# Robust Analysis of Deviance for Generalized Linear Model Fits

### Description

Compute a robust analysis of deviance table for one or more generalized linear model fits.

### Usage

1 2 |

### Arguments

`object, ...` |
objects of class |

`dispersion` |
the dispersion parameter for the fitting family. By default it is obtained from the object(s). |

`test` |
a character string, (partially) matching one of |

### Details

Specifying a single object gives a sequential analysis of deviance table for that fit. That is, 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.

If more than one object is specified, 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.

The table will optionally contain test statistics (and P values)
comparing the reduction in deviance for the row to the residuals.
For models with known dispersion (e.g., binomial and Poisson fits)
the robust chi-squared test is most appropriate, and for those with
dispersion estimated by moments (e.g., `gaussian`

,
`quasibinomial`

and `quasipoisson`

fits) the Robust F test is
most appropriate. Robust Mallows' *Cp* statistic is the residual
weighted deviance plus twice the estimate of *sigma^2* times
the residual (weighted) degrees of freedom, which is closely related to
Robust AIC (and a multiple of it if the dispersion is known).

The dispersion estimate will be taken from the largest model, using
the value returned by `summary.wle.glm`

. As this will in most
cases use a Chisquared-based estimate, the F tests are not based on
the residual deviance in the analysis of deviance table shown.

### Value

An object of class `"anova"`

inheriting from class `"data.frame"`

.

### Warning

The comparison between two or more models by `anova.wle.glm.root`

or
`anova.wleglmlist`

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,
and `anova.wleglmlist`

will detect this with an error.

Since in a model selection procedure and/or on an ANOVA table the weights of the WLE procedure must be that of the FULL model (and not that of the actual model) statistics on degrees of freedom, deviance and AIC are valid only if `object`

is the FULL model.

### References

Agostinelli, C. and Markatou, M. (2001) Test of hypotheses based on
the Weighted Likelihood Methodology, *Statistica Sinica*,
vol. 11, n. 2, 499-514.

Agostinelli, C. (2002) Robust model selection in regression via weighted likelihood methodology Statistics and Probability Letters, 56, 289-300.

Agostinelli, C. and Al-quallaf, F. (2009) Robust inference in Generalized Linear Models. Manuscript in preparation.

Hastie, T. J. and Pregibon, D. (1992)
*Generalized linear models.*
Chapter 6 of *Statistical Models in S*
eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

### See Also

`extractRoot.wle.glm`

, `wle.glm`

, `anova`

.

### Examples

1 2 3 4 5 | ```
## --- Continuing the Example from '?wle.glm':
anova(extractRoot(wle.glm.D93))
anova(extractRoot(wle.glm.D93), test = "Cp")
anova(extractRoot(wle.glm.D93), test = "Chisq")
``` |

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