# margeff: Marginal Effects for Several Categorical Response Models In VGAM: Vector Generalized Linear and Additive 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

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

## Arguments

 `object` A `vglm` object, with one of the following family functions: `multinomial`, `cumulative`, `cratio`, `sratio` or `acat`. `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.

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.

`multinomial`, `cumulative`, `propodds`, `acat`, `cratio`, `sratio`, `vglm`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```# Not a good example for multinomial() because the response is ordinal!! ii <- 3; hh <- 1/100 pneumo <- transform(pneumo, let = log(exposure.time)) fit <- vglm(cbind(normal, mild, severe) ~ let, multinomial, data = 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(digits = 3, (newp-fitted(fit)[ii, ])/hh) # Finite-difference approxn round(digits = 3, margeff(fit, subset = ii)["let",]) # Other examples round(digits = 3, margeff(fit)) round(digits = 3, margeff(fit, subset = 2)["let",]) round(digits = 3, margeff(fit, subset = c(FALSE, TRUE))["let",,]) # recycling round(digits = 3, margeff(fit, subset = c(2, 4, 6, 8))["let",,]) ```

### Example output

```Loading required package: stats4
normal       mild     severe
0.84670042 0.08509397 0.06820561
normal       mild     severe
1 0.8432994 0.08682604 0.06987459
normal  mild severe
1  -0.34 0.173  0.167
normal   mild severe
-0.337  0.172  0.165
, , 1

normal   mild severe
(Intercept)  0.058 -0.032 -0.026
let         -0.015  0.009  0.006

, , 2

normal   mild severe
(Intercept)  0.600 -0.312 -0.287
let         -0.161  0.090  0.071

, , 3

normal   mild severe
(Intercept)  1.256 -0.583 -0.673
let         -0.337  0.172  0.165

, , 4

normal   mild severe
(Intercept)  1.840 -0.708 -1.132
let         -0.494  0.216  0.278

, , 5

normal   mild severe
(Intercept)  2.241 -0.625 -1.616
let         -0.601  0.205  0.396

, , 6

normal   mild severe
(Intercept)  2.409 -0.362 -2.047
let         -0.646  0.144  0.502

, , 7

normal  mild severe
(Intercept)  2.377 0.016 -2.392
let         -0.638 0.051  0.587

, , 8

normal   mild severe
(Intercept)  2.239  0.329 -2.568
let         -0.601 -0.029  0.630

normal   mild severe
-0.161  0.090  0.071
2      4      6      8
normal -0.161 -0.494 -0.646 -0.601
mild    0.090  0.216  0.144 -0.029
severe  0.071  0.278  0.502  0.630
2      4      6      8
normal -0.161 -0.494 -0.646 -0.601
mild    0.090  0.216  0.144 -0.029
severe  0.071  0.278  0.502  0.630
```

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.