tweaks to Ch10 contrasts

10-mlm-review.qmd

@@ -586,10 +586,12 @@ the following comparisons among the formulas Old, New, Major and Alps:
 (c) Major vs. Alps. The contrasts that do this are:
 
 \begin{align*}
-L_1 & = \frac12 (\mu_O + \mu_N) - \frac12 (\mu_M + \mu_A) & \rightarrow\: & \mathbf{c}_1 = 
-\frac12 \begin{pmatrix} 
-         1 &  1 & -1 & -1 
-        \end{pmatrix} \\
+L_1 & = \textstyle{\frac12} (\mu_O + \mu_N) - 
+        \textstyle{\frac12} (\mu_M + \mu_A) & \rightarrow\: & \mathbf{c}_1 = 
+\textstyle{\frac12} 
+     \begin{pmatrix} 
+      1 &  1 & -1 & -1 
+     \end{pmatrix} \\
 L_2 & = \mu_O - \mu_N                     & \rightarrow\: & \mathbf{c}_2 = 
     \begin{pmatrix} 
      1 &  -1 & 0 & 0 
@@ -622,18 +624,21 @@ C
 t(C) %*% C
 ```
 
-For a dataset, `data`, with this factor as `group`, you can set up the analyses to use these
-contrasts by assigning the matrix `C` to `contrasts()`. When the contrasts are changed,
+For the `dogfood` data, with `formula` as the group factor,
+you can set up the analyses to use these
+contrasts by assigning the matrix `C` to `contrasts()` for that factor in the dataset itself.
+When the contrasts are changed,
 it is necessary to refit the model. The estimated coefficients then become the estimated
-mean differences of the contrasts.
+mean differences for the contrasts.
 
 ```{r dogfood-contrasts}
 contrasts(dogfood$formula) <- C
 dogfood.mod <- lm(cbind(start, amount) ~ formula, 
                   data=dogfood)
 coef(dogfood.mod)
 ```
-
+For example, Ours vs. Theirs estimated by `formulac1` takes 0.69 less time to start eating
+and eats 5.44 more on average.
 
 For multivariate tests, when all contrasts are pairwise orthogonal,
 the overall test of a factor with
@@ -668,15 +673,15 @@ Then, we can illustrate @eq-H-contrasts by extracting the 1 df $\mathbf{H}$  mat
 from the results of `linearHypothesis`.
 
 <!-- this doesn't work -->
-```{r dogfood-Eqn, results='asis', eval=FALSE, echo=FALSE}
+```{r dogfood-Eqn, results='asis'}
 options(print.latexMatrix = list(display.labels=FALSE))
 SSP_H1 <- H1$SSPH |> round(digits=2)
 SSP_H2 <- H2$SSPH |> round(digits=2)
 SSP_H3 <- H3$SSPH |> round(digits=2)
-Eqn(latexMatrix(SSP_H), "=", 
+Eqn(latexMatrix(SSP_H),  "=", 
     latexMatrix(SSP_H1), "+", 
     latexMatrix(SSP_H2), "+", 
-    latexMatrix(SSP_H3))
+    latexMatrix(SSP_H3), quarto=TRUE)
 ```
 
 $$

docs/08-collinearity-ridge.html

@@ -1026,7 +1026,7 @@ <h1 class="title"><span id="sec-collin" class="quarto-section-identifier"><span
 <p>There is a close connection with principal components regression mentioned in <a href="#sec-remedies" class="quarto-xref"><span>Section 8.3</span></a>. Ridge regression shrinks <em>all</em> dimensions in proportion to <span class="math inline">\(\text{df}_k(i)\)</span>, so the low variance dimensions are shrunk more. Principal components regression discards the low variance dimensions and leaves the high variance dimensions unchanged.</p>
 </section><section id="the-genridge-package" class="level3" data-number="8.4.2"><h3 data-number="8.4.2" class="anchored" data-anchor-id="the-genridge-package">
 <span class="header-section-number">8.4.2</span> The <code>genridge</code> package</h3>
-<p>Ridge regression and other shrinkage methods are available in several packages including <span style="color: brown;"><strong>MASS</strong></span> (the <code><a href="https://rdrr.io/pkg/MASS/man/lm.ridge.html">lm.ridge()</a></code> function), <span style="color: brown;"><strong>glmnet</strong></span> <span class="citation" data-cites="R-glmnet">(<a href="95-references.html#ref-R-glmnet" role="doc-biblioref">Friedman et al., 2023</a>)</span>, and <span style="color: brown;"><strong>penalized</strong></span> <span class="citation" data-cites="R-penalized">(<a href="95-references.html#ref-R-penalized" role="doc-biblioref"><strong>R-penalized?</strong></a>)</span>, but none of these provides insightful graphical displays. <code><a href="https://glmnet.stanford.edu/reference/glmnet.html">glmnet::glmnet()</a></code> also implements a method for multivariate responses with a `family=“mgaussian”.</p>
+<p>Ridge regression and other shrinkage methods are available in several packages including <span style="color: brown;"><strong>MASS</strong></span> (the <code><a href="https://rdrr.io/pkg/MASS/man/lm.ridge.html">lm.ridge()</a></code> function), <span style="color: brown;"><strong>glmnet</strong></span> <span class="citation" data-cites="R-glmnet">(<a href="95-references.html#ref-R-glmnet" role="doc-biblioref">Friedman et al., 2023</a>)</span>, and <span style="color: brown;"><strong>penalized</strong></span> <span class="citation" data-cites="R-penalized">(<a href="95-references.html#ref-R-penalized" role="doc-biblioref">Goeman et al., 2022</a>)</span>, but none of these provides insightful graphical displays. <code><a href="https://glmnet.stanford.edu/reference/glmnet.html">glmnet::glmnet()</a></code> also implements a method for multivariate responses with a `family=“mgaussian”.</p>
 <p>Here, I focus in the <span style="color: brown;"><strong>genridge</strong></span> package <span class="citation" data-cites="R-genridge">(<a href="95-references.html#ref-R-genridge" role="doc-biblioref">Friendly, 2024</a>)</span>, where the <code><a href="https://friendly.github.io/genridge/reference/ridge.html">ridge()</a></code> function is the workhorse and <code>pca.ridge()</code> transforms these results to PCA/SVD space. <code>vif.ridge()</code> calculates VIFs for class <code>"ridge"</code> objects and <code><a href="https://friendly.github.io/genridge/reference/precision.html">precision()</a></code> calculates precision and shrinkage measures.</p>
 <p>A variety of plotting functions is available for univariate, bivariate and 3D plots:</p>
 <ul>
@@ -1382,6 +1382,9 @@ <h1 class="title"><span id="sec-collin" class="quarto-section-identifier"><span
 <div id="ref-Gabriel:71" class="csl-entry" role="listitem">
 Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal components analysis. <em>Biometrics</em>, <em>58</em>(3), 453–467. <a href="https://doi.org/10.2307/2334381">https://doi.org/10.2307/2334381</a>
 </div>
+<div id="ref-R-penalized" class="csl-entry" role="listitem">
+Goeman, J., Meijer, R., Chaturvedi, N., &amp; Lueder, M. (2022). <em>Penalized: L1 (lasso and fused lasso) and L2 (ridge) penalized estimation in GLMs and in the cox model</em>. <a href="https://CRAN.R-project.org/package=penalized">https://CRAN.R-project.org/package=penalized</a>
+</div>
 <div id="ref-GowerHand:96" class="csl-entry" role="listitem">
 Gower, J. C., &amp; Hand, D. J. (1996). <em>Biplots</em>. Chapman &amp; Hall.
 </div>