Merge pull request #275 from d-morrison/linear.predictor

adding details about fitted/predicted values

Author: d-morrison

.gitignore

@@ -25,3 +25,5 @@ _freeze/
 *.pdf
 rsconnect
 *.md
+
+**/*.quarto_ipynb

DESCRIPTION

@@ -10,6 +10,7 @@ Authors@R:
 Description: Lecture notes for Epi 204 @ UC Davis
 Encoding: UTF-8
 Imports: 
+    arm,
     arsenal,
     cards (>= 0.6.0.9007),
     cardx (>= 0.2.4.9003),

_sec_logistic_score_fn.qmd

@@ -136,11 +136,11 @@ $$
 = \pmat{
 \sumin 1 \eps_i
 \\
-\sumin x_1 \eps_i
+\sumin x_{i,1}\eps_i
 \\
 \vdots
 \\
-\sumin x_p \eps_i
+\sumin x_{i,p} \eps_i
 }
 = \pmat{
 \v1 \cdot \veps

_sec_logreg_in_R.qmd

@@ -1,7 +1,17 @@
 :::{#tbl-beetles-model-grouped}
 
 ```{r}
-#| label: beetles-model-grouped-
+#| label: beetles-model-grouped-tbl
+
+library(glmx)
+library(dplyr)
+data(BeetleMortality)
+beetles <- BeetleMortality |>
+  mutate(
+    pct = died / n,
+    survived = n - died
+  )
+
 beetles_glm_grouped <-
   beetles |>
   glm(
@@ -21,15 +31,68 @@ logistic regression model for beetles data with grouped (binomial) data
 
 ---
 
-Fitted values:
+#### Fitted values
+
+Fitted values are provided on the probability scale (@tbl-beetles-model-fitted-values)
 
 ```{r}
-#| label: beetles-model-fitted-values
-fitted.values(beetles_glm_grouped)
+#| label: tbl-beetles-model-fitted-values
+#| code-fold: show
+
+fitted(beetles_glm_grouped)
 predict(beetles_glm_grouped, type = "response")
+```
+
+---
+
+#### Count scale
+
+For grouped data, 
+we can convert to the count scale by multiplying by the group size:
+
+```{r}
+beetles$n * fitted(beetles_glm_grouped)
+```
+
+---
+
+
+#### Logit scale
+
+```{r}
 predict(beetles_glm_grouped, type = "link")
 
-fit_y <- beetles$n * fitted.values(beetles_glm_grouped)
+```
+
+---
+
+Converting between logit and probability scales works as expected:
+
+```{r}
+predict(beetles_glm_grouped, type = "link") |> arm::invlogit()
+predict(beetles_glm_grouped, type = "response")
+
+predict(beetles_glm_grouped, type = "response") |> arm::logit()
+predict(beetles_glm_grouped, type = "link")
+```
+
+---
+
+`type = "terms"` is confusing, because the variables get centered:
+
+```{r}
+predict(beetles_glm_grouped, type = "terms")
+coef(beetles_glm_grouped)["dose"] * beetles$dose
+```
+
+---
+
+We can construct the link-scale predictions from the terms:
+
+```{r}
+terms_pred <- predict(beetles_glm_grouped, type = "terms")
+terms_pred + attr(terms_pred, "constant")
+predict(beetles_glm_grouped, type = "link")
 ```
 
 ---