R: Analysis of Robust Quasi-Deviance for "glmrob" Objects

anova.glmrob {robustbase} | R Documentation

## Analysis of Robust Quasi-Deviance for "glmrob" Objects

### Description

Compute an analysis of robust quasi-deviance table for one or more generalized linear models fitted by `glmrob`.

### Usage

    ## S3 method for class 'glmrob'
    anova(object, ..., test = c("Wald", "QD", "QDapprox"))

### Arguments

`object, ...` | objects of class `glmrob`, typically the result of a call to `glmrob`.
`test` | a character string specifying the test statistic to be used. (Partially) matching one of `"Wald"`, `"QD"` or `"QDapprox"`. See Details.

### Details

Specifying a single object gives a sequential analysis of robust quasi-deviance table for that fit. That is, the reductions in the robust residual quasi-deviance as each term of the formula is added in turn are given in as the rows of a table. (Currently not yet implemented.)

If more than one object is specified, the table has a row for the residual quasi-degrees of freedom (However, this information is never used in the asymptotic tests). For all but the first model, the change in degrees of freedom and robust quasi-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.

In addition, the table will contain test statistics and P values comparing the reduction in robust quasi-deviance for the model on the row to that on top of it. For all robust fitting methods, the “Wald”-type test between two models can be applied (`test = "Wald"`).

When using Mallows or Huber type robust estimators (`method="Mqle"` in `glmrob`), then there are additional test methods. One is the robust quasi-deviance test (`test = "QD"`), as described by Cantoni and Ronchetti (2001). The asymptotic distribution is approximated by a chi-square distibution. Another test (`test = "QDapprox"`) is based on a quadratic approximation of the robust quasi-deviance test statistic. Its asymptotic distribution is chi-square (see the reference).

The comparison between two or more models by `anova.glmrob` will only be valid if they are fitted to the same dataset and by the same robust fitting method using the same tuning constant c (`tcc` in `glmrob`).

### Value

Basically, an object of class `anova` inheriting from class `data.frame`.

### Author(s)

Andreas Ruckstuhl

### References

E. Cantoni and E. Ronchetti (2001) Robust Inference for Generalized Linear Models. JASA 96 (455), 1022–1030.

E.Cantoni (2004) Analysis of Robust Quasi-deviances for Generalized Linear Models. Journal of Statistical Software 10, https://www.jstatsoft.org/article/view/v010i04

### See Also

`glmrob`, `anova`.

### Examples

    ## Binomial response -----------
    data(carrots)
    Cfit2 <- glmrob(cbind(success, total-success) ~ logdose + block,
                    family=binomial, data=carrots, method="Mqle",
                    control=glmrobMqle.control(tcc=1.2))
    summary(Cfit2)

    Cfit4 <- glmrob(cbind(success, total-success) ~ logdose * block,
                    family=binomial, data=carrots, method="Mqle",
                    control=glmrobMqle.control(tcc=1.2))

    anova(Cfit2, Cfit4, test="Wald")

    anova(Cfit2, Cfit4, test="QD")

    anova(Cfit2, Cfit4, test="QDapprox")

    ## Poisson response ------------
    data(epilepsy)

    Efit2 <- glmrob(Ysum ~ Age10 + Base4*Trt, family=poisson, data=epilepsy,
                   method="Mqle", control=glmrobMqle.control(tcc=1.2,maxit=100))
    summary(Efit2)

    Efit3 <- glmrob(Ysum ~ Age10 + Base4 + Trt, family=poisson, data=epilepsy,
                   method="Mqle", control=glmrobMqle.control(tcc=1.2,maxit=100))

    anova(Efit3, Efit2, test = "Wald")

    anova(Efit3, Efit2, test = "QD")

    ## trivial intercept-only-model:
    E0 <- update(Efit3, . ~ 1)
    anova(E0, Efit3, Efit2, test = "QDapprox")

[Package robustbase version 0.95-0 Index]