Robust Analysis of Deviance for Generalized Linear Model Fits

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Description

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

Usage

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

Arguments

object, ...

objects of class wle.glm.root, typically the result of a call to extractRoot.wle.glm, or a list of objects each of which a result of a call to "extractRoot.wle.glm" method.

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 "Chisq", "F" or "Cp". See stat.anova.

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

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## --- 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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