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@@ -737,7 +737,7 @@ <h2><span class="header-section-number">4.4</span> Robust linear
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seed : int(0) </code></pre>
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<pre class="r fold-show"><code>confint(robustLinearRegression)</code></pre>
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<pre><code> 2.5 % 97.5 %
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(Intercept) 0.83801565 1.0499981
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(Intercept) 0.83801566 1.0499981
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bpi_antisocialT1Sum 0.44749135 0.5352118
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bpi_anxiousDepressedSum 0.09683728 0.2184779</code></pre>
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</div>
@@ -758,19 +758,19 @@ <h2><span class="header-section-number">4.5</span> Least trimmed squares
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Residuals (from reweighted LS):
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Min 1Q Median 3Q Max
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-3.9225 -0.8914 0.0000 1.0133 3.9185
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-3.9305 -0.9091 0.0000 0.9997 3.9036
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Coefficients:
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Estimate Std. Error t value Pr(&gt;|t|)
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Intercept 0.74662 0.04796 15.568 &lt; 2e-16 ***
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bpi_antisocialT1Sum 0.54341 0.01525 35.644 &lt; 2e-16 ***
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bpi_anxiousDepressedSum 0.13275 0.02343 5.665 1.62e-08 ***
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Intercept 0.74932 0.04795 15.626 &lt; 2e-16 ***
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bpi_antisocialT1Sum 0.54338 0.01524 35.647 &lt; 2e-16 ***
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bpi_anxiousDepressedSum 0.13826 0.02343 5.901 4.06e-09 ***
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---
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Signif. codes: 0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1
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Residual standard error: 1.535 on 2710 degrees of freedom
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Multiple R-Squared: 0.4103, Adjusted R-squared: 0.4099
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F-statistic: 942.9 on 2 and 2710 DF, p-value: &lt; 2.2e-16 </code></pre>
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Residual standard error: 1.534 on 2710 degrees of freedom
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Multiple R-Squared: 0.4121, Adjusted R-squared: 0.4116
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F-statistic: 949.7 on 2 and 2710 DF, p-value: &lt; 2.2e-16 </code></pre>
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</div>
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<div id="bayesian-linear-regression" class="section level2"
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number="4.6">
@@ -1852,7 +1852,7 @@ <h2><span class="header-section-number">9.4</span> Multiple
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summary(imputedData_pooledEstimates)</code></pre>
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<div data-pagedtable="false">
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<script data-pagedtable-source type="application/json">
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{"columns":[{"label":["term"],"name":[1],"type":["fct"],"align":["left"]},{"label":["estimate"],"name":[2],"type":["dbl"],"align":["right"]},{"label":["std.error"],"name":[3],"type":["dbl"],"align":["right"]},{"label":["statistic"],"name":[4],"type":["dbl"],"align":["right"]},{"label":["df"],"name":[5],"type":["dbl"],"align":["right"]},{"label":["p.value"],"name":[6],"type":["dbl"],"align":["right"]}],"data":[{"1":"(Intercept)","2":"1.2085944","3":"0.23985522","4":"5.038849","5":"4.019869","6":"0.007193186"},{"1":"bpi_antisocialT1Sum","2":"0.4103475","3":"0.06575157","4":"6.240878","5":"4.082337","6":"0.003138072"},{"1":"bpi_anxiousDepressedSum","2":"0.1579709","3":"0.11964843","4":"1.320292","5":"4.027809","6":"0.256766886"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}}
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</script>
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</div>
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</div>
@@ -1918,18 +1918,18 @@ <h2><span class="header-section-number">11.1</span> Linear
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summary(multipleRegressionModelBootstrapped)</code></pre>
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<div data-pagedtable="false">
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<script data-pagedtable-source type="application/json">
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{"columns":[{"label":[""],"name":["_rn_"],"type":[""],"align":["left"]},{"label":["R"],"name":[1],"type":["dbl"],"align":["right"]},{"label":["original"],"name":[2],"type":["dbl"],"align":["right"]},{"label":["bootBias"],"name":[3],"type":["dbl"],"align":["right"]},{"label":["bootSE"],"name":[4],"type":["dbl"],"align":["right"]},{"label":["bootMed"],"name":[5],"type":["dbl"],"align":["right"]}],"data":[{"1":"1000","2":"1.1983004","3":"-0.0020340517","4":"0.06289319","5":"1.1948314","_rn_":"(Intercept)"},{"1":"1000","2":"0.4655286","3":"0.0004412222","4":"0.02285603","5":"0.4658318","_rn_":"bpi_antisocialT1Sum"},{"1":"1000","2":"0.1607541","3":"-0.0010514914","4":"0.03441536","5":"0.1589603","_rn_":"bpi_anxiousDepressedSum"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}}
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{"columns":[{"label":[""],"name":["_rn_"],"type":[""],"align":["left"]},{"label":["R"],"name":[1],"type":["dbl"],"align":["right"]},{"label":["original"],"name":[2],"type":["dbl"],"align":["right"]},{"label":["bootBias"],"name":[3],"type":["dbl"],"align":["right"]},{"label":["bootSE"],"name":[4],"type":["dbl"],"align":["right"]},{"label":["bootMed"],"name":[5],"type":["dbl"],"align":["right"]}],"data":[{"1":"1000","2":"1.1983004","3":"0.0004575619","4":"0.06363654","5":"1.1982745","_rn_":"(Intercept)"},{"1":"1000","2":"0.4655286","3":"-0.0006590173","4":"0.02351387","5":"0.4648464","_rn_":"bpi_antisocialT1Sum"},{"1":"1000","2":"0.1607541","3":"-0.0002804489","4":"0.03434810","5":"0.1610040","_rn_":"bpi_anxiousDepressedSum"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}}
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</script>
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</div>
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<pre class="r fold-show"><code>confint(multipleRegressionModelBootstrapped, level = .95, type = &quot;bca&quot;)</code></pre>
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<pre><code>Warning in confint.boot(multipleRegressionModelBootstrapped, level = 0.95, :
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BCa method fails for this problem. Using &#39;perc&#39; instead</code></pre>
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<pre><code>Bootstrap percent confidence intervals
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2.5 % 97.5 %
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(Intercept) 1.07349576 1.3257446
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bpi_antisocialT1Sum 0.42064620 0.5100082
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bpi_anxiousDepressedSum 0.09548154 0.2289897</code></pre>
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2.5 % 97.5 %
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(Intercept) 1.0699677 1.3253791
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bpi_antisocialT1Sum 0.4167496 0.5120914
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bpi_anxiousDepressedSum 0.0918046 0.2305352</code></pre>
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<pre class="r fold-show"><code>hist(multipleRegressionModelBootstrapped)</code></pre>
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<pre><code>Warning in confint.boot(x, type = ci, level = level): BCa method fails for this
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problem. Using &#39;perc&#39; instead</code></pre>
@@ -1942,7 +1942,7 @@ <h2><span class="header-section-number">11.2</span> Generalized
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summary(generalizedRegressionModelBootstrapped)</code></pre>
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<div data-pagedtable="false">
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<script data-pagedtable-source type="application/json">
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{"columns":[{"label":[""],"name":["_rn_"],"type":[""],"align":["left"]},{"label":["R"],"name":[1],"type":["dbl"],"align":["right"]},{"label":["original"],"name":[2],"type":["dbl"],"align":["right"]},{"label":["bootBias"],"name":[3],"type":["dbl"],"align":["right"]},{"label":["bootSE"],"name":[4],"type":["dbl"],"align":["right"]},{"label":["bootMed"],"name":[5],"type":["dbl"],"align":["right"]}],"data":[{"1":"1000","2":"1.1983004","3":"-0.0013101413","4":"0.06184059","5":"1.1952085","_rn_":"(Intercept)"},{"1":"1000","2":"0.4655286","3":"-0.0002620437","4":"0.02279037","5":"0.4653162","_rn_":"bpi_antisocialT1Sum"},{"1":"1000","2":"0.1607541","3":"0.0007505728","4":"0.03302004","5":"0.1615621","_rn_":"bpi_anxiousDepressedSum"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}}
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{"columns":[{"label":[""],"name":["_rn_"],"type":[""],"align":["left"]},{"label":["R"],"name":[1],"type":["dbl"],"align":["right"]},{"label":["original"],"name":[2],"type":["dbl"],"align":["right"]},{"label":["bootBias"],"name":[3],"type":["dbl"],"align":["right"]},{"label":["bootSE"],"name":[4],"type":["dbl"],"align":["right"]},{"label":["bootMed"],"name":[5],"type":["dbl"],"align":["right"]}],"data":[{"1":"1000","2":"1.1983004","3":"-7.667005e-05","4":"0.06222045","5":"1.1986654","_rn_":"(Intercept)"},{"1":"1000","2":"0.4655286","3":"4.961828e-04","4":"0.02301143","5":"0.4663421","_rn_":"bpi_antisocialT1Sum"},{"1":"1000","2":"0.1607541","3":"-1.325790e-03","4":"0.03235557","5":"0.1599957","_rn_":"bpi_anxiousDepressedSum"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}}
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</script>
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</div>
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<pre class="r fold-show"><code>confint(generalizedRegressionModelBootstrapped, level = .95, type = &quot;bca&quot;)</code></pre>
@@ -1951,9 +1951,9 @@ <h2><span class="header-section-number">11.2</span> Generalized
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<pre><code>Bootstrap percent confidence intervals
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2.5 % 97.5 %
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(Intercept) 1.07498282 1.3214226
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bpi_antisocialT1Sum 0.41859059 0.5075609
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bpi_anxiousDepressedSum 0.09722923 0.2213951</code></pre>
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(Intercept) 1.07299901 1.3194043
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bpi_antisocialT1Sum 0.41889417 0.5117848
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bpi_anxiousDepressedSum 0.09540227 0.2229572</code></pre>
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<pre class="r fold-show"><code>hist(generalizedRegressionModelBootstrapped)</code></pre>
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<pre><code>Warning in confint.boot(x, type = ci, level = level): BCa method fails for this
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problem. Using &#39;perc&#39; instead</code></pre>
@@ -2015,9 +2015,9 @@ <h2><span class="header-section-number">12.1</span> K-fold cross
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<pre><code>
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10-fold CV results:
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Fit CV
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1 OLS 1.980613
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2 MM 1.026745
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3 LTS 1.007103
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1 OLS 1.980924
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2 MM 1.026443
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3 LTS 1.007390
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Best model:
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CV
@@ -3152,7 +3152,7 @@ <h6><span class="header-section-number">14.1.6.2.3.1</span> Robust
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bpi_antisocialT2Sum 1.493955 3.122528
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$msg
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[1] &quot;155 singular samples of size 3 out of 1500&quot;
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[1] &quot;149 singular samples of size 3 out of 1500&quot;
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$crit
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[1] 3.737972
@@ -3289,10 +3289,10 @@ <h6><span class="header-section-number">14.1.6.2.3.1</span> Robust
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bpi_antisocialT2Sum 1.096437 2.482409
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$msg
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[1] &quot;149 singular samples of size 3 out of 1500&quot;
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[1] &quot;126 singular samples of size 3 out of 1500&quot;
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$crit
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[1] -0.3839279
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[1] -0.3817849
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$best
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