Two different ways of calculating "average effects" in conditional logit models

clogit_mes.R

### Purpose of this code: estimate a conditional logit model, and 
### calculate the average effect of changing one non-induced 
### observation in each stratum to an induced observation.

library(survival)
library(marginaleffects)
data("infert")

## Create a subset, and identify a non-induced observation as a
## "focal" observation for which we will later change the value
infert2 <- infert |>
    filter(induced %in% c(0, 1)) |>
    mutate(randno = rnorm(n())) |>
    group_by(stratum) |>
    arrange(induced, randno) |>
    mutate(focal = c(1, rep(0, n() - 1))) |>
    as.data.frame()

## Estimate the model
mod <- mclogit(cbind(case, stratum) ~ spontaneous + induced,
               data = infert2)


## Create a data frame with alternative specifications
altspec <- data.frame(
    low = infert2$induced,
    high = ifelse(infert2$focal, 1, infert2$induced)
)

## Calculate the marginal effect one way
## averaging over values of focal
marg_fx <- comparisons(mod,
                       newdata = infert2,
                       variables = list(induced = altspec),
                       type = "response",
                       by = "focal")


 ##    Term Contrast focal Estimate Std. Error     z Pr(>|z|)   S   2.5 % 97.5 %
 ## induced   custom     0    0.065     0.0211  3.08  0.00206 8.9  0.0237  0.106
 ## induced   custom     1   -0.104     0.0339 -3.08  0.00206 8.9 -0.1707 -0.038

### Now calculate changes in predicted probabilities manually
p1 <- marginaleffects::predictions(mod,
                                   newdata = infert2,
                                   type = "response")

p2 <- marginaleffects::predictions(mod,
                                   newdata = infert2 |>
                                       mutate(induced = ifelse(focal, 1, induced)),
                                   type = "response")

p1 <- p1 |> filter(focal == 1) |> pull(estimate)
p2 <- p2 |> filter(focal == 1) |> pull(estimate)

## This value is much greater than what is shown above
## difference in probabilities of 18 percentage points
## compared to difference of 10 percentage points
mean(p1 - p2)
## [1] -0.1795952