VGAM (version 1.1-1)

anova.vglm: Analysis of Deviance for Vector Generalized Linear Model Fits


Compute an analysis of deviance table for one or more vector generalized linear model fits.


# S3 method for vglm
anova(object, …, type = c("II", "I", "III", 2, 1, 3),
     test = c("LRT", "none"), trydev = TRUE, silent = TRUE)


object, …

objects of class vglm, typically the result of a call to vglm, or a list of objects for the "vglmlist" method. Each model must have an intercept term. If "vglmlist" is used then type = 1 or type = "I" must be specified.


character or numeric; any one of the (effectively three) choices given. Note that anova.glm has 1 or "I" as its default; and that Anova.glm has 2 or "II" as its default (and allows for type = "III"), so one can think of this function as a combination of anova.glm and Anova.glm, but with the default of the latter. See Details below for more information.


a character string, (partially) matching one of "LRT" and "none". In the future it is hoped that "Rao" be also supported, to conduct score tests. The first value is the default.


logical; if TRUE then the deviance is used if possible. Note that only a few VGAM family functions have a deviance that is defined and implemented. Setting it FALSE means the log-likelihood will be used.


logical; if TRUE then any warnings will be suppressed. These may arise by IRLS iterations not converging during the fitting of submodels. Setting it FALSE means that any warnings are given.


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


See anova.glm. Several VGAM family functions implement distributions which do not satisfying the usual regularity conditions needed for the LRT to work. No checking or warning is given for these.

As car says, be careful of Type III tests because they violate marginality. Type II tests (the default) do not have this problem.


anova.vglm is intended to be similar to anova.glm so specifying a single object and type = 1 gives a sequential analysis of deviance table for that fit. By analysis of deviance, it is meant loosely that if the deviance of the model is not defined or implemented, then twice the difference between the log-likelihoods of two nested models remains asymptotically chi-squared distributed with degrees of freedom equal to the difference in the number of parameters of the two models. Of course, the usual regularity conditions are assumed to hold. For Type I, the analysis of deviance table has 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. 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 the each term is added sequentially from first to last.

The Anova() function in car allows for testing Type II and Type III (SAS jargon) hypothesis tests, although the definitions used are not precisely that of SAS. As car notes, Type I rarely test interesting hypotheses in unbalanced designs. Type III enter each term last, keeping all the other terms in the model. Type II tests, according to SAS, add the term after all other terms have been added to the model except terms that contain the effect being tested; an effect is contained in another effect if it can be derived by deleting variables from the latter effect. Type II tests are currently the default.

As in anova.glm, but not as Anova.glm, if more than one object is specified, then 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. It is necessary to have type = 1 with more than one objects are specified.

See anova.glm for more details and warnings. The VGAM package now implements full likelihood models only, therefore no dispersion parameters are estimated.

See Also

anova.glm, stat.anova, stats:::print.anova, Anova.glm if car is installed, vglm, lrtest, lrt.stat.vlm, score.stat.vlm, wald.stat.vlm.


Run this code
# Example 1: a proportional odds model fitted to pneumo.
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, type = "I")
anova(fit2, type = "III")

# Example 2: a proportional odds model fitted to backPain.
data("backPain", package = "VGAM")
backPain$x1 <- factor(backPain$x1)
backPain$x2 <- factor(backPain$x2)
backPain$x3 <- factor(backPain$x3)
fitlogit <- vglm(pain ~ x1 * x2 * x3, propodds, data = backPain)
anova(fitlogit, type = "I")
anova(fitlogit, type = "III")
# }

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