secondDiff: Calculate Cross-Derivative and its Variability
In DAMisc: Dave Armstrong's Miscellaneous Functions

Description Usage Arguments Details Value Author(s)

Calculates the cross-derivative required to evaluate interactions in logistic/probit regression models.

secondDiff(
  obj,
  vars,
  data,
  method = c("AME", "MER"),
  vals = NULL,
  typical = NULL
)

`obj`	An object of class `glm` that will be used to find the cross-derivative.
`vars`	A vector of two variables to be used in calculating the derivative.
`data`	A data frame.
`method`	Indicate whether you want to use average marginal effects (AME) or marginal effects at representative values (MER).
`vals`	A named list of length 2 where each element gives the minimum and maximum values used in the calculation.
`typical`	A named vector of values at which to hold variables constant.

The function calculates the second difference as (Pr(Y=1|x1=max, x2=max) - Pr(Y=1|x1=min, x2=max)) - (Pr(Y=1|x1=max, x2=min) - Pr(Y=1|x1=min, x2=min)). The function uses a parametric bootstrap to calculate the sampling distribution of the second difference.

A list with two elements:

`ave`	The average second difference in each iteration of the bootstrap.
`ind`	If `type == 'AME'`, `ind` is returned with the second difference and measures of uncertainty for each individual observation in the original dataset
`probs`	If `type == 'MER'`, `probs` is returned with the full matrix of simulated predicted probabilities for the four conditions.