margeff: Marginal Effects for Several Categorical Response Models

In VGAM: Vector Generalized Linear and Additive Models

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

object	A vglm object, with one of the following family functions: multinomial, cumulative, cratio, sratio, acat, poissonff, negbinomial or posnegbinomial.
subset	Numerical or logical vector, denoting the required observation(s). Recycling is used if possible. The default means all observations.
...	further arguments passed into the other methods functions.

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.

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.

Warning

Care is needed in interpretation, e.g., the change is not universally accurate for a unit change in each explanatory variable because eventually the ‘new’ probabilities may become negative or greater than unity. Also, the ‘new’ probabilities will not sum to one.

This function is not applicable for models with data-dependent terms such as bs and poly. Also the function should not be applied to models with any terms that have generated more than one column of the LM model matrix, such as bs and poly. For such try using numerical methods such as finite-differences. The formula in object should comprise of simple terms of the form ~ x2 + x3 + x4, etc.

Some numerical problems may occur if the fitted values are close to 0 or 1 for the cratio and sratio models. Models with offsets may result in an incorrect answer.

Note

For multinomial this function should handle any value of refLevel and also any constraint matrices. However, it does not currently handle the xij or form2 arguments, nor vgam objects.

If marginal effects are to be computed for some values not equal to those used in the training set, then the @x and the @predictors slots both need to be assigned. See Example 3 below.

Some other limitations are imposed, e.g., for acat models only a loglink link is allowed.

Author(s)

T. W. Yee, with some help and motivation from Stasha Rmandic.

See Also

multinomial, cumulative, propodds, acat, cratio, sratio, poissonff, negbinomial, vglm.

Examples

# 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

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.