---
title: "second.diff.fitted"
output: rmarkdown::html_vignette
description: >
  This vignette explains the rationale and implementation for the second.diff.fitted function.
vignette: >
  %\VignetteIndexEntry{second.diff.fitted}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

Computes the second difference in fitted values from an estimated regression model. Inference in supported via the delta method or bootstrapping.


For example:
```{r}
library(catregs)
data("Mize19AH")
m1 <- glm(alcB ~woman*parrole + age + race2 + race3 + race4 + income + ed1 + ed2 + ed3 + ed4,family="binomial",data=Mize19AH)
des2<-margins.des(m1,expand.grid(woman=c(0,1),parrole=c(0,1)))
des2
second.diff.fitted(m1,des2,compare=c(4,2,3,1),rounded=5) # [Pr(Drink | Mothers) - Pr(Drink | Childless Women)] - [Pr(Drink | Fathers) - Pr(Drink | Childless Men)]
# Note that this is reported as the "Second Difference" in Table 3 of Mize (2019: 104, "Best Practices for Estimating, Interpreting, and Presenting Nonlinear Interaction Effect. Sociological Science. 6(4): 81-117.")
```