| anova.vglm {VGAM} | R Documentation |
Description
Compute an analysis of deviance table for one or morevector 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 |
type | character or numeric;any one of the(effectively three) choices given.Note that |
test | a character string,(partially) matching one of |
trydev | logical; if |
silent | logical; if |
Details
anova.vglm is intended to be similar toanova.glmso specifying a single object and type = 1 gives asequential analysis of deviance table for that fit.By analysis of deviance, it is meant looselythat if the deviance of the model is not defined or implemented,then twice the difference between the log-likelihoods of twonested models remains asymptotically chi-squared distributedwith degrees of freedom equal to the difference in the numberof parameters of the two models.Of course, the usual regularity conditions are assumed to hold.For Type I,the analysis of deviance table hasthe reductions in the residual devianceas each term of the formula is added in turn are given in asthe 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 theeach term is added sequentially from first to last.
The Anova() function in car allows for testingType II and Type III (SAS jargon) hypothesistests, although the definitions used are not preciselythat of SAS.As car notes,Type I rarely test interesting hypotheses in unbalanceddesigns. Type III enter each term last, keeping allthe other terms in the model.
Type II tests,according to SAS,add the term after all other terms have been added to the modelexcept terms that contain the effect being tested; an effectis contained in another effect if it can be derived by deletingvariables from the latter effect.Type II tests are currently the default.
As in anova.glm, but not asAnova.glm() in car,if more than one object is specified, thenthe table has a row for theresidual degrees of freedom and deviance for each model.For all but the first model, the change in degrees of freedomand deviance is also given. (This only makes statistical senseif the models are nested.) It is conventional to list themodels from smallest to largest, but this is up to the user.It is necessary to have type = 1 with more than oneobjects are specified.
See anova.glm for more detailsand warnings.The VGAM package now implements full likelihood modelsonly, therefore no dispersion parameters are estimated.
Value
An object of class "anova" inheriting fromclass "data.frame".
Warning
See anova.glm.Several VGAM family functions implement distributionswhich do not satisfying the usual regularity conditions needed forthe LRT to work. No checking or warning is given for these.
As car says, be careful of Type III testsbecause they violate marginality.Type II tests (the default) do not have this problem.
Note
It is possible for this function to stopwhen type = 2 or 3, e.g.,anova(vglm(cans ~ myfactor, poissonff, data = boxcar))where myfactor is a factor.
The code was adapteddirectly from anova.glmand Anova.glm() in carby T. W. Yee.Hence the Type II and Type III tests do notcorrespond precisely with the SAS definition.
See Also
anova.glm,stat.anova,stats:::print.anova,Anova.glm() in car 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 1.1-11 Index]
