R: Likelihood-Ratio Tests for Nested ML Models

anova-methods {aod} | R Documentation

## 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

      ## S4 method for signature 'glimML'
    anova(object, ...)

### Arguments

`object` | Fitted model of class “glimML”.
`...` | Further models to be tested or arguments passed to the `print` function.

### 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-squared distribution with degrees of freedom = the difference in the number of parameters between the compared models (Mc Cullagh and Nelder, 1989).

### 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.
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.

### 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)

[Package aod version 1.3 Index]