edits to Ch10

10-mlm-review.qmd

@@ -955,13 +955,15 @@ group minus the average of the other two, which is negative on `caring` and `emo
 `group2` is the difference in means for the physical vs. mental groups.
 
 Before doing multivariate tests, it is useful to see what would happen if we ran univariate ANOVAs on each
-of the responses. These can be extracted from an MLM using `stats::summary.aov()`:
+of the responses. These can be extracted from an MLM using `stats::summary.aov()` and they give tests
+of the model terms for each response variable separately:
 
 ```{r parenting-summary-aov}
 summary.aov(parenting.mlm)
 ```
-If you like, you can also extract the univariate model fit statistics from the `"mlm"` object using the
-`broom::glance()` method for a multivariate model object.
+For a more condensed summary, you can instead extract the univariate model fit statistics from the `"mlm"` object using the
+`heplots::glance()` method for a multivariate model object. The code below selects just the $R^2$ and
+$F$-statistic for the overall model for each response, together with the associated $p$-value.
 
 ```{r}
 glance(parenting.mlm) |>
@@ -1084,7 +1086,7 @@ or, expressed in terms of the variables,
 
 
 \begin{eqnarray*}
-\begin{bmatrix} y_{\text{anx}} \\y_{\text{dep}} \end{bmatrix} & = &
+\begin{bmatrix} y_{\text{anx}} \\y_{\text{dep}} \end{bmatrix} & = 
 \begin{bmatrix} \beta_{0,\text{anx}} \\ \beta_{0,\text{dep}} \end{bmatrix} +
 \begin{bmatrix} \beta_{1,\text{anx}} \\ \beta_{1,\text{dep}} \end{bmatrix} \text{grade} +
 \begin{bmatrix} \beta_{2,\text{anx}} \\ \beta_{2,\text{dep}} \end{bmatrix} \text{grade}^2 \\
@@ -1101,11 +1103,7 @@ Some exploratory analysis is useful before fitting and visualizing models.
 As a first step, we find the means, standard deviations, and standard errors of the means.
 
 ```{r addhealth-means}
-#| code-fold: true
-#| code-summary: Show the code
-library(ggplot2)
-library(dplyr)
-
+#| code-fold: false
 means <- AddHealth |>
   group_by(grade) |>
   summarise(
@@ -1171,7 +1169,7 @@ Now, let's fit the MLM for both responses jointly in relation to `grade`. The nu
 $$
 \HO : \mathbf{\mu}_7 = \mathbf{\mu}_8 = \cdots = \mathbf{\mu}_{12} \; ,
 $$
-or equivalently, that all coefficients except the intercept in the model \@ref(eq:AH-mod) are zero,
+or equivalently, that all coefficients except the intercept in the model @eq-AH-mod are zero,
 $$
 \HO : \boldsymbol{\beta}_1 =  \boldsymbol{\beta}_2  = \cdots =  \boldsymbol{\beta}_5 = \boldsymbol{0} \; .
 $$