Anova {car} | R Documentation |
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.
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"), ...)
mod |
lm or glm 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 estimated. If not specified, mod is used. |
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 binomial and Poisson models; or base the dispersion estimate on
the residual deviance (deviance ). |
... |
arguments to be passed to linear.hypothesis ; only use
white.adjust for a linear model. |
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 all but type-II likelihood-ratio and F 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.
An object of class anova
, usually printed.
Be careful of type-III tests.
John Fox jfox@mcmaster.ca
Fox, J. (1997) Applied Regression, Linear Models, and Related Methods. Sage.
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