R: Likelihood Ratio Test Statistics Evaluated at the Null Values

lrt.stat {VGAM} | R Documentation

## Likelihood Ratio Test Statistics Evaluated at the Null Values

### Description

Generic function that computes likelihood ratio test (LRT) statistics evaluated at the null values (consequently they do not suffer from the Hauck-Donner effect).

### Usage

    lrt.stat(object, ...)
    lrt.stat.vlm(object, values0 = 0, subset = NULL, omit1s = TRUE,
              all.out = FALSE, trace = FALSE, ...)

### Arguments

`object, values0, subset` | Same as in `wald.stat.vlm`.
`omit1s, all.out, trace` | Same as in `wald.stat.vlm`.
`...` | Ignored for now.

### Details

When `summary()` is applied to a `vglm` object a 4-column Wald table is produced. The corresponding p-values are generally viewed as inferior to those from a likelihood ratio test (LRT). For example, the Hauck and Donner (1977) effect (HDE) produces p-values that are biased upwards (see `hdeff`). Other reasons are that the Wald test is often less accurate (especially in small samples) and is not invariant to parameterization. By default, this function returns p-values based on the LRT by deleting one column at a time from the big VLM matrix and then starting up IRLS to convergence (hopefully). Twice the difference between the log-likelihoods (or equivalently, the difference in the deviances if they are defined) is asymptotically chi-squared with 1 degree of freedom. One might expect the p-values from this function therefore to be more accurate and not suffer from the HDE. Thus this function is a recommended alternative (if it works) to `summaryvglm` for testing for the significance of a regression coefficient.

### Value

By default, a vector of signed square root of the LRT statistics; these are asymptotically standard normal under the null hypotheses. If `all.out = TRUE` then a list is returned with the following components: `lrt.stat` the signed LRT statistics, `pvalues` the 2-sided p-values, `Lrt.stat2` the usual LRT statistic, `values0` the null values.

### Warning

See `wald.stat.vlm`.

### Author(s)

T. W. Yee.

### See Also

`score.stat`, `wald.stat`, `summaryvglm`, `anova.vglm`, `vglm`, `lrtest`, `confintvglm`, `pchisq`, `profilevglm`, `hdeff`.

### Examples

    pneumo <- transform(pneumo, let = log(exposure.time))
    fit <- vglm(cbind(normal, mild, severe) ~ let, propodds, data = pneumo)
    cbind(coef(summary(fit)),
          "signed LRT stat" = lrt.stat(fit, omit1s = FALSE))
    summary(fit, lrt0 = TRUE)  # Easy way to get it

[Package VGAM version 1.1-3 Index]