Anova: Anova Tables for Linear and Generalized Linear Models

Description

Calculates type-II or type-III analysis-of-variance tables for model objects produced by lm and glm. For linear models, F-tests are calculated; for generalized linear models, likelihood-ratio chisquare, Wald chisquare, or F-tests are calculated.

Usage

Anova(mod, ...)

## S3 method for class 'lm':
Anova(mod, error, type=c("II", "III"), ...)

## S3 method for class 'aov':
Anova(mod, ...)

## S3 method for class 'glm':
Anova(mod, type=c("II", "III"), test.statistic=c("LR", "Wald", "F"), 
    error, error.estimate=c("pearson", "dispersion", "deviance"), ...)
    
## S3 method for class 'multinom':
Anova(mod, type = c("II", "III"), ...)

## S3 method for class 'polr':
Anova(mod, type = c("II", "III"), ...)

Arguments

mod

lm, aov, glm, multinom, or polr model object.

error

for a linear model, an lm model object from which the error sum of squares and degrees of freedom are to be calculated. For F-tests for a generalized linear model, a glm object from which the dispersion is to be e

type

type of test, "II" or "III".

test.statistic

for a generalized linear model, whether to calculate "LR" (likelihood-ratio), "Wald", or "F" tests.

error.estimate

for F-tests for a generalized linear model, base the dispersion estimate on the Pearson residuals (pearson, the default); use the dispersion estimate in the model object (dispersion), which, e.g., is fixed to 1 for

...

arguments to be passed to linear.hypothesis; only use white.adjust for a linear model.

Value

An object of class anova, usually printed.

Warning

Be careful of type-III tests.

Details

The designations "type-II" and "type-III" are borrowed from SAS, but the definitions used here do not correspond precisely to those employed by SAS. Type-II tests are calculated according to the principle of marginality, testing each term after all others, except ignoring the term's higher-order relatives; so-called type-III tests violate marginality, testing each term in the model after all of the others. This definition of Type-II tests corresponds to the tests produced by SAS for analysis-of-variance models, where all of the predictors are factors, but not more generally (i.e., when there are quantitative predictors). Be very careful in formulating the model for type-III tests, or the hypotheses tested will not make sense. As implemented here, type-II Wald tests for generalized linear models are actually differences of Wald statistics. For tests for linear models, and Wald tests for generalized linear models, Anova finds the test statistics without refitting the model. The standard R anova function calculates sequential ("type-I") tests. These rarely test interesting hypotheses.

References

Fox, J. (1997) Applied Regression, Linear Models, and Related Methods. Sage.

Examples

Run this code

data(Moore)
mod<-lm(conformity~fcategory*partner.status, data=Moore, 
  contrasts=list(fcategory=contr.sum, partner.status=contr.sum))
Anova(mod)
## Anova Table (Type II tests)
##
## Response: conformity
##                         Sum Sq Df F value   Pr(>F)
## fcategory                 11.61  2  0.2770 0.759564
## partner.status           212.21  1 10.1207 0.002874
## fcategory:partner.status 175.49  2  4.1846 0.022572
## Residuals                817.76 39                 
Anova(mod, type="III")
## Anova Table (Type III tests)
##
## Response: conformity
##                          Sum Sq Df  F value    Pr(>F)
## (Intercept)              5752.8  1 274.3592 < 2.2e-16
## fcategory                  36.0  2   0.8589  0.431492
## partner.status            239.6  1  11.4250  0.001657
## fcategory:partner.status  175.5  2   4.1846  0.022572
## Residuals                 817.8 39

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