_sec_hers_lm_diagnostics_lm2.qmd

::: notes
We repeat the same checks for the interaction model
(`hers_lm2`, @eq-hers-interact, fitted in @tbl-hers-lm2).
:::

#### Residuals vs fitted for `hers_lm2`

:::{#fig-hers-resid-fitted-lm2}

```{r}
#| code-fold: true
hers_diag2 <- hers_lm_data |>
  dplyr::mutate(
    .fitted = fitted(hers_lm2),
    .resid = residuals(hers_lm2)
  )

ggplot(hers_diag2, aes(x = .fitted, y = .resid)) +
  geom_point(alpha = 0.3) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  facet_wrap(~statins, labeller = label_both) +
  xlab("Fitted values") +
  ylab("Residuals") +
  theme_bw()
```

Residuals vs fitted values for `hers_lm2` (interaction model)

:::

#### QQ plot for `hers_lm2`

:::{#fig-hers-qq-lm2}

```{r}
#| code-fold: true
ggplot(hers_diag2, aes(sample = .resid)) +
  stat_qq() +
  stat_qq_line() +
  facet_wrap(~statins, labeller = label_both) +
  theme_bw()
```

QQ plot of residuals for `hers_lm2` (interaction model)

:::

::: notes
The residual and QQ plots for the interaction model
(@fig-hers-resid-fitted-lm2, @fig-hers-qq-lm2)
look essentially identical to those for the parallel-planes model:
adding the age-BMI interaction barely changes the residual structure.
This similarity previews the model-selection result ---
the likelihood ratio test (@tbl-hers-lrt) shows the interaction
does not improve the fit enough to justify the extra parameter.
:::