margeff: Marginal Effects for Several Categorical Response Models

Description

Marginal effects for the multinomial logit model and cumulative logit/probit/... models and continuation ratio models and stopping ratio models and adjacent categories models: the derivative of the fitted probabilities with respect to each explanatory variable.

Usage

margeff(object, subset = NULL, ...)

Arguments

Value

A \(p\) by \(M+1\) by \(n\) array, where \(p\) is the number of explanatory variables and the (hopefully) nominal response has \(M+1\) levels, and there are \(n\)

observations.

In general, if

is.numeric(subset)

and

length(subset) == 1 then a

\(p\) by \(M+1\) matrix is returned.

Details

Computes the derivative of the fitted probabilities of the categorical response model with respect to each explanatory variable. Formerly one big function, this function now uses S4 dispatch to break up the computations.

The function margeff() is not generic. However, it calls the function margeffS4VGAM() which is. This is based on the class of the VGAMff argument, and it uses the S4 function setMethod to correctly dispatch to the required methods function. The inheritance is given by the vfamily slot of the VGAM family function.

Examples

Run this code

# Not a good example for multinomial() since the response is ordinal!!
ii <- 3; hh <- 1/100
pneumo <- transform(pneumo, let = log(exposure.time))
fit <- vglm(cbind(normal, mild, severe) ~ let, multinomial, pneumo)
fit <- vglm(cbind(normal, mild, severe) ~ let,
            cumulative(reverse = TRUE,  parallel = TRUE),
            data = pneumo)
fitted(fit)[ii, ]

mynewdata <- with(pneumo, data.frame(let = let[ii] + hh))
(newp <- predict(fit, newdata = mynewdata, type = "response"))

# Compare the difference. Should be the same as hh --> 0.
round((newp-fitted(fit)[ii, ]) / hh, 3)  # Finite-diff approxn
round(margeff(fit, subset = ii)["let",], 3)

# Other examples
round(margeff(fit), 3)
round(margeff(fit, subset = 2)["let",], 3)
round(margeff(fit, subset = c(FALSE, TRUE))["let",,], 3)  # Recycling
round(margeff(fit, subset = c(2, 4, 6, 8))["let",,], 3)

# Example 3; margeffs at a new value
mynewdata2a <- data.frame(let = 2)  # New value
mynewdata2b <- data.frame(let = 2 + hh)  # For finite-diff approxn
(neweta2 <- predict(fit, newdata = mynewdata2a))
fit@x[1, ] <- c(1, unlist(mynewdata2a))
fit@predictors[1, ] <- neweta2  # Needed
max(abs(margeff(fit, subset = 1)["let", ] - (
        predict(fit, newdata = mynewdata2b, type = "response") -
        predict(fit, newdata = mynewdata2a, type = "response")) / hh
))  # Should be 0