Likelihood-Ratio Tests for Nested ML Models

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

# S4 method for class '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 \(\chi^2\) 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)
#> Analysis of Deviance Table (beta-binomial models)
#> 
#> fm1: fixed = cbind(y, n - y) ~ seed; random = ~1 
#> fm2: fixed = cbind(y, n - y) ~ seed + root; random = ~1 
#> 
#>       logL k   AIC  AICc   BIC Resid. dev. Resid. Df    Test Deviance Df
#> fm1 -63.55 3 133.1 134.5 136.2       50.51        18                    
#> fm2 -55.83 4 119.7 122.2 123.8       35.07        17 fm1-fm2    15.44  1
#>     P(> Chi2)
#> fm1          
#> fm2 8.509e-05