| Anova {car} | R Documentation |
Calculates type-II or type-III analysis-of-variance tables for
model objects produced by lm, glm, multinom
(in the nnet package), and polr (in the MASS
package). For linear
models, F-tests are calculated; for generalized linear models,
likelihood-ratio chisquare, Wald chisquare, or F-tests are calculated;
for multinomial logit and proportional-odds logit models, likelihood-ratio
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"), ...)
## S3 method for class 'multinom':
Anova(mod, type = c("II", "III"), ...)
## S3 method for class 'polr':
Anova(mod, type = c("II", "III"), ...)
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 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 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.
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.
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