# Anova

##### Anova Tables for Various Statistical Models

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.

- Keywords
- models, regression, htest

##### 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.

##### 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.

##### Value

- An object of class
`anova`

, usually printed.

##### Warning

Be careful of type-III tests.

##### References

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

##### See Also

##### Examples

```
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
```

*Documentation reproduced from package car, version 1.1-0, License: GPL version 2 or newer*