R: Analysis of Deviance for Generalized Nonlinear Models

anova.gnm {gnm} | R Documentation

## Analysis of Deviance for Generalized Nonlinear Models

### Description

Compute an analysis of deviance table for one or more generalized nonlinear models

### Usage

    ## S3 method for class 'gnm'
    anova(object, ..., dispersion = NULL, test = NULL)

### Arguments

`object` | an object of class `gnm`
`...` | additional objects of class `gnm` or `glm`
`dispersion` | the dispersion parameter for the fitting family. By default it is derived from `object`
`test` | (optional) a character string, (partially) matching one of `"Chisq"`, `"F"`, or `"Cp"`. See `stat.anova`.

### Details

Specifying a single object gives a sequential analysis of deviance table for that fit. The rows of the table show the reduction in the residual deviance and the current residual deviance as each term in the formula is added in turn.

If more than one object is specified, the rows of the table show the residual deviance of the current model and the change in the residual deviance from the previous model. (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.

If `test` is specified, the table will include test statistics and/or p values for the reduction in deviance. For models with known dispersion (e.g., binomial and Poisson fits) the chi-squared test is most appropriate, and for those with dispersion estimated by moments (e.g., 'gaussian', 'quasibinomial' and 'quasipoisson' fits) the F test is most appropriate. Mallows' Cp statistic is the residual deviance plus twice the estimate of sigma^2 times the residual degrees of freedom, which is closely related to AIC (and a multiple of it if the dispersion is known).

### Value

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

### Warning

The comparison between two or more models will only be valid if they are fitted to the same dataset. This may be a problem if there are missing values and R's default of `na.action = na.omit` is used; an error will be given in this case.

### Author(s)

Modification of `anova.glm` by the R Core Team. Adapted for `"gnm"` objects by Heather Turner.

### See Also

`gnm`, `anova`

### Examples

    set.seed(1)

    ##  Fit a uniform association model separating diagonal effects
    Rscore <- scale(as.numeric(row(occupationalStatus)), scale = FALSE)
    Cscore <- scale(as.numeric(col(occupationalStatus)), scale = FALSE)
    Uniform <- glm(Freq ~ origin + destination + Diag(origin, destination) +
                   Rscore:Cscore, family = poisson, data = occupationalStatus)

    ##  Fit an association model with homogeneous row-column effects
    RChomog <- gnm(Freq ~ origin + destination + Diag(origin, destination) +
                   MultHomog(origin, destination), family = poisson,
                   data = occupationalStatus)

    ##  Fit an association model with separate row and column effects
    RC <- gnm(Freq ~ origin + destination + Diag(origin, destination) +
              Mult(origin, destination), family = poisson,
              data = occupationalStatus)

    anova(RC, test = "Chisq")

    anova(Uniform, RChomog, RC, test = "Chisq")

[Package gnm version 1.1-2 Index]