aod (version 1.1-35)

anova-methods: Likelihood-Ratio Tests for Nested ML Models

Description

Performs likelihood-ratio tests on nested models. Currently, one method was implemented for beta-binomial models (betabin) or negative-binomial models (negbin).

Usage

## S3 method for class 'glimML':
anova(object, \dots)

Arguments

object

Fitted model of class glimML.

...

Further models to be tested or arguments passed to the print function.

Value

• An object of formal class anova.glimML with 3 slots:
• models
  A vector of character strings with each component giving the name of the models and the formulas for the fixed and random effects.
• anova.table
  A data frame containing the results. Row names correspond to the models. lll{ logL numeric maximized log-likelihood k numeric number of parameters in the model AIC numeric Akaike information criterion for the model AICc numeric Corrected Akaike information criterion for the model BIC numeric Bayesian information criterion the model Resid. dev. numeric Residual deviance Resid. Df numeric df of the residuals Test character Nested models which are tested Deviance numeric Deviance difference between the 2 models Df numeric df associated with deviance difference P(> Chi2) numeric P value associated with H0. }
• type
  A character chain indicating the kind of fitted model: BB for beta-binomial, or NB for negative-binomial model.

Warning

The comparison between 2 or more models will only be valid if they are fitted to the same data set.

Details

The anova method for models of formal class glimML needs at least 2 nested models of the same type (either beta-binomial or negative-binomial models: they cannot be mixed). The quantity of interest is the deviance difference between the compared models: it is a log-likelihood ratio statistic. Under the null hypothesis that 2 nested models fit the data equally well, the deviance difference has an approximate $\chi^2$ distribution with degrees of freedom = the difference in the number of parameters between the compared models (Mc Cullagh and Nelder, 1989).

References

McCullagh, P., Nelder, J.A., 1989. Generalized linear models. London, Chapman & Hall, 511 p. See Appendix C. Likelihood ratio statistics, p. 476-478.

See Also

anova.glm, AIC

Examples

data(orob2)
  # likelihood ratio test for the effect of root
  fm1 <- betabin(cbind(y, n - y) ~ seed, ~ 1, data = orob2)
  fm2 <- betabin(cbind(y, n - y) ~ seed + root, ~ 1, data = orob2)
  anova(fm1, fm2)