R: Analysis of Deviance for Vector Generalized Linear Model Fits

anova.vglm {VGAM} | R Documentation

## Analysis of Deviance for Vector Generalized Linear Model Fits

### Description

Compute an analysis of deviance table for one or more vector generalized linear model fits.

### Usage

    ## S3 method for class 'vglm'
    anova(object, ..., type = c("II", "I", "III", 2, 1, 3),
         test = c("LRT", "none"), trydev = TRUE, silent = TRUE)

### Arguments

`object, ...` | objects of class `vglm`, typically the result of a call to `vglm`, or a list of `objects` for the `"vglmlist"` method. Each model must have an intercept term. If `"vglmlist"` is used then `type = 1` or `type = "I"` must be specified.

`type` | character or numeric; any one of the (effectively three) choices given. Note that `anova.glm` has `1` or `"I"` as its default; and that `Anova.glm` has `2` or `"II"` as its default (and allows for `type = "III"`), so one can think of this function as a combination of `anova.glm` and `Anova.glm`, but with the default of the latter. See Details below for more information.
`test` | a character string, (partially) matching one of `"LRT"` and `"none"`. In the future it is hoped that `"Rao"` be also supported, to conduct score tests. The first value is the default.
`trydev` | logical; if `TRUE` then the deviance is used if possible. Note that only a few VGAM family functions have a deviance that is defined and implemented. Setting it `FALSE` means the log-likelihood will be used.
`silent` | logical; if `TRUE` then any warnings will be suppressed. These may arise by IRLS iterations not converging during the fitting of submodels. Setting it `FALSE` means that any warnings are given.

### Details

`anova.vglm` is intended to be similar to `anova.glm` so specifying a single object and `type = 1` gives a sequential analysis of deviance table for that fit. By analysis of deviance, it is meant loosely that if the deviance of the model is not defined or implemented, then twice the difference between the log-likelihoods of two nested models remains asymptotically chi-squared distributed with degrees of freedom equal to the difference in the number of parameters of the two models. Of course, the usual regularity conditions are assumed to hold. For Type I, the analysis of deviance table has the reductions in the residual deviance as each term of the formula is added in turn are given in as the rows of a table, plus the residual deviances themselves. Type I or sequential tests (as in `anova.glm`). are computationally the easiest of the three methods. For this, the order of the terms is important, and the each term is added sequentially from first to last.

The `Anova()` function in car allows for testing Type II and Type III (SAS jargon) hypothesis tests, although the definitions used are not precisely that of SAS. As car notes, Type I rarely test interesting hypotheses in unbalanced designs. Type III enter each term last, keeping all the other terms in the model. Type II tests, according to SAS, add the term after all other terms have been added to the model except terms that contain the effect being tested; an effect is contained in another effect if it can be derived by deleting variables from the latter effect. Type II tests are currently the default.

As in `anova.glm`, but not as `Anova.glm`, if more than one object is specified, then the table has a row for the residual degrees of freedom and deviance for each model. For all but the first model, the change in degrees of freedom and deviance is also given. (This only makes statistical sense if the models are nested.) It is conventional to list the models from smallest to largest, but this is up to the user. It is necessary to have `type = 1` with more than one objects are specified.

See `anova.glm` for more details and warnings. The VGAM package now implements full likelihood models only, therefore no dispersion parameters are estimated.

### Value

An object of class `"anova"` inheriting from class `"data.frame"`.

### Warning

See `anova.glm`. Several VGAM family functions implement distributions which do not satisfying the usual regularity conditions needed for the LRT to work. No checking or warning is given for these.

As car says, be careful of Type III tests because they violate marginality. Type II tests (the default) do not have this problem.

### Note

It is possible for this function to `stop` when `type = 2` or `3`, e.g., `anova(vglm(cans ~ myfactor, poissonff, data = boxcar))` where `myfactor` is a factor.

The code was adapted directly from `anova.glm` and `Anova.glm` by T. W. Yee. Hence the Type II and Type III tests do not correspond precisely with the SAS definition.

### See Also

`anova.glm`, `stat.anova`, `stats:::print.anova`, `Anova.glm` if car is installed, `vglm`, `lrtest`, `add1.vglm`, `drop1.vglm`, `lrt.stat.vlm`, `score.stat.vlm`, `wald.stat.vlm`, `backPain2`, `update`.

### Examples

    # Example 1: a proportional odds model fitted to pneumo.
    set.seed(1)
    pneumo <- transform(pneumo, let = log(exposure.time), x3 = runif(8))
    fit1 <- vglm(cbind(normal, mild, severe) ~ let     , propodds, pneumo)
    fit2 <- vglm(cbind(normal, mild, severe) ~ let + x3, propodds, pneumo)
    fit3 <- vglm(cbind(normal, mild, severe) ~ let + x3, cumulative, pneumo)
    anova(fit1, fit2, fit3, type = 1)  # Remember to specify 'type'!!
    anova(fit2)
    anova(fit2, type = "I")
    anova(fit2, type = "III")

    # Example 2: a proportional odds model fitted to backPain2.
    data("backPain2", package = "VGAM")
    summary(backPain2)
    fitlogit <- vglm(pain ~ x2 * x3 * x4, propodds, data = backPain2)
    coef(fitlogit)
    anova(fitlogit)
    anova(fitlogit, type = "I")
    anova(fitlogit, type = "III")

[Package VGAM version 1.1-3 Index]