirical autocovariance is +\eqn{1/N(h) \sum (r1 \times r2)}, where \eqn{N(h)} is the number of (unique) +pairs in the set of observations whose distance separation is \code{h} and +\code{r1} and \code{r2} are residuals corresponding to observations whose +distance separation is \code{h}. In spmodel, these distance bins actually +contain observations whose distance separation is \code{h +- c}, +where \code{c} is a constant determined implicitly by \code{bins}. Typically, +only observations whose distance separation is below some cutoff are used +to compute the empirical semivariogram (this cutoff is determined by \code{cutoff}). +} +\examples{ +eacf(sulfate ~ 1, sulfate) +plot(eacf(sulfate ~ 1, sulfate)) +} diff --git a/tests/testthat/test-extras.R b/tests/testthat/test-extras.R index 9107633..537bea8 100644 --- a/tests/testthat/test-extras.R +++ b/tests/testthat/test-extras.R @@ -445,6 +445,98 @@ if (test_local) { expect_error(deviance(spmod)) }) + ############################################################################## + ############################ eacf (test-acf.R) + ############################################################################## + + test_that("eacf works", { + + # regular implementation + eacf1 <- eacf(y ~ x, exdata, xcoord, ycoord) + expect_s3_class(eacf1, "eacf") + expect_s3_class(eacf1, "tbl_df") + expect_s3_class(eacf1, "tbl") + expect_s3_class(eacf1, "data.frame") + expect_equal(NROW(eacf1), 15) + expect_equal(NCOL(eacf1), 4) + + eacf1_q <- eacf(y ~ x, exdata, "xcoord", "ycoord") + expect_s3_class(eacf1_q, "eacf") + expect_s3_class(eacf1_q, "tbl_df") + expect_s3_class(eacf1_q, "tbl") + expect_s3_class(eacf1_q, "data.frame") + expect_equal(NROW(eacf1_q), 15) + expect_equal(NCOL(eacf1_q), 4) + + + # quoting works (need to NULL out call attribute as that is different) + eacf1_cn <- eacf1 + attr(eacf1_cn, "call") <- NULL + eacf1_q_cn <- eacf1_q + attr(eacf1_q_cn, "call") <- NULL + expect_equal(eacf1_cn, eacf1_q_cn) + + # specifying bins and cutoff + eacf2 <- eacf(y ~ x, exdata, xcoord, ycoord, bins = 30, cutoff = 5) + expect_s3_class(eacf2, "eacf") + expect_s3_class(eacf2, "tbl_df") + expect_s3_class(eacf2, "tbl") + expect_s3_class(eacf2, "data.frame") + expect_equal(NROW(eacf2), 30) + expect_equal(NCOL(eacf2), 4) + dist_matrix <- spdist(exdata, "xcoord", "ycoord") + + # specifying distance matrix + eacf3 <- eacf(y ~ x, exdata, dist_matrix = dist_matrix) + expect_s3_class(eacf3, "eacf") + expect_s3_class(eacf3, "tbl_df") + expect_s3_class(eacf3, "tbl") + expect_s3_class(eacf3, "data.frame") + expect_equal(NROW(eacf3), 15) + expect_equal(NCOL(eacf3), 4) + + # specifying partition factor + eacf4 <- eacf(y ~ x, exdata, xcoord, ycoord, partition_factor = ~group) + expect_s3_class(eacf4, "eacf") + expect_s3_class(eacf4, "tbl_df") + expect_s3_class(eacf4, "tbl") + expect_s3_class(eacf4, "data.frame") + expect_equal(NROW(eacf4), 15) + expect_equal(NCOL(eacf4), 4) + expect_false(identical(eacf1, eacf4)) # make sure results are not identical to full eacf + + # works with sf object + exdata_sf <- sf::st_as_sf(exdata, coords = c("xcoord", "ycoord")) + expect_error(eacf(y ~ x, exdata_sf), NA) + eacf5 <- eacf(y ~ x, exdata_sf) + eacf5_cn <- eacf5 + attr(eacf5_cn, "call") <- NULL + expect_true(identical(eacf1_cn, eacf5_cn)) + + # works with one dimension + expect_error(eacf(y ~ x, exdata, xcoord), NA) + + # errors occur + expect_error(eacf(y ~ x, exdata)) + expect_error(eacf(y ~ x, exdata, xcoord_xyz)) + expect_error(eacf(y ~ x, exdata, xcoord, ycoord_xyz)) + + # works with cloud argument + eacf1c <- eacf(y ~ x, exdata, xcoord, ycoord, cloud = TRUE) + expect_s3_class(eacf1c, "eacf") + expect_s3_class(eacf1c, "tbl_df") + expect_s3_class(eacf1c, "tbl") + expect_s3_class(eacf1c, "data.frame") + expect_equal(NROW(eacf1c), 3965) + expect_equal(NCOL(eacf1c), 2) + + # plot works + expect_error(plot(eacf1), NA) + expect_error(plot(eacf1, pch = 1), NA) + expect_error(plot(eacf1c), NA) + expect_error(plot(eacf1c, pch = 19), NA) + }) + ############################################################################## ############################ esv (test-esv.R) ############################################################################## diff --git a/tests/testthat/test-spglm.R b/tests/testthat/test-spglm.R index 85f7a0e..405383f 100644 --- a/tests/testthat/test-spglm.R +++ b/tests/testthat/test-spglm.R @@ -55,6 +55,9 @@ test_that("generics work spglm point data", { # deviance expect_vector(deviance(spmod1)) + # eacf + expect_s3_class(eacf(y ~ x, exdata, xcoord = xcoord, ycoord = ycoord), "data.frame") + # esv expect_s3_class(esv(y ~ x, exdata, xcoord = xcoord, ycoord = ycoord), "data.frame") @@ -220,6 +223,9 @@ test_that("generics work spglm point data with missing", { # deviance expect_vector(deviance(spmod1)) + # eacf + expect_s3_class(eacf(y ~ x, exdata_M, xcoord = xcoord, ycoord = ycoord), "data.frame") + # esv expect_s3_class(esv(y ~ x, exdata_M, xcoord = xcoord, ycoord = ycoord), "data.frame") @@ -380,6 +386,9 @@ test_that("generics work spglm polygon data with missing", { # deviance expect_vector(deviance(spmod1)) + # eacf + expect_s3_class(eacf(y ~ x, exdata_Mpoly, xcoord = xcoord, ycoord = ycoord), "data.frame") + # esv expect_s3_class(esv(y ~ x, exdata_Mpoly, xcoord = xcoord, ycoord = ycoord), "data.frame") diff --git a/tests/testthat/test-splm.R b/tests/testthat/test-splm.R index f07b6a9..3b1b3df 100644 --- a/tests/testthat/test-splm.R +++ b/tests/testthat/test-splm.R @@ -51,6 +51,9 @@ test_that("generics work splm point data", { # deviance expect_vector(deviance(spmod1)) + # eacf + expect_s3_class(eacf(y ~ x, exdata, xcoord = xcoord, ycoord = ycoord), "data.frame") + # esv expect_s3_class(esv(y ~ x, exdata, xcoord = xcoord, ycoord = ycoord), "data.frame") @@ -213,6 +216,9 @@ test_that("generics work splm point data with missing", { # deviance expect_vector(deviance(spmod1)) + # eacf + expect_s3_class(eacf(y ~ x, exdata_M, xcoord = xcoord, ycoord = ycoord), "data.frame") + # esv expect_s3_class(esv(y ~ x, exdata_M, xcoord = xcoord, ycoord = ycoord), "data.frame") @@ -370,6 +376,9 @@ test_that("generics work splm polygon data with missing", { # deviance expect_vector(deviance(spmod1)) + # eacf + expect_s3_class(eacf(y ~ x, exdata_Mpoly, xcoord = xcoord, ycoord = ycoord), "data.frame") + # esv expect_s3_class(esv(y ~ x, exdata_Mpoly, xcoord = xcoord, ycoord = ycoord), "data.frame") From 0319e417f616cc589985e5cc52ac837dc430e84b Mon Sep 17 00:00:00 2001 From: Michael Dumelle Date: Tue, 25 Nov 2025 12:09:08 -0800 Subject: [PATCH 5/9] update introductory vignette to include all five website articles --- vignettes/introduction.Rmd | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/vignettes/introduction.Rmd b/vignettes/introduction.Rmd index 4bac858..38a6212 100644 --- a/vignettes/introduction.Rmd +++ b/vignettes/introduction.Rmd @@ -43,11 +43,13 @@ If you use `spmodel` in a formal publication or report, please cite it. Citing ` citation(package = "spmodel") ``` -There are three more `spmodel` vignettes available on our website at [https://usepa.github.io/spmodel/](https://usepa.github.io/spmodel/): +There are five more `spmodel` vignettes available on our website at [https://usepa.github.io/spmodel/](https://usepa.github.io/spmodel/): 1. A Detailed Guide to `spmodel` -2. Spatial Generalized Linear Models in `spmodel -3. Technical Details +2. Spatial Generalized Linear Models in `spmodel` +3. Using `emmeans` to Estimate Marginal Means of `spmodel` Objects +4. Block Prediction (i.e., Blocking Kriging) in `spmodel` +5. Technical Details Additionally, there are two workbooks that have accompanied recent `spmodel` workshops: From 3ff815683e827dd7fbddc357cd09672644f192f5 Mon Sep 17 00:00:00 2001 From: Michael Dumelle Date: Fri, 28 Nov 2025 17:07:25 -0800 Subject: [PATCH 6/9] update tech docs for eacf --- vignettes/articles/technical.Rmd | 12 +++++++++--- 1 file changed, 9 insertions(+), 3 deletions(-) diff --git a/vignettes/articles/technical.Rmd b/vignettes/articles/technical.Rmd index 95c751d..e79de11 100644 --- a/vignettes/articles/technical.Rmd +++ b/vignettes/articles/technical.Rmd @@ -1330,14 +1330,20 @@ The following table contains a table of inverse link functions, $d_i$, and $D_{i : A table of inverse link functions and relevant quantities for each spatial generalized linear model family. -# The Empirical Semivariogram (`esv()`) {#sec:esv} +# The Empirical Semivariogram and Autocovariance (`esv()` and `eacf()`) {#sec:esv} -The empirical semivariogram is a moment-based estimate of the theoretical semivariogram. The empirical semivariogram quantifies half of the average squared difference in the response among observations in several distance classes. More formally, the empirical semivariogram is defined as \begin{equation}\label{eq:esv} +The empirical semivariogram is a moment-based estimate of the theoretical semivariogram. The empirical semivariogram quantifies half of the average squared difference in the response among observations in several distance classes. More formally, the empirical semivariogram, $\hat{\gamma}(h)$, is defined as \begin{equation}\label{eq:esv} \hat{\gamma}(h) = \frac{1}{2|N(h)|} \sum_{N(h)} (y_i - y_j)^2, -\end{equation} where $N(h)$ is the set of observations in $\mathbf{y}$ that are $h$ distance apart (distance classes) and $|N(h)|$ is the cardinality of $N(h)$ [@cressie1993statistics]. Often the set $N(h)$ contains observations that are $h \pm c$ apart, where $c$ is some constant. This approach is known as "binning" the empirical semivariogram. The default in `spmodel` is to construct the semivariogram using 15 equally spaced bins where $h$ is contained in $(0, h_{max}]$, and $h_{max}$ is known as a "distance cutoff". Distance cutoffs are commonly used when constructing $\hat{\gamma}(h)$ because there tend to be few pairs with large distances. The default in `spmodel` is to use a cutoff of half the maximum distance (hypotenuse) of the domain's bounding box. +\end{equation} where $N(h)$ is the set of observations in $\mathbf{y}$ that are $h$ distance apart (distance classes) and $|N(h)|$ is the cardinality of $N(h)$ [@cressie1993statistics]. Often the set $N(h)$ contains observations that are $h \pm c$ apart, where $c$ is some constant. This approach is known as "binning" the empirical semivariogram. The default in `spmodel` is to construct the semivariogram using 15 equally spaced bins where $h$ is contained in $(0, h_{max}]$, and $h_{max}$ is known as a "distance cutoff". Distance cutoffs are commonly used when constructing $\hat{\gamma}(h)$ because there tend to be few pairs with large distances. The default in `spmodel` is to use a cutoff of half the maximum distance (hypotenuse) of the domain's bounding box. Because we are typically interested in characterizing residual semivariance, $y_i$ and $y_j$ tend to represent residuals from an ordinary least squares fit given some fixed effects design matrix, $\mathbf{X}$, and fixed effects, $\hat{\boldsymbol{\beta}}$. The main purpose of the empirical semivariogram is its use in semivariogram weighted least squares estimation for spatial linear models, though it can also be used as a visual diagnostic to assess the fit of a spatial covariance function. +The empirical semivariogram is closely related to the empirical autocovariance [@zimmerman2024spatial]. The empirical autocovariance quantifies the average covariance among observations in several distance classes. Using similar notation as for the empirical semivariogram, +\begin{equation}\label{eq:eacf} + \hat{eacf}(h) = \frac{1}{|N(h)|} \sum_{N(h)} (y_i - \hat{y})(y_j - \hat{y}), +\end{equation} +where $\hat{y} = \bar{y}$, the sample mean of all the observations. Like with `esv()`, the default is to use 15 equally spaced bins with a distance cutoff of half the maximum distance (hypotenuse) of the domain's bounding box. Because we are typically interested in characterizing residual autocovariance, $y_i - \hat{y}$ and $y_j - \hat{y}$ tend to represent residuals from an ordinary least squares fit given some fixed effects design matrix, $\mathbf{X}$, and fixed effects, $\hat{\boldsymbol{\beta}}$. + # A Note on Covariance Square Roots and Inverse Products {#sec:iprod} Often $\boldsymbol{\Sigma}^{-1}$ is not strictly needed for estimation, prediction, or other purposes, but at least the product between $\boldsymbol{\Sigma}^{-1}$ and some other matrix is needed. Consider the example of the covariance matrix of $\hat{\boldsymbol{\beta}}$ and observe $\mathbf{X}^\top \boldsymbol{\Sigma}^{-1} \mathbf{X}$ is needed. The most direct way to find this product is certainly to obtain $\boldsymbol{\Sigma}^{-1}$ and then multiply by $\mathbf{X}^\top$ on the left and $\mathbf{X}$ on the right. This is both computationally expensive and cannot be used to compute products that involve $\boldsymbol{\Sigma}^{-1/2}$, which are often useful. It is helpful to define $\boldsymbol{\Sigma} = \mathbf{S} \mathbf{S}^\top$ for some matrix $\mathbf{S}$ and rewrite $\mathbf{X}^\top \boldsymbol{\Sigma}^{-1} \mathbf{X}$ as $\mathbf{X}^\top (\mathbf{S}^\top)^{-1} \mathbf{S}^{-1} \mathbf{X} = (\mathbf{S}^{-1} \mathbf{X})^\top \mathbf{S}^{-1} \mathbf{X}$. Then one computes the inverse products by finding $\mathbf{S}$. From f481deeafa20c930754b12e65336ab9123d797b2 Mon Sep 17 00:00:00 2001 From: Michael Dumelle Date: Wed, 10 Dec 2025 09:37:11 -0800 Subject: [PATCH 7/9] added warning message that clarifies xcoord and ycoord are ignored when data is an sf object --- NEWS.md | 1 + R/get_data_object.R | 3 +++ R/get_data_object_glm.R | 3 +++ 3 files changed, 7 insertions(+) diff --git a/NEWS.md b/NEWS.md index 0ff0240..41a80bf 100644 --- a/NEWS.md +++ b/NEWS.md @@ -8,6 +8,7 @@ * Changed the default `size` argument to the local argument in `predict(..., block = TRUE)` and `augment(..., block = TRUE)` from 1000 to 4000. This enhances the block prediction (i.e., Kriging) approximation's accuracy but can slightly increase computational complexity. * Enhanced efficiency of block prediction (i.e., Kriging) for large `newdata` objects. +* Added a warning message that clarifies `xcoord` and `ycoord` are ignored when `data` is an `sf` object. * Minor documentation updates. # spmodel 0.11.1 diff --git a/R/get_data_object.R b/R/get_data_object.R index 8d319de..4f7107b 100644 --- a/R/get_data_object.R +++ b/R/get_data_object.R @@ -23,6 +23,9 @@ get_data_object_splm <- function(formula, data, spcov_initial, xcoord, ycoord, e data_sf <- suppressWarnings(sf::st_centroid(data)) # store as data frame data <- sf_to_df(data_sf) + if (!missing(xcoord) || !missing(ycoord)) { + warning("data is an sf object. Ignoring xcoord and ycoord arguments.", call. = FALSE) + } ## name xcoord ".xcoord" to be used later xcoord <- ".xcoord" ## name ycoord ".ycoord" to be used later diff --git a/R/get_data_object_glm.R b/R/get_data_object_glm.R index f8b405f..65d1704 100644 --- a/R/get_data_object_glm.R +++ b/R/get_data_object_glm.R @@ -24,6 +24,9 @@ get_data_object_spglm <- function(formula, family, data, spcov_initial, xcoord, data_sf <- suppressWarnings(sf::st_centroid(data)) # store as data frame data <- sf_to_df(data_sf) + if (!missing(xcoord) || !missing(ycoord)) { + warning("data is an sf object. Ignoring xcoord and ycoord arguments.", call. = FALSE) + } ## name xcoord ".xcoord" to be used later xcoord <- ".xcoord" ## name ycoord ".ycoord" to be used later From 122eab355764f3ce4bc1b2ddb33d0ef4d2ffda98 Mon Sep 17 00:00:00 2001 From: Michael Dumelle Date: Mon, 12 Jan 2026 13:42:10 -0800 Subject: [PATCH 8/9] fix bug in prediction that caused NA values with matern spatial covariance when a location in newdata matches a location in data --- NEWS.md | 4 ++++ R/spcov_matrix.R | 2 +- R/spcov_vector.R | 2 ++ 3 files changed, 7 insertions(+), 1 deletion(-) diff --git a/NEWS.md b/NEWS.md index 41a80bf..2258d52 100644 --- a/NEWS.md +++ b/NEWS.md @@ -11,6 +11,10 @@ * Added a warning message that clarifies `xcoord` and `ycoord` are ignored when `data` is an `sf` object. * Minor documentation updates. +## Bug Fixes + +* Fixed a bug in `predict(object, newdata)` and `augment(object, newdata)` that could cause `NA` values when the spatial covariance was `"matern"` and a location in `newdata` was the exact same as a location in `data` (the `data` argument used to fit `object`). + # spmodel 0.11.1 ## Minor Updates diff --git a/R/spcov_matrix.R b/R/spcov_matrix.R index 4e7dbd5..aaa563a 100644 --- a/R/spcov_matrix.R +++ b/R/spcov_matrix.R @@ -160,7 +160,7 @@ spcov_matrix.magnetic <- function(spcov_params, dist_matrix, diagtol = 0, ...) { spcov_matrix.matern <- function(spcov_params, dist_matrix, diagtol = 0, ...) { eta <- sqrt(2 * spcov_params[["extra"]]) * (dist_matrix / spcov_params[["range"]]) spcov_matrix_val <- spcov_params[["de"]] * 2^(1 - spcov_params[["extra"]]) / gamma(spcov_params[["extra"]]) * eta^spcov_params[["extra"]] * besselK(as.matrix(eta), nu = spcov_params[["extra"]]) # eta as sparse matrix causes error - dist_matrix_zero <- which(dist_matrix == 0) + dist_matrix_zero <- which(dist_matrix == 0) # consider epsilon threshold instead of exactly zero? spcov_matrix_val[dist_matrix_zero] <- spcov_params[["de"]] spcov_params[["ie"]] <- max(spcov_params[["ie"]], 1e-4 * spcov_params[["de"]], diagtol) diag(spcov_matrix_val) <- spcov_params[["de"]] + spcov_params[["ie"]] diff --git a/R/spcov_vector.R b/R/spcov_vector.R index 9eb941a..1b327f3 100644 --- a/R/spcov_vector.R +++ b/R/spcov_vector.R @@ -133,6 +133,8 @@ spcov_vector.magnetic <- function(spcov_params, dist_vector) { spcov_vector.matern <- function(spcov_params, dist_vector) { eta <- sqrt(2 * spcov_params[["extra"]]) * (dist_vector / spcov_params[["range"]]) spcov_vector_val <- spcov_params[["de"]] * 2^(1 - spcov_params[["extra"]]) / gamma(spcov_params[["extra"]]) * eta^spcov_params[["extra"]] * besselK(as.matrix(eta), nu = spcov_params[["extra"]]) + dist_vector_zero <- which(dist_vector == 0) # consider epsilon threshold instead of exactly zero? + spcov_vector_val[dist_vector_zero] <- spcov_params[["de"]] spcov_vector_val } From 6b2f971361a5baf53f26b53b6502f0e4b3e9a115 Mon Sep 17 00:00:00 2001 From: Michael Dumelle Date: Mon, 26 Jan 2026 11:57:01 -0800 Subject: [PATCH 9/9] website updates --- docs/404.html | 2 +- docs/LICENSE.html | 2 +- docs/articles/SPGLMs.html | 2 +- docs/articles/block.html | 2 +- docs/articles/emmeans.html | 2 +- docs/articles/guide.html | 2 +- docs/articles/index.html | 2 +- docs/articles/introduction.html | 12 +- docs/articles/technical.html | 30 ++- docs/authors.html | 2 +- docs/index.html | 2 +- docs/news/index.html | 20 +- docs/pkgdown.yml | 2 +- docs/reference/AICc.html | 2 +- docs/reference/AUROC.html | 2 +- docs/reference/anova.spmodel.html | 2 +- docs/reference/augment.spmodel.html | 2 +- docs/reference/caribou.html | 2 +- docs/reference/coef.spmodel.html | 2 +- docs/reference/confint.spmodel.html | 2 +- docs/reference/cooks.distance.spmodel.html | 2 +- docs/reference/covmatrix.html | 2 +- docs/reference/deviance.spmodel.html | 2 +- docs/reference/dispersion_initial.html | 2 +- docs/reference/dispersion_params.html | 2 +- docs/reference/eacf-1.png | Bin 0 -> 34794 bytes docs/reference/eacf.html | 235 +++++++++++++++++++++ docs/reference/esv.html | 2 +- docs/reference/fc_borders.html | 2 +- docs/reference/fitted.spmodel.html | 2 +- docs/reference/formula.spmodel.html | 4 +- docs/reference/glance.spmodel.html | 2 +- docs/reference/glances.html | 2 +- docs/reference/hatvalues.spmodel.html | 2 +- docs/reference/index.html | 6 +- docs/reference/influence.spmodel.html | 2 +- docs/reference/labels.spmodel.html | 2 +- docs/reference/lake.html | 2 +- docs/reference/lake_preds.html | 2 +- docs/reference/logLik.spmodel.html | 2 +- docs/reference/loocv.html | 2 +- docs/reference/model.frame.spmodel.html | 2 +- docs/reference/model.matrix.spmodel.html | 2 +- docs/reference/moose.html | 2 +- docs/reference/moose_preds.html | 2 +- docs/reference/moss.html | 2 +- docs/reference/plot.spmodel.html | 2 +- docs/reference/predict.spmodel.html | 5 +- docs/reference/print.spmodel.html | 2 +- docs/reference/pseudoR2.html | 2 +- docs/reference/randcov_initial.html | 2 +- docs/reference/randcov_params.html | 2 +- docs/reference/reexports.html | 2 +- docs/reference/residuals.spmodel.html | 2 +- docs/reference/seal.html | 2 +- docs/reference/spautor.html | 2 +- docs/reference/spautorRF.html | 2 +- docs/reference/spcov_initial.html | 2 +- docs/reference/spcov_params.html | 2 +- docs/reference/spgautor.html | 2 +- docs/reference/spglm.html | 2 +- docs/reference/splm.html | 2 +- docs/reference/splmRF.html | 2 +- docs/reference/spmodel-package.html | 2 +- docs/reference/sprbeta.html | 2 +- docs/reference/sprbinom.html | 2 +- docs/reference/sprgamma.html | 2 +- docs/reference/sprinvgauss.html | 2 +- docs/reference/sprnbinom.html | 2 +- docs/reference/sprnorm.html | 2 +- docs/reference/sprpois.html | 2 +- docs/reference/sulfate.html | 2 +- docs/reference/sulfate_preds.html | 2 +- docs/reference/summary.spmodel.html | 2 +- docs/reference/texas.html | 2 +- docs/reference/tidy.spmodel.html | 2 +- docs/reference/varcomp.html | 2 +- docs/reference/vcov.spmodel.html | 2 +- docs/sitemap.xml | 3 + 79 files changed, 371 insertions(+), 84 deletions(-) create mode 100644 docs/reference/eacf-1.png create mode 100644 docs/reference/eacf.html diff --git a/docs/404.html b/docs/404.html index 75f8099..e49b0c4 100644 --- a/docs/404.html +++ b/docs/404.html @@ -39,7 +39,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/LICENSE.html b/docs/LICENSE.html index 7b9ff1d..a4a1ae8 100644 --- a/docs/LICENSE.html +++ b/docs/LICENSE.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/articles/SPGLMs.html b/docs/articles/SPGLMs.html index d2ebaea..ed777b2 100644 --- a/docs/articles/SPGLMs.html +++ b/docs/articles/SPGLMs.html @@ -40,7 +40,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/articles/block.html b/docs/articles/block.html index 75a3637..0ff3f7b 100644 --- a/docs/articles/block.html +++ b/docs/articles/block.html @@ -40,7 +40,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/articles/emmeans.html b/docs/articles/emmeans.html index a1a5b73..596b52f 100644 --- a/docs/articles/emmeans.html +++ b/docs/articles/emmeans.html @@ -40,7 +40,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/articles/guide.html b/docs/articles/guide.html index 73d2589..2833809 100644 --- a/docs/articles/guide.html +++ b/docs/articles/guide.html @@ -40,7 +40,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/articles/index.html b/docs/articles/index.html index 1691d7c..e3ff4bf 100644 --- a/docs/articles/index.html +++ b/docs/articles/index.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/articles/introduction.html b/docs/articles/introduction.html index fa5eb64..37a1007 100644 --- a/docs/articles/introduction.html +++ b/docs/articles/introduction.html @@ -40,7 +40,7 @@ spmodel - 0.11.1 + 0.12.0 @@ -147,12 +147,18 @@

Introduction#> doi = {10.1371/journal.pone.0282524}, #> url = {https://doi.org/10.1371/journal.pone.0282524}, #> } -

There are three more spmodel vignettes available on our +

There are five more spmodel vignettes available on our website at https://usepa.github.io/spmodel/:

  1. A Detailed Guide to spmodel
    2. -
  2. Spatial Generalized Linear Models in `spmodel
    3. +
  3. Spatial Generalized Linear Models in spmodel +
    4. +
  4. Using emmeans to Estimate Marginal Means of +spmodel Objects
    5. +
  5. Block Prediction (i.e., Blocking Kriging) in +spmodel +
  6. Technical Details

Additionally, there are two workbooks that have accompanied recent diff --git a/docs/articles/technical.html b/docs/articles/technical.html index 71d0404..89d8f97 100644 --- a/docs/articles/technical.html +++ b/docs/articles/technical.html @@ -40,7 +40,7 @@ spmodel - 0.11.1 + 0.12.0 @@ -3461,13 +3461,15 @@

Table of Inverse Link Functions, -

The Empirical Semivariogram (esv()) +

The Empirical Semivariogram and Autocovariance (esv() +and eacf())

The empirical semivariogram is a moment-based estimate of the theoretical semivariogram. The empirical semivariogram quantifies half of the average squared difference in the response among observations in -several distance classes. More formally, the empirical semivariogram is -defined as \[\begin{equation}\label{eq:esv} +several distance classes. More formally, the empirical semivariogram, +\(\hat{\gamma}(h)\), is defined as +\[\begin{equation}\label{eq:esv} \hat{\gamma}(h) = \frac{1}{2|N(h)|} \sum_{N(h)} (y_i - y_j)^2, \end{equation}\] where \(N(h)\) is the set of observations in \(\mathbf{y}\) that are \(h\) distance apart (distance classes) and @@ -3481,11 +3483,29 @@

The Empirical Semivariogram (esv())\(\hat{\gamma}(h)\) because there tend to be few pairs with large distances. The default in spmodel is to use a cutoff of half the maximum distance (hypotenuse) of the -domain’s bounding box.

+domain’s bounding box. Because we are typically interested in +characterizing residual semivariance, \(y_i\) and \(y_j\) tend to represent residuals from an +ordinary least squares fit given some fixed effects design matrix, \(\mathbf{X}\), and fixed effects, \(\hat{\boldsymbol{\beta}}\).

The main purpose of the empirical semivariogram is its use in semivariogram weighted least squares estimation for spatial linear models, though it can also be used as a visual diagnostic to assess the fit of a spatial covariance function.

+

The empirical semivariogram is closely related to the empirical +autocovariance (Zimmerman and Ver Hoef +2024). The empirical autocovariance quantifies the average +covariance among observations in several distance classes. Using similar +notation as for the empirical semivariogram, \[\begin{equation}\label{eq:eacf} + \hat{eacf}(h) = \frac{1}{|N(h)|} \sum_{N(h)} (y_i - \hat{y})(y_j - +\hat{y}), +\end{equation}\] where \(\hat{y} = +\bar{y}\), the sample mean of all the observations. Like with +esv(), the default is to use 15 equally spaced bins with a +distance cutoff of half the maximum distance (hypotenuse) of the +domain’s bounding box. Because we are typically interested in +characterizing residual autocovariance, \(y_i +- \hat{y}\) and \(y_j - +\hat{y}\) tend to represent residuals from an ordinary least +squares fit given some fixed effects design matrix, \(\mathbf{X}\), and fixed effects, \(\hat{\boldsymbol{\beta}}\).

A Note on Covariance Square Roots and Inverse Products diff --git a/docs/authors.html b/docs/authors.html index 836bdb4..79dde4a 100644 --- a/docs/authors.html +++ b/docs/authors.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0

diff --git a/docs/index.html b/docs/index.html index 34b99f9..9e014ff 100644 --- a/docs/index.html +++ b/docs/index.html @@ -40,7 +40,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/news/index.html b/docs/news/index.html index fc09fd1..18a5d2f 100644 --- a/docs/news/index.html +++ b/docs/news/index.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 @@ -72,6 +72,24 @@

Changelog

Source: NEWS.md +
+

spmodel 0.12.02026-01-24

+
+

Major Updates

+
  • Added eacf() to compute the empirical autocovariance function.
    • +
+
+

Minor Updates

+
  • Changed the default size argument to the local argument in predict(..., block = TRUE) and augment(..., block = TRUE) from 1000 to 4000. This enhances the block prediction (i.e., Kriging) approximation’s accuracy but can slightly increase computational complexity.
    • +
  • Enhanced efficiency of block prediction (i.e., Kriging) for large newdata objects.
    • +
  • Added a warning message that clarifies xcoord and ycoord are ignored when data is an sf object.
    • +
  • Minor documentation updates.
    • +
+
+

Bug Fixes

+
  • Fixed a bug in predict(object, newdata) and augment(object, newdata) that could cause NA values when the spatial covariance was "matern" and a location in newdata was the exact same as a location in data (the data argument used to fit object).
    • +
+

spmodel 0.11.12025-11-14

diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml index 9366708..b10b1b1 100644 --- a/docs/pkgdown.yml +++ b/docs/pkgdown.yml @@ -8,7 +8,7 @@ articles: introduction: introduction.html SPGLMs: SPGLMs.html technical: technical.html -last_built: 2025-11-17T17:09Z +last_built: 2026-01-26T19:45Z urls: reference: https://usepa.github.io/spmodel/reference article: https://usepa.github.io/spmodel/articles diff --git a/docs/reference/AICc.html b/docs/reference/AICc.html index dddc62a..12654b8 100644 --- a/docs/reference/AICc.html +++ b/docs/reference/AICc.html @@ -19,7 +19,7 @@ spmodel - 0.11.1 + 0.12.0
diff --git a/docs/reference/AUROC.html b/docs/reference/AUROC.html index 033f0a8..0b301de 100644 --- a/docs/reference/AUROC.html +++ b/docs/reference/AUROC.html @@ -19,7 +19,7 @@ spmodel - 0.11.1 + 0.12.0
diff --git a/docs/reference/anova.spmodel.html b/docs/reference/anova.spmodel.html index 87432d2..8f38a19 100644 --- a/docs/reference/anova.spmodel.html +++ b/docs/reference/anova.spmodel.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/augment.spmodel.html b/docs/reference/augment.spmodel.html index 79801c2..23af733 100644 --- a/docs/reference/augment.spmodel.html +++ b/docs/reference/augment.spmodel.html @@ -27,7 +27,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/caribou.html b/docs/reference/caribou.html index f366bb0..24a9550 100644 --- a/docs/reference/caribou.html +++ b/docs/reference/caribou.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/coef.spmodel.html b/docs/reference/coef.spmodel.html index 11663d2..79dc35e 100644 --- a/docs/reference/coef.spmodel.html +++ b/docs/reference/coef.spmodel.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/confint.spmodel.html b/docs/reference/confint.spmodel.html index 03fa535..06ab4ee 100644 --- a/docs/reference/confint.spmodel.html +++ b/docs/reference/confint.spmodel.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/cooks.distance.spmodel.html b/docs/reference/cooks.distance.spmodel.html index 2bc67ab..b4f0031 100644 --- a/docs/reference/cooks.distance.spmodel.html +++ b/docs/reference/cooks.distance.spmodel.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/covmatrix.html b/docs/reference/covmatrix.html index f01d3ee..27fc1f3 100644 --- a/docs/reference/covmatrix.html +++ b/docs/reference/covmatrix.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/deviance.spmodel.html b/docs/reference/deviance.spmodel.html index 0f81db2..d190d72 100644 --- a/docs/reference/deviance.spmodel.html +++ b/docs/reference/deviance.spmodel.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/dispersion_initial.html b/docs/reference/dispersion_initial.html index f8a3ced..fbe0f0e 100644 --- a/docs/reference/dispersion_initial.html +++ b/docs/reference/dispersion_initial.html @@ -19,7 +19,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/dispersion_params.html b/docs/reference/dispersion_params.html index 2846b8e..abd6cb8 100644 --- a/docs/reference/dispersion_params.html +++ b/docs/reference/dispersion_params.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/eacf-1.png b/docs/reference/eacf-1.png new file mode 100644 index 0000000000000000000000000000000000000000..83ffc4c73aa01966963f9b8984f31f48b932b5d9 GIT binary patch literal 34794 zcmeFZX;@R)_C6S#Eeg@H1Z9x2yd~vT0hM_ywFFBARE98xfCz|?M8GhG08YUwhLq(1 z%A}$U2@sGWkOYWEL1hy0Fo!{e$RQ*kCV_+`y~F+8|G%H^FWn#dTjzN+=A3=@u=ZN- zde>U}_~#iHCynoPzC$1o8h@Pl{Tu?ZHV%PUeSX6_aAoNJ<2mrP?))jI-@!NdEFEJe zgRhO3Pk2Wo5c;XAKWgO3`CtU%C&VAWA90V%<#XffBakSbQsRttJaq6R;?Li**FM;C z=GLtzbwAaeKm5*h%e}W(A6Grwrg!AW&HQz1)z<#F<B(f&+JST`~* zW)7uh`6@D_JG7L!`zN*sc}>O3Ki>^Pxy!#@%e26)r=}v2+nJkV?lwwCRFf&2_y)h% zqmzy4%lf?Z|31_kukS%jcvrQ_qae?=$xXjRaE@5^cw}FO?3zN})HB&vew#t!&*2lLG)o2cze^+Wha(=<0XQv{-NujAY*wjz4Ee=U2} zGTkg$c}|qQcQ)zb##+_X*>xQ{F9;b2)6S!PzHJy;4W;&dQ|7)6N~TXKjNP5O=KF_& z*BAraI1m1=M3HGmKGi7f*ZwL<;*s3H`3td1T1;v4ox@XxC` zq95v9I^kq4G<#1w zrj)eXvc=TNtbIbN3yoT=d7y2YD;$8x?#Ph~Xpi+&rn@V3q<;<xV(&~!aeo#3`3jaI|8&eAeZ<4&LZp{e(f;f~c3%_t})AnRJ3-;GnB&!1%$D{{m zjLDzvZM7_AL?81ySWdb(yOSzy2s(zarOvK}FukP{WqW1A&lqQq)wBHdapg@R*B6HQ zzkVdRgvD0FeZ5wSjlQ-mKBMl$OV^|Q2J*f2=|_@dFK$RN?-_keVkb5Jo!GrQuE6G* z(yh-*98P~PnavDP8oCVdQu}JG!cXRS52c0Z@xDT776Yx!!G!lV!kJ4WX6X2qB;B>i zJtMlt`Dc~3X!W)vTz2TJMfL}ULZkUrj(MMGaQ2AqN5&wF#=H(~H6Iw=eP{y!&lLR& z?J1J@!f*^k62J7qa?(*sjh~y;g!##FL`@1K)_vco=n1I3svP zLXTmdHCvdj=>y_7VR)+vU!%m-I$ey=hiBQdYNR|u8&f533;h_`Yd&N7ajup-5&Erp zASKx6R`rN@*6DKkHpx&+gMH}9WJA-$TImTHOPX#?Pw@AR9NkNFh;q&;b_rXE&fzB; zu4DCuEe5yVR@m4@T$l2Qr~}WZY@EYnk3-16+r9s`Mc(JzgWW>A8Qf^G|A{zEP3TFF z)-7s#5IoYyy-M0^llin+o91Q+=DEM4EJbpnPErw_D_S*@YLWPh>^HoRs8v^ww@V}X z>CTJU(NVo`sMp@t;x6@Ph!CH5s z?cSSwiXZ%OT`GfrYckb2Y(YV~oweR(S-2Q6Ri@lJ=)Z}q)=KBB92R+gY9Wa>D6Z_szyu3*5VPg+w)&p*5Ha|M%dIxISp zGu&n9DrNfN3wE?BNI(Dq7lPKaBn2PDH}IK}1$$>{W`(mg#|fPeyT!B4N~z##k?Sv! zkv&ciFy;Z?#;@YppRFt@f!$9GY+eR^tbEj6lUy8zK4Aa8GNorw+~w1Q9emR=({8B{ zx`xTJcVOsIVEg2I<^CTxOUun?7&5VW-Io*zJAE+Zz-hd2$1KjeP#y{S7S$+=cg$)> zq7E>o3LbnA|9N;&(R;T}lK0_%?<3Ht^$!(_1fQPb)(2+J9AF>byK9A}6N_{pHIKuC zs{piqNZ&D+L>WNePHMd?Hh9pT)cd6+tZ+fK9<7;=Nl`t`=1I)G7z^FX_U|I|Yh3hw z?OMv_K2^+oBhHZC^ZO{munmd5B*QE!c4V_r&1o_f6AClIyjyh>-E$z^-^@gJx#D#9T0fdT*GL zvUj$i$wlVs64or^`=nZ4x|9k-R%R*!i$Cu-3wPKzJm4aQ`QU z&y|jSMQayhy?UmGifZBoQ?9{99Zg#I=SM0%a>|LGY{DmNqC?n8S*t5hxEbu=%RJq+ z(>;z`x^#j!A#C2A4blb{#eH_lvPIS#&tGs8_~LHNX%`LC&t7DHGSEpnf$kbT-5}fp zY`D7V!}3&a`Sjz@&or)zpXgoOpx<08y$6$vY6iYEw3l6+ zC-ysP|7X%9nAMc< zk=IByC~f*^V#tpz8{qB6EZ53?_~C&gLXGeP&&6FeNwesY3l2a}IZUR|molNNvZsIPjQ>%iE2M|)|)zw80En!!em(sH6k2XEJ?tP8bpscZVVnsBx5s*!^1 z4@r%$TknfhyM62cO`Nf6xTA??{E3lcKKt4gf59yZ!Ok=sTZ<4s&oNt*G?Vdb)9hWD z0@I0aCt!!Y3l$aaa$b7tCiC1rw0knLv3z{r+`htMGSz=H_}F7%nAdjPY_uf?3k9c- z*%eJkmttGXb(%iNAMYhQtCyNTd^r(LM|FQYn_-X}H9D`+^V4bdbI2U?Ya)Z*Wg^(- z^~Lk_F-IunL7@dWx zRb=UEF&=9D?dqF&aYtGix1qzivC2a;A1KZAv5JrU_&9R7bd{^G*=)45IA>>^d~O{P zRn6$QD^o^wjQ$6CYl{xli9hU>$fefA{R=Cb&HZZakJ-}49d#Yx`D1LACJ6q?RsM(o z8UdT7Ve7fvWhA?&Ft$ivms1>1zGdTXhkqw`#fo!p_gtfm3NB;l55F#!ttDmR;sm`u zEp$#2_8n1panX+uuyyDxX)M_;gp6 zT+8TASCGs74^1kX!@b7BG0KG|l^XcaFkbGM+S;qKP@SS*vx6VdZpJrT@bCA{Ujo)L z(i@y?6`d%m-yzTYu=xiEDkGU=R$bCi14w*8j|*<`Mf|Ke=2dS@*?#w$1Yg{hk%i(K zr2s$J9CT8q>lzl@dpBm^P^+$EUHKYqWJOZAWXPuL{$N^ z>kE$npg6>Fh-}f0XZ)}qT|K@Win>12xX0e=nVhpnp8p=Hv_Vyjhs(o<(C6eAQ+ey{ z`!DO~9xlv39P;rHpprYxXrjd(GTb*EbX7^;%R|8Xd&o43Y6!x0X38&jiAiCOLqM+_ z4i<6`Q>dp0^*m6tgqgcB+NLap%JG|4zpPB7re$7c&fJ~glTu=QYHcs)`CMx1gPvdVpAEP8GV|~1*m5n2k5>zU^W+lx3fp&~S&)gz&XNFz*SC(h z9-zlw9YlcAim~gJ?LU}aR-p|vY9^`-c7HPsXrUDVmu4FweqE1fXJ$CNZmv1@}e1j2(0J(yYQx0#z>J*h{33oy>hqM{vSd2qG1z^AGQtv)l*QQIYBFiWH@MO{MXZ8R

v^{uGNB&*%3r_ z82a5nGa}Bvz<#nS%q>N4I=(!nct`CpHcehuFHTp4tUW#YzVcR2LRXuiZV{$laJRLW z;H=kkS)-y)QezeGO7pLJk+g5fMyKhorfmz1iu>LRe+hHDd3hEM%Aft!+Y)eIzt6U9 zf5AKtcr$-_lN@4f@5Px_X* z-px_DkO_UxS9glcs^4`ZJ`yj4KRS!?)uiL(5&P+hVG<4F@YEXP!Nld969(}T{rCA> zJtG^Nrt|I2;c`CkUPFFM|=zg9!7zwC9pc~HJePbzkqHa}`3#rmRti^vB=soA2v zS{%HNRhvB{_(qCOKFhgctBpkGep9BC_TCC{?p_TPc>fFUa)UX*`S?~-0O7%>|CuUq z2Os8L;Eup2AnONJ1JL9gz%1}dL7il)qC-UGsf}@}aQ^@Q{J)gIeLlN?ZKcq!JmDh# zQ~yoX(UQx>U~7v>Ln|>Y3|H!ONuRo37MBiWgdOGK?hV#D}Pz#FJ|u6 zh^20FkIg~uTDj(-x~5BJIjDZ=9aJ-xaVMQd3{<}|vs1FW=vlw)%C62faMspBU_zV~ljAVA1l{ ze_+)RDGye}{8Irf>ACbZX$!-mwBii0NSXyh5YLgiN!3B`=DC-_#G-^3{l`^5*^Z~X zRp0;H3}g0!yjgXw4>4LKf;@DRc6}Rwb72k0uw|bHXqN))I1A5&&q7>EP;Zz-3R_Se zsGANvHd6J{YjS*b<)^QZfqODq-q))cOBJ}w!;ZZt%)Y*_$}zJ|SNT7J8IS`~Vs(w! z+>j8C=QVh$_KHnf!(#WDrN3QyD6Wohxza~E0M?$f~MZD zXid&fs_SQ=4qpH0JzXt-mDUDqT*InN&hxYjQIn5UFOgbQ9ki<&&NM-9)nVBSby)Rq ziifHlQFu*eU&&Uel;{LoT?U0i#>z zUMjA<+iA73oTfdX>*<$vQQxaNB|3vndRnQ+)a_fGw1!n(u$v55TEP11eB~23Po1yo zB?XLL(0J)8vAKy6a8<6F`QItp;_6X!z-X6mz$o~QIK3gRHTE>#2cLi!!4zoHP{R4S zu~6Ex_M0pp{zd)E$}-H>u-anJ;hW)Y8tB005~-i4igdix-k%r~rEGu-JT%KHEFG)( z@#M13g6IOxQltFn0#)ZGl&us)WNKZNU7>a4z|F1!H{H(3;#Q*@N}gdD05l4MY4W$fBm!HeTKip6O3c9}7m-`=(y6Bw(s(Od32RqYw0Xtzp>= zZKD=@pf61XNdAFeLk|kwRizDn%qstwo7$#+C0!5Pl3jDYNhnq#dc>*`?)XVi5;gm~vmSo658YPXgop{ZXa6`sK@75_z1c1ipJ?1?Jf|wy@gp{-PW3 zpO6P-#AcF{eBuE_oEqkFDTZAQuG=|RVRML%9PKwbq&x{lLQ5LE=SRKe&Z58Gj;hRW z>L{BTjVfg%9EMd8!iypz_5WY7o`W`$55p^Af z%HyIL2<@y;X)4<&@)09ObO3VB*;zSSlt4H(SDip`#rI9#Z8(DqvnA=JRAU}ePJfoKnloPy=vf91EB~990PP4D5Ryd4AURcuLe;=k1>V@D=wHTy>DCPi zs0H;{B#!L$DPA>C7vNTrmXEFJoFkn*6ed!$+}^xFh=J1fBqxRAC-=&8hfQL6CmoR9 zSH{(W&#7k8`_3GUSX3O666BstmgL6~5aCm3)+0@nfskkT2GMB-o7$fLFK}r^P z%IJXoFlxZwE3f`;HSi}X^Bd!MV9 zmS&O2C6p@oifOGC@XS=&zWB%cpSNJ=uOGlg*47Rk_l^L9O=;}~H9>Yr zxg3J@Df=weyokka-^lv97=GVZ;kPkv;6Q$FoSN`4T$kpc@}b-BrDUNdzQB^4ou63s z*6&SFExMsK-i^e1ZX@Cjkn5*=8M<>LvGc_$4_^4gT<2A*xU7kPU^U2@imp)9BwWHX zNe$+j9$6rnwfWy2Ut1v!ouVrUt(mX84U{#v$ts-TujPFr)@s7s!u6WSH@_&0+<)1RG2>LvceEIW) zF((o#r|Kg6C@x{!t%ymY+i)(a;jM#(=T*={We*_bMZP%ed%$ zJ2BUxJpcJv(0(A)v_15;Z+BtG|EPGn3tPRiDw)<)EgillO~&9yNjJGMOear^?c?>W zp2~f0W}vgmE|5bs=N*77JPdN9o0Hw;S@1P0i4Dn3H+IuFu2f+AX&%TrU>b~>Bk2U_ zXVCeWwm?~LvHu70q}4b2R@)Nm;Lkcc?Y^$GD+TR*7nVrVKQ=u};B4V12a4KZDTG6& zP9X=s>@A+u2?g%*Q`MY7W6xxNyE2BO=x=x;%{a2O zv#cqJ|Fez)&6KUsM)q?(JtpvQZ+a9b|9cidfZj6{MA=FWMVYerWt-AbDo(in zdWv>ReEo9&+OnwAoGUw2?Ra4SvQsC3FV4vGR2jzp8>&W&pFpFk9vDa|<>uzORVJDR zs?Iyhjr9Jr%5}hzFU;jvse4UwRmpJ#qV4CgwE;UvOk>ojtVq6!KL>b&*|l?YDW_VD z&VQ=?KR2^SHiiHROpOvn|04mgW7%1uWYlk>Yj9hTw#pP%di3}AZ;XC5f%cQP+-e2k zK*}>4%NR8Te@B)lxy;|}!+e1!@$%Ckyo-e!z_hOa_s^EGr`J8f;#8+-|F!woQW3`N^~SueU7 zRL0F++3JMRy%532zg{*;I$KWYn549N6wJOU$WfN@Iqu1){cy=Dgb=kHB68e0ilM zBSDm-@BN+-#*wvP?)!_PY?~%;GWQL+8cnL|FZY)Xw zB=79MQJFU8Yx>(Z#TiquO*a;Rp=SdQvmVeaz}$H(c-At3jKLV zc*qz2qscB;u81->k^f0Z!uOaPR2YW~4N1Xm* z1K=J^{NnmA{}(Ebz~5`p#3ON8o~_2;(!s)wP66R+dHb>qvWM;I(n5?_^c9}IP zhp1+fKa+uC>#V07ZZ%RdjqOz(5#9K&9;!4q1rV5gvxdeH(G=X`)Zc}t zSm5I_UyTlgpb+W2)j`@OuU*PEsL5N;WP|L}-l>HQavIvx(WYwV+G6PqnrRCQ{oowXQ+_{<(TV zHQh9~wXMZyO~3`*MVZpDJ^b)206G&AF!9q-z{CeSPIp(@8q+G==>V-VgGPbE#?Nz?*@jxlpH-QO1vf#}Z@Sz6(XDzq-N zZV0?YQm1x#D!WaH9IHFct1IctfgI(=^^O%2PheNaiolUg?iQFual1EkK)1;L;Zz&c z?3s*eqy%0NJyWNtqV)S;igk`ob#(jS^YXYMDgL)i2bm@2+~-{rsPZPYankv){X zw;c=&Dw3KQFaHT&k4TZf`B9_tU#=GwS6_~*peCj$$1Gh-f8TIp38V96SJeC_cL{EB zs*RPOv!GMtVU7Kh2lPsok&h4-FzgSLf=0A7v%eNWe!KX?hyGK-R zzt)W+sa?J-0Zd2L1tVHCt)=usdD&h3g9m()>`xWh`%SdCN%?4TWG~s_S%>`ZrJz%# zago4xWZ~1`<@?%#q&kM;TxUe2U|=)L=rJUo2)jOSn_G1{w(tH{ucRu5{GZOSvjTtAhbRvB-fZ&z@nvA|&70?* z@AIQ^9DZz~N{iqU4>CF&n!tsLO}`Iy5u?Kh_trwpi-6}12!>4#bUk_b))h%d4G!#Y zIY3p{F$C;hz?`dI17v@M-BwX~Nc7U_p?%*t?(|NjJO0x;VxDPOY>D)NRd4-i(1{4u z%uzqr8BGWh;oEF7Zd%qRBu|i-sX9eH{j+XTR9}xg^sY-m$+0XOUFTd@etRmS^aJCC#j1@xR-L-fb7% zGJ(#uO}g$ZrXPC7xjAHv`4P;agLz35uHm*X!YpO^cab`@Ez4hYe)u_~X8t-C8VX6a z0;qJ_a4hfoak8yd69bF)H8IbdgAD0RGvM+U?9bX2 zF?;}r?x7@OvwsdKkESL^c=az-KxR5x^ULk${*7XxO8^IXr9%$KrKbbMsZT#l&59Yg zZA5J>kuu?LllSYcG>={uG#{FnM?bVpQaXzzbAQN?*yftE+h3?x64z7OkbPxMb=Kv1 z+DV-~&N|68g0hYi0M;#|9OndQ$Pr@ABh*HG)TlP~@O|&Ge~5(CuH-?}@B8v?#Z@FL z?Y?LqaLg`wOfTGT51=l-wa){lU4|8xuJS;rLdZ*rUC(e$O&)7_D&@d`QU$)Vzfc9r z07C5Je+q3_pCmUm&{e1zkvd~)>$;xG zi?L)8PvXh&5GB=vHbYI$UhbT{?|=lk{kl&r83v!QHQd<1PykzmoRrwqrFl~F-{dQC zyDEJg#>#hn0maGi$54jQ2U7OGo0@$eJqy59W>Lg`P!Ja=3B)Rp#TQ72?K6 zujlpmVGQZY`q%Q#2gCVRtv)f7Q&gqRfJ-UXA4LzmBCORZ3b$lfHz%Nv{kmKSqjih0 zz%)WE67A~+D_%#|XS;eNXb(MWXP^f9LC^u_iw0=MP#0ms-3A!wRwD<%>=0~)S=U~j z5%Y$|ZY>E@1kU9}m#szg>l#_asO4OaNKNhrTUP15@O>QGu7T)>54a=KbF+*5%4>cI za?k9MO5LJg88wVJ{?EXx$iwp0ghFR5u6Oew_Q$U~k&X4%L0=`>?NwTc0Gws4YJn`$ zy<{-%eJp62N;Py~QeJ-^1Vr)B5S46t`d;MQ&*Ej$ z>qzCJga}TkLt48Uf_-Aj?i!tR(=i_qX;Y&KF8vAs)I zSIfr+%RkyX&!|$*zP^=WfZGs*<4VK#>W$6~2tud=S)6DXjy)U zCn?mU10{E+X=dY18pEA2+-GwFj9w?##CW%=i*R<6J2_%IhWUl}1xG!c z6%8`{{G$K^e(S4fdOxly5@vS`Rue_3$|0j?)-fOpiE#R)3}5~&c2-<-Jb&(*o}1jI zjhJsgT3G^e>}9`6*?r?PelJeRsC9QkaItZ1?v;3?E8X?e$i3EpPJ;{zvB znW+?l@uHvh_&|m%msm4C1d4W*AVnh`I+#8#%<6rQ;L$C$Az+MCKJhD{eP-ZsP!sL*EN2WNW?D# zZ{O6^Bs~WP-Zw-u7GF_A^dDctioX0&Pi7q%MHttT*d#|08dRkezH=%i)zesKydPK5 zR4o0vq1FDJlSlG<6Q#gq-VMrFVU*&(;@7c+Im1}dY8ieHows5>LdMf^i)B~zr-NuW zZi96B2eOssD2jW9|8uXUmz+lG?gz?b-f?)0`1-S0yY9X4DqMBPLAj(Cu7(iTouU?$ z?R;MuF!Mz3(qhB{+IqRXko)-{AcP!mh})v#v5S}bgmc4}nxU3m!jr(sbvbMK=-b@1 z0-+*39H}f`>e>c0NH;5P=R!AtVQP$fwNo&cD%SLH@I%q8%L6k< zdUT2|)Vqo*JTPc$$Ex(BV0)ej01X-vURi^;P znKym%Kf?^LR*&p+H>L?L-;k+;^0PQg2@)EB{dY|5nA=&Vs9?O%lL1qiiRpO~Y_Q{h z-AZyz<#3}Zt?t6oPO4GfL?pNs&b+fLsuetxVpcD@D=|9-rzrL?C=6 zP4M9$?W&E*wkls!IRw;GUi@};Z!~`^h?{KO<*)mXM~p4Q9xFKrCKouYEElZMywzR} zVR^`P2Qx*3#R|L)=x2Z~Se(LNGzmvSeeG4C5K$-SfM&qF^o_T#EKwaa0Ms)Ge}!Yq z8uiVyZB*?5iJIFKAE<5qcnhp3EZ6$SoFSl()M;a(c0 z;9|BRDE0IoF}k$)s3{L)Z1XrFYKV}Oe>Sfka0C7U4c^!1Ai0r3{KSA7Fv{pbRvp@h zKfMZ3nZ~LdKm2K>KAZzQl%%Vnx$(0q9CkA)TM37^bgIJPxJ|CqivL@cY8^s+OXBI^ z*LZ<{loIRVx?PnlN-6hxa3?PK$qgmr+OJ%FzD7EDaGyyfzZiggir4df z=_vNK#OLD{Tj&qnk}V#5lYlsw9-*4dV$xIT$uxro8Rc{v*bi{6^Tp3ok#=Xe_2c1j zhR#+kS4r_2zlF zMKx7fQa#F%vr5Ow`dyH*&yFfqj!ivQ^W=Fru1vheCFh5|+(nI%(iIK}>#-&Xh#C z0JmY})x!j;6B6kiGY;VJ(y9^tDVfdkE+rq%q0E@A$x&gx1*mm{U}^5Nf^K?xpb~_C zoUXPZ-6ERh4}GO0RTNqe?;Q6l@J9imHdWG2P?>JVEiTWG!|Kp8C>cboc7+LE9Cu$W z!CJ)Fi4AeF+1jSd*I5m;{8N%FLy1F-vn)tQYsAuB{`t^%dfl30sL;>;jQk{?PKp;+ zpis5DzE?aXl^S7vxV2IPsJUW5c?3Xk1#o7Spu#QsL2J4n{%dyj1+efTmEY?OTU@_% z)l8Dy_gP^9UPtJM@7!sn)xU>ZVkPj)ItMye^8jAzA@yMVb0gL0PW^8P}e0}(0hdlJkB4_r+UYT9u*M3*y8b;puXVR92 zg7BH>A048eE3qp_Ew9aZbn)k|T=3=EqvVcwd9d~-MCJ7jal8PZv4p3aoUzTUDTQl= zbOF@QH~P+s?hG+KUGswMY`Rxc1m^pXMsZ;sja`dxp?PrF!ogSWB;==_-WL zgbvh&bQl&F`PZN47|$7aH$G1A;|#X|nEC~<-BDj|88|erSG})k*n}a8f@&ENY~~OC zBUnJ;ucYc+6S`tQUQVs|=GeYm@cL~MzB3f0s_nC%g9=#VOO9^RUI*9MGJm99Bj6wC zhtW#V@!l@%1|tJ-j;qggC*kwm)~3L({jbyZWndB_hYD=sX2nyg;vD-nGlZkZSWwuS zVn7X0Hkqr1V1GH?ZL)qr?}ZG8ophS~#i>xJr=6HVy1h{|ESog`!Gp{tM9BnJz0Z-k z_6_nb_@6B^aaTn2j?lGVoXitzBWF*5@F4F?FVse*8coObl`D!8E{n>3(cg+dP^=$w z)XP!*o2M%3|44QEW%*QW4D867$npmFc&c z;q+67{{hj0EFBO4LHD@kGojByzp`s2FZEOmBvK^Dez^L#+RM%VT6634ZSQqwLmsSI zqt^K7+7rLuC;zQYOL4e8{$$m6Pg4GhgVe93eE#>7TU)QMI<)(Z?Yj#b)*So$w{<`5 z`a`Mchs1vrr}psp6coO5Mr1ovYVT3or{GhfDY3+G$Oi|r4XgTm{Mzq52B)%2GKMTp z?=n9g85_&29A5?}0;%W5^j~aG3n>@91DQ=8MIyit5vkKn)1~GUbKaRu=iJqR4}7VFPs-{Qw?OoOG)@0P48iBEoqG6EaJGKo zBJ~Ym&H)ef{TqwIoCE@{OIxZ8!S21V#(3Y6tCD|yj8jVq7QZSo{vx2-5%bq;AWXKb z9ofRqwPu^ojlp+G-EAJ|GXIa#?`p_7sQeGTc`sLiWWHZR!po1l#1mCeL5*^67XWrE z>!t)>f@6SfvEACy)m3kF5bRI34bx8W&JuZ0Z4lN;6HyuGIF}i)dv}~eZ3y#@I9l$A zd3JQlC)6{xWT&?rD_Vdw-6a+FhXMf!S?A^MT*kvKs^V0JNGi1XXrh- z&r?AGvbmO*UC^&UUNpa^jR-inbKu+VD}6ml7=KNG)N9g#P#qnIldd=n%?cBYrhA|a z9hc7Jssta7ZKI^rCC>yHLyWkxbah#eribe#+4q@X5zk^~NYlD8>+oeaLm_8dH7oFnp9`~fE)ty*t|Hnx}X5r_>2Kx_!Bt&0^voaTgZVz zVS%dF&=%CbO1PThfDO+uN8O-#I1HK`=U7mNJc^N;C)IW$0=8fe<5P}ZX)Fc)pwhNw z|4#}p&Tz2i_NuPg&qC@}s)cF#Pgc($oj(BhQ#{MrgpB{ToEyQ%EWul3!`LQ2Zn^ZW zNS|4K&F~<< zSY$D^VT9LdWH5U9<=d%TPkC=yo?WCCh=E&!50`)p#)E_EtS+j*r(I>>LsAa!6|l&b zm>7|$^ca}5UQ6zi@!L=;1?MiwuB9wc+^Fik-K_^4+rg4%sxGFI5laHOw>;+m`j2Gpm$C`ZR{nVa<=z+%Z=U&fA6{@v z1uf&-gF1)xp$t$)Yvl(S*ibmsHuL@L7(cuWHmV*1ExPl4x#8fEIi4GcLjxMpQDb(c z3CE5_0-oUc+QIZRboox{bv^d+2LK0C8q=+gbGAUfLtc>*b*S2@9YiUq=aHiJ(qnqB zgdWAN`apQ)GgmbXTbPvQGQpWVzdUQE;5L*2G{C_(&zz~S({MAdv||;I$0tvIJOUB~ zQNN1@#JN32ZZb0b-Ga>(M9LqmnsGngF1Pi8bN`SGKci4lM%?0#isVoJ5{D<_)XPkY zvi4TW{`sL;}3_7E?QnyaKVWqUV1i= zi}@!cWe6FYZ|>-!^p~ID=oXZJra*QSrU#N{gx0rVvLZy&@b2)zW>0kPzxIN#FAB@~ zlZO{G6mP`o_LhMLL)?g%Au8`-W^kbD-OukTJc&&JobpGWb(JFr=pL@PuBEZZHR`&Z z2Esg%4I*G4IKA|iMIYa|lt~<}V=fYy#Nn8X0Sr11ZF>I}P?O4kS8(SrHGBVJqAz(p zirZHoB3dT>JiDFTQ3@%s+vn90W#$0Z^vutrh54wF7z4U|Mh!b;ClPe-4gq`FAwA7O z-0U-oYc9ZKH;wI99})If_{lv*f5PJ#7GK3akQ+s_Mz04HS|fI7UhKMfy;1wL?A`#T z0RC`%GPE5lyBx6|Fh&G5Bvi!GIvgcg(pY$3!NAd6!Vi)Ma7d>EQ7 z`sSYIqUHRDL)gLmt(6X#?EB;YhJyP1lL`De7lNkqWu?^vhcof_!YgaQ9P^kaF!2Ib<gIVWQ&CgSAd(&VjKQ*$MnIOY=v>_Ka1+4KbaMyZSs0 zJz8h+awIj!!{MU|JiZ9)Lk6aagPRZt>Zg|^%`)_WNtEa_@NXKFpwQW`)osd)zuF40 z2AJ%Z0sEFJU~jk760BEa5#tm`2Jk!Jf=ZSV2apvm7-=^%d?;-yo{eB%RH1q{dLuI$ z|LPV%3Pjs%CH(rpXo8MrIo1Kc0c2aZSF>eFh@hZ+>XM4-^c(!710Y5h5_h|4N(goSg%2_SsC7AjX04cJjuRF z%7xS61Jy%hy~t$XU9Jeua6{nD>*qhGe_D&Es|V0VD;2n*9s|lEFr#yuKt9YLAgnov8)5Wwowc=A)@o&+v2ELYdjEQy!Xeyp4(7#O~0or3ZO{|Lp}=~*1ij3 z>i+sd-KMMblNAS7+C7N9D)FVR_aIkPF#0gc?lT|lp4qJ&#AurxgvQ-cEq^z3(FZ&1 zKXrDj(FdHsI|u<}n0*3khR$BsxbrJ;8`PlIk80*@6>n+N0sC198M|AIwqkH4N!1BN zyy6x}A0RBVw-y2QGBFO)ibH$pS55J{Ji)sJ{&Lt05wK zPw6UXNpC(L@f^tB9XD!u9_`x^38gZ=!Hot~`*V5z#Al4kaVx6|MuMt}94=5EhU64q zkI;6DLm))!(WZ8}_vKr^*<}K_P5<+j{3n4pLwAd^iawKVFRY+2RUx!1ezfh=99%xT zSJ3oST26W?xH;3G6v_!&`~nA7Cyn^$u{vkf5CIW5T#jG&D;(iuz zU=2q(xs^-cFSO4BznVF_<4@_>mg@a?$X!ObgXfY*t(ePW zCsfSCG514d%GX1LK)iUxB*FlHlZR%xQktH3VmixrTF4|6Bb^u%S~kj_${5}wvo4Zy z2bz@$cZlHWki_bQP8EbWP=SuCOg*t7@Px>DQzY|F=nw{S?Iq*7kgx3BxpCL!est;F z!zP#Qzi>Z2cmlR*#*!hu(Bt~Lk|v(B+G&9>+2m%L9>BXrM8(7`WgHvEO5|jngKdYb zsuM1X3^iVJH9ZQ#7EglrW{RFKo)p!>Pe^AWC-e5O#G{;-S2R`UR_O&5O_kY;fTf{% z9u8iOjdsHI_g~oP7KI`ZW1Csb$Db6$)OxO@CiKdTXG}A^Z0_*GcwpKl`$M}`(#$Ww zO1ChXL*AHW-)IE;yvldwkIda*Q3tC!F){AAhZuVMLTtulKRmBtn3o#$PeOvIe?Uxi zxe5sR%)r^kr_*Uno+tgmLe(n7#90+~yP2|{N}s_tlwx;RY}~a?pEpAKp~|H0Ti*8} zD~+3Tq3+1?3N$F4mp+aoT;TjVYK&AldU{^l_uX@Xo4Cp$_8 zfOg!Hl@J3mJA@-W+wQBSWT;4eQ07?q_}j(b@Ux_!1v#O8$<@|OMk4-||4`y%>Gtw)^tSCT~NF^iOuNH<|#r8)wScV#_}2T049kUg z#96gwQ}?*HGF)OSs~PQOhD)H`10e1{*6AE>Q{o-y^^qPTwj#?VdlrCHoU@ zADApak|`BdsG7IKjD+JN5eYrgWtMnz_UW-N6KiL!N>RswuSX2E213`Vu4dRsNrwin z7s0;dHWnPL=V?bsXb7DQT=~Yj_>2IF9h0o;}L_iX-(&286 z!Z^ufCxr2B&-H5?D@A?%{H;fWD)X=G6X7VCwkOc4fy$mw=sJp;O2&0D+O@)Kf>2$p zprjblqfJTq-y_O)t{wRW{~Erj;o7M#jxIp9V;yQ4)7PS$CtrzkpEfZWEf0q_(FCZx zswsP6sSzPXp|bb>lQE{>Zvq9BI(SG|D|8*A&K~r0B@d>~?)@z(&Osu(lC^wA!PNQ( ztJD1Pa(bxw{@>`vSycbN{MHGPMq24?nkqs7T=yz)benXmXuB!&I$n?1!jnAEMZ|f? zFXB7-ygvNcSt^x3Qr*^Sw!fmz7)=vEbK7btO!s2b^bpnah-~Ki+RzKrlJe-B3F<<~ z&~krnl=Cc~G~wHIezOhLqJ|f_TuU5o1uhAE>Q?QJb20%@6W8_CVM;TKXCCTF9u1e3 zhe(b_X_rkjX?se_6nOE%)r{#WS?OSu+8 zQH?v3lK#LmtBwIu0~{a@;Lh3Vwgt^dW^`zl6B)es$%>3wdfMwyEEs@dJx6op%SF8w zuYq#{ooA$bkI6stzqWwR@u67;x}fv;xBRa$keiP(DCrWuc%WI6Hi9I^{^v~&#MD@y z&Yt5*$uq|11sAiQ1R_Ozt4W`AG;G()iv=Y~b#||Zt~baYVq(qOd%{)eZ4mzC9q+y0 zPOmMVTO8ix|CxK%F0#YiA}^c~2L2D0`cqn$Ty1X53jI+vePWfm0EIaO_VQcS>|XnP zANlY2D7+s>ud&ta^xL`J8foO&CgHxK4a@)=YO4ntXF1iUzbMFx%7a($1-1c}WcKTv z(c`w-;uQLbcwD^yeVsnP410!~xO!-(C$~Al_kYF!oc11T;NSaa*p<9p?f-UUhkzKyh){|8UFDdqMgf9XRSDA zq`r5aTVC(wm-GKeb?+V2bo%{^2g|Z9g6ryHq3KEyMFdok7S=_?C`E)&LX zh%+CgTk)PT2k%IULS{3!u>V;7svP=ZzJe)C$h1Md?BmivD21FwAq-Qn$^u7*c(IQo?QX!L^#{Khtifj2`sdYcX+`eoY_gl zAf3byYliP=IlVW;&~NZAn(x=TgQ7|G*8cXF$GRE4T+4HL@%DxxTy`nmJxvC6-&X_L z9LC(n+YY&);u^(WtL#*OBW$MBrz{gP`MfBB@ddH|Q=4c7=Vq(4?ipSj-3hTi3~r0B zHYtLC*oWIw*=ZY>CO8E6caKiheXLUiLxFNVdm21+Qk(Ss^8K`6bDHN%Ba8Yk= z;H@&Yo>SV=@NAV4?hWv7nUqdt!w2By`lwFD;(7}UNLaG z2aNX>%mxT__-CL{*`tT|#KqICCacX2Qj?OZ{++z|u<&+Kg{t8^h$YMnk?|J5S)`wu zW6Lc7LGeriu;s&zIcu8>t8A|s={d-PBft_8(n0z>nv|5B1x}uM@8Z`%e?ZE-fmx+n?f9a~Q}R==Rq@*Mu(i83g2lb}&J!yWvJyDX z%CJr+D{6MP3k(H_!#R^2t(IRTnTMny4pHhAZ)k6aQD(v1zMWhGv?3lOMpQ=d7iOnS zeGUQcZaFrjii{Km7bH@y2Dm`{sS;v-JQ**QPK1}AHW+Sl>R$n-=hZ#}c_r3->Kn~b z8(o)i5YdASHdYEuidn{m3-gwIYh-0pN%&>`7vJ&;yGoxWJRk%TPr}_SN$LV_j9gh6 z=>wGD58sU9HZteJ?NDa=QCuXoFmng^y38Q^znAfT3%hxw*6~H;$#_B7vBh#BzHqBo zB+y+-O~I3>!(^$X<&8zP6SqKw@+#@|8Sq&?^eqkPbt97$*(fidL+p zZyFfb&jDnF3k=g;7Nt2_ue2JUu1*RVZmUG#HuhWXZ@-ST5|6_*3ZzwsC*M+aiN3KL z7cgD7vSC1gZ=W)`d1Anlu9X7Wj&`E>os|L~mZk;+7%#&^@l3?Q?zq%)T{ldO7-W6o zx#&7u$C-J^t9#~P&Kq`y)~_NPLgh9IWJRG>QS9YA%-;fad?16yQK)U5D#C2vx5_fA z?!SSZw}qiONrn2ettTxI*#eS4JFkrK-^?zAD;R?lD+>`+5-@-FY8UDU8%)BSM36gNnuEPB&`TtvI=}|_tdtu zL@R*yJO5(NY?Gv9s zDl1()L)sy{{0;5b*C1>X9sP7JYWC(gkFHva0qa118&xKLgXYwT<_7cDOgbCUvK9;{ z+wcQ8aocBocQ==Y*&~a0uhPuW+@hx3FfZifuly}79~vIVVb#LccPyxh3PAi=iBySZT)prF3=Lm(xMHCB9cRGTNT>O->S9& z5f7{qbUYDL?0C4W{C*MwWNJ$_wR}#iozaNJ*!Lxg_ZUCg=b-dkqt_0@(^+-d@2<=? zUqiNuLFsJ-fe$)TKd_oPM0KNum@S+T6}c``JvO^o^W{^?Ung7Y_J-7^aY}ABFyr07 zJ?9TIXQaO6ew<~N3L4<${52~na8I_po-Hsbk*3aLK3%5Xv0FvIs;81IK-{jpfwIkJ zpCe&os1Ptzq!jf8(fnXeSMh8BwURcn;}yGh6<>E;Fi1%7>BfO?DaY+Yz+*! z4k|@|p~m%(th*6-@LEE5ny)iplI^n|-(1HAhV9wAb8PIKn7>mK3FMn02w}+Z%Q%9b z$2uP4V-RB{GpUd!ic&Fm9Y0u(gp&Atc ziBQ?mnr_@P)9aw#lbUe4YhQJ8Q|`wQgvwPc`P2+s=BL3O8MlfsMs(4ww26+#{(*=I z{CTg}GS+tkZ!W?+O(7To+Tr0Bge7uXidoXYX?N->wx<+R((v{ozqtK2alO>PIXGxx z_5%f|OTPkXEo3DBY{_afvnNk%3q%5WqxF_M!k2+}ZFYN0meDbOMadfQ8yS!)Bq!2N zRkuCWA%E5Th~aG!6bumAzZmOX<^DZaI)(ZIu}#_Ccx15a*U?r9`C4oMatb}NwjwBp zE^WSI_fF*{inJ1fd|<=t`<0KLnq9bkWU1Od;bz*wPxHH1wVr=`<)vLbFQCn6#V+yH zQRaQo-ZPMvtE2#qi0Hce9RJ=#DAgDEQ-Wu!>D#?~b~l=Oon@I1e~)NwKfSjTbtX2= z-e9BMg8C;$1}2I1f@a!1_eH2i{z!;I1?dWjWM|E1L~Ausg~p5;h=PrXgp#i~xgTQ4r& zCeFl_A;9Q0F+CtOmu=!1lCTpZa_T}9s<;%6?N@=f)>@htcMs1%xy4X3bk&o=@V+;K zs;9wgCLn00ReZ?=QuDA}q|r0`nr^*TNyBB1MmQaFo9QCDeQckl2Hpuo#2}UfguNzK z8+6wZX(ZVVmc66#3CH0HH?9BnDh5@=C?NrsvDO6|JPRn+2xp*=z4RU&oi9OJatuX# zHAZq*o1zT{!9xz%VE9Qqc<6f@01|^3al0|Pw-x6j(@a#Pl3p4%b$(+g%t^4kbB)!G zgnuB`1%}v{toflF!dotxP4ZoU}Xo_ zpRLk>Rvm2K7}#2lbnrfbk*0OAHLImmppAz!H|%fXYoia`Ph$rH6{MI2?HYd%n zw?kul_lB<5H<%(vxAA_7yeu$W0FpO08;6f(Opp-%x4 z>oEn038pv?3ZwE@`;{IDBkph1?u+LVx%mbCdiOhKF znSrW3#6V)N>s+Ad;aQRU2Af7Ir0D3zIw6sN zJ{JgLu#=}s6(G49BH8sPF_GXT;jv@N5>aGARL)V^*HV+e@zCttK>#L5mbJz4j2?b> z=_sP9JPgjM@fg^$AOzVHYTAljF3r*cxl)kSvS$t999pzlJxTo?)J``~%k{-j6m{uC z^gw)!k(6_C`o@C3Era^@8PL-2=(5kNYN8t)Ux-md3P;v2{v%k`@W4lEqC~TIXv}V2 z(|6 zRMxRc7SHfuFqT7lrBKnfA483fEGSnkM;C5Ydh?OG8?3D+FIy1329^$!NcAM}0Hd7T z2ghn6?`qazKn8g{h(Cj*!5n(LC)d6gGSjUJvx-?e3lao8kjZ!Qqox6~`^GmV7vJ zZuhD-A?y-ol<9h8N!V-8CXIC)tHL__4j;V#R!;+Y*SNul!(s|gz2k}!P?mZsG0jmY zE^d-O#*S)gF=dkVc?Z={p}XvW#!c(}b76ra?T@Gk3qAFAG{pAbO)ikZ-#oftG6APn z%8#tO+BJn4b54j14meUph-|x-=Ey%c4`sNslh|%j#z0x@DpAgHU^orhWM8%OjN<7u zhS_k6MMf0LZv0^F&|uD&?JSUr+C(Tl;fHq$_d@3HSPlmsU~2r1WznKYa3&6NSr&A% zKlJyrnBeJF!QFG`2XpF~2}GxIj8W_viGw&pt*jqpmtIUW!3`K$+xp+VoPxNP;30~z}Kjkr_#?#80_UI{2w z>a!kB*viWLTY@y0aT;9#%B~(Wtq6%4LyQ4}UO|p!b~U9r<;9;we3sUE{ljZ(R0Ie_ zM$XOYisHK(H+kWD$4Ba}(~WMV$NCbEt1m#3D_lG$tQpfVZOCT%j9#v!0_OwpiUQFa zNmnMUdGyB@`yl8gjuvcKa{plO0 zQg(6*SfkZ*9&X4OV5|D4Gi#`N#!}m?r9rX{*f+!h26DGS*fqRV*Ja>jP?FhP317Q1>}%g)LXRa@6+F7K`KaVzsYX}3 z_VfH|og??6E3nb7jJ) zbD(9$zI}}hd;zp(487&}`HgGhfQFib22a%ObL=UC9^xI~_D$_ohG7@7th1r*=<9td z0o?k)5#cg}AM453Wm#La<}Zc@1=c9eOU)(G9|!^x!-{3*h#v9ok$ggaK$x=7C>+)L z2iu~)Vc|o{RQGAbRyBdk!8Din@|j3w!v~6`&9il{X*t*qYJ!L{V3~F|&c@{j2S$2>g40YQwupt0^8a<% zK0nNZGX%hgi=nCT5AsGDXf}oga9GjP`_)0?iUBt?-7gXSqC;R10~X#LPgoc(sfk zH~pClKt*+h>Xlh+$RJ2sJ}4;|yS0q0XZ8?}E8WDZX#RM8;u_UgDFi=IlG8ATe(C(< z@zi{cSb|*@XqS-YKrZv!;WZh(xUHSQGYi7;z(in4L4@*Y;pA9|& zeE~k+<6@nWz$Eam-Wl3=)ziFk8Ui>tzl|*ZW#sxV1&+ z=Y*&7#Z&?@NLJrrhn&rg?H?wC>pq!CZ8MLF45a}k(|W4a;OLXlN_aq9oc^Gp&?PvE zGP89xFsBPeD9~ve`;(M8$bKG1 z6c*}Rte-}L04Ip=6?qKE(}1htxL$MqM{98DK|USCp(Lk&l6ff88zfz1^UNv^ob(PU zkyb-KguC94ZUgr5733%T0c_Fg#nvzMQj2}+ItuL|bqa(xK<+U%4|I$pGGkXR2!P~Z z5>N|_AjToA4YK<@FZzzzST?zpSX+}{$HOse5B^5lSK`FW26x8LYF8#_ahW-e^Z~Xw zMCFdD#$KEJ{n?>roUR?q+R4uVlpX+O&2}|frH)rV8cK*aRSrsey+aQ#QX_@ED@u9A z(=$<-v!2H`T!WEwpEE@7yf!fHnIC>|w(g!?bJ%%KbaZu=*iuNAO;cTiVYSo!GM?l8 zUo2lV*2xfGTyLE1%yX&&#+EI(mZh=4lm$MS#jKcv{Zp=|WR1*Jdl1)rrPh1o z#LDP=sYBj!v%BDHVT+CSs%LAYMxdrH`}0CG zzwoZuJpr&yg)SJqWzEi?2@ypevix@o`+GKAs+2r;S4A-`@7(rA5D-2TjbT(sm0bngD{Unpv>pRD|h?WzJSz3Tp1DjAlF5F3M^vN$ z?Z$b|d`%@=>DkVuDGR(RkjrCTOat(wh63%R1V}?I1|GN(^w8|o6x`R{`Ys5806TTY zUGzcmi4Vk6>#PnS21f@7GQ})&^s@##WEkhMj^HW--;z5uQM``4NHBzx#Oq8iJdUi> zS!>oR57Tdb>Y4BSRS?ULoSQ`v$hPmArOnU*=Xf^&Z*@*|f}V>2?+F$TNhH+?68SXQ zQ>jF~>_uo=B0%qBSAn~xz}}WWKig25_dpPNZ~3>okY&azjx|>9Ti6>Z($^D|DPcNgjW@SG05b9yQTTus2Av8K{T| zCnWe(l&)LR>%!Vx^@VuB=fa`JLmr?O2s|;E)k>5pvS+B6vcoRSVyYdly~{LthyvaF zq(H|j!O=NXU$NKxT1Kj$IW@d+4WSkjJdoIHr;~x4*YbsiER;43)dh!OMtFTp|w$g{=Jbrm!<{b1)W2_nq}C2 z)zm7~@?ien@}+lb^So*!6&%ChUi$!zL>Wxvb z=KM)Xsr00k8?fV(54`ByYm%)6QL&nWV>JL&4nTBy3VFE=q}#29+lx48lX$ZWvC9$9 z_U%tE?Gz9dxMz-pr1pY<+Q$Es^ft^Ba41O|P!g0#Zc0mtwb>@hfgHcINud9ggJ%U;V-CfhdKuBq@NighsNT~7tS zIs62WE!jjXlGqbEAA;t8IadQxc-oN8wEO(n*a%tIJ?pYILFY_N4rUj2??#aq37fhRertlBg&u49u0e-)wzVK_TnpKN;*RL`oA=q|k%=xdZs`>*VP2Efk84JM zZYQ<9Y6>+qO$BN1Q*W5ro-9-*dc{0=!aiud(vqpb6koR+tSgJ^vT z-Hw{CJ-;O4nSUdc3iUzMFi@r2?LijXFztPg=^X@^q1&rRq7@yt<=gr&iRS<#u9}Q7 z(jEPN|MQ_^=_7AG{v-FjRBUQbdrZqe!rhhka4-73v-rOM zIpac?1LYA94n8@(U-a=^xm#sVOFFhC8SLKsi~s8bZtG`Ft?b>hxoz6LRQsx=oc-sCrGqBuyisTsu&Zy|-E)%Zn*!IQQ&yNWS zWU2ST#?<8xf4=Lfx)F7Ukf^oqc?36c{B>+HAR(%Riy`d8FRvhyHNvMz{R$HFP+MI+u{!sGg(+o(#&C94zR;%E{eqD{VAfr>y1-v>P+4ro*W<7}{Qu*ot?a=PJIlq-c9P zPxGSgTuXEg?^r>Go7(-D!}aFi^^>6anS$lSKDiYv%szE|FsbcNbvaEv3Rb@U5FdLm zCZ_iMK%MYA;Seng8vC)w3Ev5_>yO4!i8@LXdVW)KD+cE41F%tQe!>yr zf}PXsVhp_AJ~Ui&`BbsBLqBb)$-`F9`~LRjexT-;-y4OUMI0p#s4|HZMa;$5@j8>@G%MR#bWic;=A}g zBii9iwpB7JuAG6eoCqtAo){Dyyp8A2v$po?{5tx?xZJ2xCM}@}7okM))#xd`lN>$8BLI9ywSg zO5uSVS+C(0*0r%~EjwZJTa-@B5Eh!?E5h*l=JNgHgOdz|>`?jt`&|BWFfWsZY}pv~ z9!AD^SM1t7?9UxuytU6^xj*l_K}c5U`-IXC&ZP!MNe5Z;X~G$p`k9H&aAt~=fM5T6 zw+^P(K3p;H`z{&$mZSNyE0=IhnN#a0D8ydu$5-~=+6+69>p*0+g&A~+j<94+W!?wF zJ9?B*`QHt&-lqH$#&iwCrNHaeJ^Q$YhGx^5lEfKNd zC#*|;PID+fH=H$VWV6%%>VJ)IKuco9wM-dSp*^U}FQFU`_M5uc^c2==PK;?zmK3mP z*?xK0e9h0B+|^z;aBCv$#~oOzJWMG`T68tU8TM4-YqHrT+d&VQvcHNi1?V?uY{jZQ zrne?~dD2Ew*Al<$9imILWoAq@<(SRQd=lba`?2gq*^uF%_iNH=#PdZ!(~o-)2FCGj znCey(`9l0JNoOr_6_Y}(SNwJnry!^K*F@<`>1A%-4HPIXnVBWf=U{7P)9Yr6M^IYG zTDc+A9gg4z)4(3&=YC$b#EkK4W!Kq1q|vqPog>NPy0B5*$!DmH(4^#ebQa46>TGa~DuMEf2P*5%yn{mX&W3R~iV9QEyXwi+TK6#6!JjjFsvYV_e~4m;4{cQU8}L!20o&!jS4Ge-thg7a>ns zfyGNzvOP2AeA9j21ZHK8t3KH5<^H#4cD6HDM>%blL&c0Fr!&kpuz)6JL+a}_S=xO6=OpZA&LeFJsR%7{MP@oike3$D+5FZlRUtl;7 zbvr*yg-K_s+3CAw@^D3nE{O2p^|msXUqE7_!**NU88D)QG$whR2s633@O-iw34@-k zybC`31t=_tbw`bYrY@x?b1Gj>(?`(zpe08Rci$383Vz&>o0wIvYJOIZLsDPXWPnBUxk&w zJNou|3cpH|9XNx=GjzyU98iyeitN^G7&JpoVZLt0+skO-b<&+LEaLz}oT-AQ=XoWm z7>%#jha`LKV9J+68Osu<1dcw4!@W#ru~B}9~X>X)^$SmMP|~YXW4Ty@60uhz91cQk@a>X4Jc?TQr^R)v&WOuGtcYR(}L}A zqOi3(0@i(z7M-;1W_uw#Q#-Ly$Hl)UMn2Rzun|#0^D#yP zivjx7o>bn_qonsu0~T{W7Z2D(7~u@%Le1f|Cn&eWYY^FL9ksoatFF8_SiJFyl5Zii zN8uayw5=={H|hJ#1m8gBmr|7ze0_+)&6 z?i15Y3F0aVCrQhHOY1UTkOt+j2n!DT;=1!fFHv3QOQCixf#lb+9ImipLG^LMs|zU5 zqE`NH8=FU%)7Y4$`7v#B>@b?F?ec2IV1?s6S+I>Qq`2dQZ(i(()Z|w}HRZU(O>9xcF_T7(rdhK-PN)u-f ze&}JyYbsHwiaSQbaXN?TT<)zUELn?X4D%tYP%5vAr;~gyhJ#oI08EgU0J9zv3GG0v zFEN5$DKS|f$hygeTH#FdVojuK@hjI-)dIfN$(nYJY^Oxa6{6%;h90hlhb^0Fmmfo@ z{?*(gr`bGJtpJ~xo7OWvKi5x)aK`z@-P{EV=QnPSvb0^YuS{TOIPSX%?sDc-jO+?= z@{#O%&bY2IKVhHr4e8|ZuB1Xqb+@IX^mCZgPcbOCJ=Gj_9WKp96TAr>_;kPFBY%OF zs=)sMQ8^`HB2K3wY%Os|O_LJEOtDuqE3rQCgAWX4PdCl$8Vcv?d)w=4G+-#LzEtc5sYVt4(X)H zf&?rlN6nXYgrMGI6kv{vaj6J(=3WYbH-I8^J&HCiqEK=DsLSDsrCHzdzVZZZEB|7Q zugpWW9%TsRl$uu?@NHQiV;XcR+yAYnofvV3B7u|49FLUkF-Co@)KC1r_Afdo-6w#H zPt?(&FrIg<^IC%vNw5kmoRxje@tO~zWAQ*-xIP@}990hP+}|5JNAmJzowY~Lyr{wE zjDLnfbsw+g!<1nQNz7_mI1Xsp-xzG#A=!}lErt+b_6tLXTyzXul+Vf`G$QccGrLQt#J*s?d)d*< zYP4{bUBMiz+qa`VS4nx`BqiJdhf<%gHJ{vRg7cn^PlFzkD}>%uW~9olJWC3VOSp7k z_lDz3N#89$HkzKTwu?mymtIdAZ&eIzVG(F76PT8?ZZ6w1Gq{%1*nEug9IiKzt5gvbrKZ&hW6UsV+o^q#o!n!;-UKn+zCc_)>Q3tGPj z$0Besv3CU-Vi4<>%x!GhgdP{x>0kLf0f=z9AJvmkjyH9g587t6-?d%KiUn98Mfbs!*XFS3_O8 z?HDZ=lBjl!n=9*U8emt6mwFq#Pkt!tV<5HU@x zhQO8hzyHr+m-b-_DRBfhK03+Ziryq?QKk~TOcxM9t0&g$QsQN;#N1C&zAE=oVA7Qr z(I*XJeJ z1lM%oV;=hi_zlcLnjWQCkxl7WrO6CdHJzc1KG?sJnWY3H;zqK4aEom)b$LyBmt2=p zQDYJSkG{Lw&K5fE7=JZpyP_6u!+bhR^q zDF}fmQYz!mnI8RV2h-|8yW<}^)r|gvM3VHDhu@W-+8K)Ec z@rl6U`*%P{$M?rpdEfv2UXt{0|K+QBTlTj@Vci!4{Bfmc_#>&~!;0p=>L^fXsytfS zcpR+6IKUSNq@b3I)}2x4Xo|BTE<2r9xgz!UvpIkk*Q+%{F76~IW@U^w!J3C9JH27h zoP}n|v(CfAnP`M&t}#yM>HWnnD2JbSGi@m(aRn>DNB!o1%o3J44~5###4Q#Y=cKZ} zB9g{myq(c-tx!Cu1%2t-eCIp>~6l!DSEv@j4mc^yx=gu z=yCw%F4V`==3>!jY}`$(dk+-a+lZk*JS&|vzN#8Ol_fO1D^t5R*o!(4_#uPga#nOo<{fq zWR!E2x{e0Os7vZOuZ8gT_%D(@ge0?)?BG(>(F08LEeJ@~ym~@61ttlk$s?o;(8uUDsge&siMi6(&AS zIPlKZoSKLDa0Xx*lT3_WC8BGaZ+pS#>`AxEdICcYIL@+6KhsDJ;i4)wTFY&BFo&Rd6LeDcZ_nMODv9>$Aa#O zzz`f84@$h;BmImYPF!xia8Yb=o{+F_sW01t%AdZAF}VyYYEqy$QfEHPhLFLeN#{$Z z45d#0flLBZDyYs@!Y(L;aK~4I&H;y(v^Q+NIq&{-f#U0J5S8+#3mQU@$1XV*$+Zfa zLFak4#Dzz&<}QEFw(J*FU=p*IyK07>adL?an_}VhsDumuSy(@92}l z8&^Onfr*VOE;$o+irBp&wu`>DeN!u|=>|fO-+{i5e17xrj^{j%4)#jNb%O0LRqK~J zUS88PSxDGQ(hS z(fDQK6+=Z44>`(_=%qje+`edgJ_erL4lD3BUU(||1JRAIq=!rX0CX(Xpx6vDYVbyY z$eH3ES4qG~mbg_N8ICaMKxuFWZ=e8bd5a|o3x`F%OmzkAxx1cKVLbq#niGI(d+rLL znmx6*#~2=3jwxx@mMct8au<4CeTrh0*m&5*tZM7kJV@QMLcP-zHrJ~cCZBLHdv$Eb zr?kE*aGpjp5!YbM#fb7eIU&gY2cUCJ%ZETDT)O5c^(fgYxui^7$)ktSVZb-iFirT6r$txOc%b&;-#;w_sXU&&GPzk)U$UN3CG=?8r;nh zQT^{tCG6BYIQSdHVb?q)KFDZFW~izz1yWc6C3lwMzt$A z%%D9F0m?JW-9&k6D-lij(hlLBHv@0r-13#GYStswVF8}-H5*fU|0F|SEu!PzIyBek zNglYAE=z%iWZt@aw&`(-6LDdetN3=v-vY#$^3+@LUR|!N)=A3P`SHuR?`9o3Rff-F z9p(xQeR8xNc-1gyinBh4)~xFd%x$uwOkzcy4Ox~Q1sfeo@-(OU)ah;fp-kQ0%1q7M^ZRp3#GMJvL5W>x3ldvHr=GKlMKWI~{>i2)%*#ZU-(a z3i-6RkMsvuyN)2SXYn)U2Xv%foWji>te8`{nx}7Fw9QwI-ZOb0I=tMSsuQ>9u9)t7 zi@WOs`lOij`;GYd1uc0BL$+Sc#d)GzRzt4-tcy@NKzqhlFXT0AQbga@pcLwr=5UQT*XHZ7njx!%%9A9br#rU36yz6Te$C$E25sj}$Oc)=TT zC3WUW3vv%2N`b@=##hBM@`S`Y&rQp}!3Mqt))9aMxTU_NZNoK5^;kz!&65)&q=5dY zjW4cNA9MLyMTd3g_$w7j@^V4qiZ;dnRQv{dO{sFa`iD2_)lvK9*!A>)ZoAVne+%An z&NJ!hXh}!L{VWSmtc*>cz-1&UjVwCUgp^dgCyktufJaI Zx=^F6)U;D#kgwobn1RXpl7Ad-{SS_W(YpWu literal 0 HcmV?d00001 diff --git a/docs/reference/eacf.html b/docs/reference/eacf.html new file mode 100644 index 0000000..7ae19a8 --- /dev/null +++ b/docs/reference/eacf.html @@ -0,0 +1,235 @@ + +Compute the empirical autocovariance — eacf • spmodel + + +

+
+ + + +
+
+
+

Compute the empirical autocovariance

+ Source: R/eacf.R + +
+ +
+

Compute the empirical autocovariance (i.e., empirical covariance) +for varying bin sizes and cutoff values.

+
+ +
+ 
eacf(
+  formula,
+  data,
+  xcoord,
+  ycoord,
+  cloud = FALSE,
+  bins = 15,
+  cutoff,
+  dist_matrix,
+  partition_factor
+)
+
+# S3 method for eacf
+plot(x, ...)
+
+ +
+

Arguments

+
formula
+

A formula describing the fixed effect structure.

+ + +
data
+

A data frame or sf object containing the variables in formula +and geographic information.

+ + +
xcoord
+

Name of the variable in data representing the x-coordinate. +Can be quoted or unquoted. Not required if data is an sf object.

+ + +
ycoord
+

Name of the variable in data representing the y-coordinate. +Can be quoted or unquoted. Not required if data is an sf object.

+ + +
cloud
+

A logical indicating whether the empirical autocovariance should +be summarized by distance class or not. When cloud = FALSE (the default), pairwise autocovariances +are binned and averaged within distance classes. When cloud = TRUE, +all pairwise autocovariances and distances are returned (this is known as +the "cloud" autocovariance).

+ + +
bins
+

The number of equally spaced bins. The default is 15. Ignored if +cloud = TRUE.

+ + +
cutoff
+

The maximum distance considered. +The default is half the diagonal of the bounding box from the coordinates.

+ + +
dist_matrix
+

A distance matrix to be used instead of providing coordinate names.

+ + +
partition_factor
+

An optional formula specifying the partition factor. +If specified, autocovariances are only computed for observations sharing the +same level of the partition factor.

+ + +
x
+

An object from eacf().

+ + +
...
+

Other arguments passed to other methods.

+ +
+
+

Value

+ + +

If cloud = FALSE, a tibble (data.frame) with distance bins +(bins), the average distance (dist), the average autocovariance (acov), and the +number of (unique) pairs (np). If cloud = TRUE, a tibble +(data.frame) with distance (dist) and autocovariance (acov) +for each unique pair.

+
+
+

Details

+

The empirical autocovariance (i.e., empirical covariance) is a tool used to visualize and model +spatial dependence by estimating the semivariance of a process at varying distances. +For a constant-mean process, the +autocovariance at distance \(h\) is denoted \(Cov(h)\) and defined as +\(Cov(z1, z2)\). Under second-order stationarity, +\(Cov(h) = Cov(0) - \gamma(h)\), where \(gamma(h)\) is the semivariance function at distance h. Typically the residuals from an ordinary +least squares fit defined by formula are second-order stationary with +mean zero. These residuals are used to compute the empirical autocovariance +At a distance h, the empirical autocovariance is +\(1/N(h) \sum (r1 \times r2)\), where \(N(h)\) is the number of (unique) +pairs in the set of observations whose distance separation is h and +r1 and r2 are residuals corresponding to observations whose +distance separation is h. In spmodel, these distance bins actually +contain observations whose distance separation is h +- c, +where c is a constant determined implicitly by bins. Typically, +only observations whose distance separation is below some cutoff are used +to compute the empirical semivariogram (this cutoff is determined by cutoff).

+
+ +
+

Examples

+ 
eacf(sulfate ~ 1, sulfate)
+#> # A tibble: 15 × 4
+#>    bins                    dist   acov    np
+#>  * <fct>                  <dbl>  <dbl> <dbl>
+#>  1 (0,1.5e+05]          103340.  93.2    149
+#>  2 (1.5e+05,3.01e+05]   232014.  86.4    456
+#>  3 (3.01e+05,4.51e+05]  379255.  75.7    749
+#>  4 (4.51e+05,6.02e+05]  529543.  70.0    887
+#>  5 (6.02e+05,7.52e+05]  677949.  62.3    918
+#>  6 (7.52e+05,9.03e+05]  826917.  54.8   1113
+#>  7 (9.03e+05,1.05e+06]  978773.  47.6   1161
+#>  8 (1.05e+06,1.2e+06]  1127232.  35.0   1230
+#>  9 (1.2e+06,1.35e+06]  1275415.  24.8   1239
+#> 10 (1.35e+06,1.5e+06]  1429184.   8.00  1236
+#> 11 (1.5e+06,1.65e+06]  1577636.  -2.08  1139
+#> 12 (1.65e+06,1.81e+06] 1729098. -15.3   1047
+#> 13 (1.81e+06,1.96e+06] 1879679. -22.2    934
+#> 14 (1.96e+06,2.11e+06] 2029566. -32.9    842
+#> 15 (2.11e+06,2.26e+06] 2181337. -39.8    788
+plot(eacf(sulfate ~ 1, sulfate))
+
+
+
+
+ +
+ + +
+

Developed by Michael Dumelle, Matt Higham, Jay M. Ver Hoef.

+
+ +
+

Site built with pkgdown 2.0.9.

+
+ +
+ + + + + + + + diff --git a/docs/reference/esv.html b/docs/reference/esv.html index e4e34e7..51d5fa8 100644 --- a/docs/reference/esv.html +++ b/docs/reference/esv.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/fc_borders.html b/docs/reference/fc_borders.html index 43c5fa1..5a8156d 100644 --- a/docs/reference/fc_borders.html +++ b/docs/reference/fc_borders.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/fitted.spmodel.html b/docs/reference/fitted.spmodel.html index 2c90930..d9d9f37 100644 --- a/docs/reference/fitted.spmodel.html +++ b/docs/reference/fitted.spmodel.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/formula.spmodel.html b/docs/reference/formula.spmodel.html index 92fcfbc..8ee0fd7 100644 --- a/docs/reference/formula.spmodel.html +++ b/docs/reference/formula.spmodel.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 @@ -116,7 +116,7 @@

Examples

) formula(spmod) #> z ~ water + tarp -#> <environment: 0x000002c75df7bab0> +#> <environment: 0x000002225f416500> diff --git a/docs/reference/glance.spmodel.html b/docs/reference/glance.spmodel.html index c089e68..20d613d 100644 --- a/docs/reference/glance.spmodel.html +++ b/docs/reference/glance.spmodel.html @@ -21,7 +21,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/glances.html b/docs/reference/glances.html index df7dde1..8619038 100644 --- a/docs/reference/glances.html +++ b/docs/reference/glances.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/hatvalues.spmodel.html b/docs/reference/hatvalues.spmodel.html index 43127a7..58d0abc 100644 --- a/docs/reference/hatvalues.spmodel.html +++ b/docs/reference/hatvalues.spmodel.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/index.html b/docs/reference/index.html index 5671733..bda1f76 100644 --- a/docs/reference/index.html +++ b/docs/reference/index.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 @@ -123,6 +123,10 @@

All functions dispersion_params()

Create a dispersion parameter object

+ +

eacf() plot(<eacf>)

+ +

Compute the empirical autocovariance

esv() plot(<esv>)

diff --git a/docs/reference/influence.spmodel.html b/docs/reference/influence.spmodel.html index 5cc82d0..aee4af7 100644 --- a/docs/reference/influence.spmodel.html +++ b/docs/reference/influence.spmodel.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/labels.spmodel.html b/docs/reference/labels.spmodel.html index 72a812c..9622c91 100644 --- a/docs/reference/labels.spmodel.html +++ b/docs/reference/labels.spmodel.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/lake.html b/docs/reference/lake.html index ac2752c..0333d7c 100644 --- a/docs/reference/lake.html +++ b/docs/reference/lake.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/lake_preds.html b/docs/reference/lake_preds.html index 2565101..d9c155d 100644 --- a/docs/reference/lake_preds.html +++ b/docs/reference/lake_preds.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/logLik.spmodel.html b/docs/reference/logLik.spmodel.html index b241775..c949c09 100644 --- a/docs/reference/logLik.spmodel.html +++ b/docs/reference/logLik.spmodel.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/loocv.html b/docs/reference/loocv.html index deb68f4..018855b 100644 --- a/docs/reference/loocv.html +++ b/docs/reference/loocv.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/model.frame.spmodel.html b/docs/reference/model.frame.spmodel.html index 85afcee..669ca2f 100644 --- a/docs/reference/model.frame.spmodel.html +++ b/docs/reference/model.frame.spmodel.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/model.matrix.spmodel.html b/docs/reference/model.matrix.spmodel.html index cf82917..b7ffc5e 100644 --- a/docs/reference/model.matrix.spmodel.html +++ b/docs/reference/model.matrix.spmodel.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/moose.html b/docs/reference/moose.html index d70fc38..09980fa 100644 --- a/docs/reference/moose.html +++ b/docs/reference/moose.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/moose_preds.html b/docs/reference/moose_preds.html index 510f595..6da6bea 100644 --- a/docs/reference/moose_preds.html +++ b/docs/reference/moose_preds.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/moss.html b/docs/reference/moss.html index 556bc8a..49e36de 100644 --- a/docs/reference/moss.html +++ b/docs/reference/moss.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/plot.spmodel.html b/docs/reference/plot.spmodel.html index af1cd27..5d478d1 100644 --- a/docs/reference/plot.spmodel.html +++ b/docs/reference/plot.spmodel.html @@ -20,7 +20,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/predict.spmodel.html b/docs/reference/predict.spmodel.html index 9f4fb5a..8b55d32 100644 --- a/docs/reference/predict.spmodel.html +++ b/docs/reference/predict.spmodel.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 @@ -326,7 +326,7 @@

Arguments

If block is TRUE, local accepts method and size, and method takes values of "all", "covariance", and "distance", similar as when block is FALSE. -The default method is "distance" with size 1000. This default size is +The default method is "covariance" with size 4000. This default size is much larger than when block is FALSE. This is because when block is TRUE, covariances and explanatory variables are averaged before prediction, which greatly reduces computational burden, only requiring the Cholesky decomposition @@ -418,6 +418,7 @@

Examples

data = sulfate, spcov_type = "exponential", xcoord = x, ycoord = y ) +#> Warning: data is an sf object. Ignoring xcoord and ycoord arguments. predict(spmod, sulfate_preds) #> 1 2 3 4 5 6 7 8 #> 1.618435 24.371803 8.945102 16.452377 4.925139 26.795441 2.869041 14.255129 diff --git a/docs/reference/print.spmodel.html b/docs/reference/print.spmodel.html index 477279f..bc43291 100644 --- a/docs/reference/print.spmodel.html +++ b/docs/reference/print.spmodel.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/pseudoR2.html b/docs/reference/pseudoR2.html index 7878ef7..55b15af 100644 --- a/docs/reference/pseudoR2.html +++ b/docs/reference/pseudoR2.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/randcov_initial.html b/docs/reference/randcov_initial.html index 3e16862..825570a 100644 --- a/docs/reference/randcov_initial.html +++ b/docs/reference/randcov_initial.html @@ -19,7 +19,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/randcov_params.html b/docs/reference/randcov_params.html index a31be6c..fac9303 100644 --- a/docs/reference/randcov_params.html +++ b/docs/reference/randcov_params.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/reexports.html b/docs/reference/reexports.html index 7cd5947..5013573 100644 --- a/docs/reference/reexports.html +++ b/docs/reference/reexports.html @@ -24,7 +24,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/residuals.spmodel.html b/docs/reference/residuals.spmodel.html index 7b2ef26..ee777b8 100644 --- a/docs/reference/residuals.spmodel.html +++ b/docs/reference/residuals.spmodel.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/seal.html b/docs/reference/seal.html index 6b1bdc3..040c751 100644 --- a/docs/reference/seal.html +++ b/docs/reference/seal.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/spautor.html b/docs/reference/spautor.html index e18799a..efdbc8f 100644 --- a/docs/reference/spautor.html +++ b/docs/reference/spautor.html @@ -19,7 +19,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/spautorRF.html b/docs/reference/spautorRF.html index bc1756e..6865515 100644 --- a/docs/reference/spautorRF.html +++ b/docs/reference/spautorRF.html @@ -22,7 +22,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/spcov_initial.html b/docs/reference/spcov_initial.html index bb2b30e..c15dc24 100644 --- a/docs/reference/spcov_initial.html +++ b/docs/reference/spcov_initial.html @@ -19,7 +19,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/spcov_params.html b/docs/reference/spcov_params.html index 2861425..61868ea 100644 --- a/docs/reference/spcov_params.html +++ b/docs/reference/spcov_params.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/spgautor.html b/docs/reference/spgautor.html index d2dc8ae..1666980 100644 --- a/docs/reference/spgautor.html +++ b/docs/reference/spgautor.html @@ -20,7 +20,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/spglm.html b/docs/reference/spglm.html index 8e1a79c..8dd8781 100644 --- a/docs/reference/spglm.html +++ b/docs/reference/spglm.html @@ -20,7 +20,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/splm.html b/docs/reference/splm.html index 1668fe4..ea8aebd 100644 --- a/docs/reference/splm.html +++ b/docs/reference/splm.html @@ -20,7 +20,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/splmRF.html b/docs/reference/splmRF.html index fcbb029..8d938cd 100644 --- a/docs/reference/splmRF.html +++ b/docs/reference/splmRF.html @@ -21,7 +21,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/spmodel-package.html b/docs/reference/spmodel-package.html index 271ac97..417791b 100644 --- a/docs/reference/spmodel-package.html +++ b/docs/reference/spmodel-package.html @@ -19,7 +19,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/sprbeta.html b/docs/reference/sprbeta.html index 264bed6..f8fdb12 100644 --- a/docs/reference/sprbeta.html +++ b/docs/reference/sprbeta.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/sprbinom.html b/docs/reference/sprbinom.html index 624a1b8..8c4283a 100644 --- a/docs/reference/sprbinom.html +++ b/docs/reference/sprbinom.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/sprgamma.html b/docs/reference/sprgamma.html index 6c63bfb..5751aac 100644 --- a/docs/reference/sprgamma.html +++ b/docs/reference/sprgamma.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/sprinvgauss.html b/docs/reference/sprinvgauss.html index d0f655e..c1f4f25 100644 --- a/docs/reference/sprinvgauss.html +++ b/docs/reference/sprinvgauss.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/sprnbinom.html b/docs/reference/sprnbinom.html index e07cb6d..ef7477a 100644 --- a/docs/reference/sprnbinom.html +++ b/docs/reference/sprnbinom.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/sprnorm.html b/docs/reference/sprnorm.html index 04baf31..ac20c4d 100644 --- a/docs/reference/sprnorm.html +++ b/docs/reference/sprnorm.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/sprpois.html b/docs/reference/sprpois.html index a3e2ad2..16cb3af 100644 --- a/docs/reference/sprpois.html +++ b/docs/reference/sprpois.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/sulfate.html b/docs/reference/sulfate.html index d66aec6..5440116 100644 --- a/docs/reference/sulfate.html +++ b/docs/reference/sulfate.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/sulfate_preds.html b/docs/reference/sulfate_preds.html index ddd159e..9c689d4 100644 --- a/docs/reference/sulfate_preds.html +++ b/docs/reference/sulfate_preds.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/summary.spmodel.html b/docs/reference/summary.spmodel.html index 386b313..c701e4c 100644 --- a/docs/reference/summary.spmodel.html +++ b/docs/reference/summary.spmodel.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/texas.html b/docs/reference/texas.html index 824a776..08ecd19 100644 --- a/docs/reference/texas.html +++ b/docs/reference/texas.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/tidy.spmodel.html b/docs/reference/tidy.spmodel.html index ee09ddc..da72f8f 100644 --- a/docs/reference/tidy.spmodel.html +++ b/docs/reference/tidy.spmodel.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/varcomp.html b/docs/reference/varcomp.html index b534aa6..a47cb10 100644 --- a/docs/reference/varcomp.html +++ b/docs/reference/varcomp.html @@ -18,7 +18,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/reference/vcov.spmodel.html b/docs/reference/vcov.spmodel.html index 5c59fa5..229ecb7 100644 --- a/docs/reference/vcov.spmodel.html +++ b/docs/reference/vcov.spmodel.html @@ -17,7 +17,7 @@ spmodel - 0.11.1 + 0.12.0 diff --git a/docs/sitemap.xml b/docs/sitemap.xml index 65fcc2b..0bde21c 100644 --- a/docs/sitemap.xml +++ b/docs/sitemap.xml @@ -117,6 +117,9 @@ https://usepa.github.io/spmodel/reference/dispersion_params.html + + https://usepa.github.io/spmodel/reference/eacf.html + https://usepa.github.io/spmodel/reference/esv.html