lrp {VGAM} | R Documentation

## Likelihood ratio p-values

### Description

Returns a vector of p-values from testing whether each estimated coefficient of a VGLM regression model is 0 or not. The methodology is based on a likelihood ratio test.

### Usage

    lrp(object, ...)
    lrp.vglm(object, which = NULL, omit1s = TRUE,
             trace = NULL, ...)

### Arguments

`object` | A `vglm` object.
`which` | Numeric or character. Specifies which regression coefficient are to be selected. The default is to select them all, except the intercepts.
`trace` | Logical. If `TRUE` then some output is produced as each regression coefficient is deleted (set to 0) and the IRLS iterations proceed. The default is to use the `trace` value of the fitted object; see `vglm.control`.
`omit1s` | Logical. If `TRUE` (the default) then regression coefficients deriving from the intercept term are not selected. This is because, for some models such as `propodds` and `cumulative`, setting an intercept equal to 0 does not make much sense.
`...` | further arguments passed into the other methods functions.

### Details

When `summary()` is applied to a `vglm` object a 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. 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 an alternative to `summaryvglm` for testing for the significance of a regression coefficient.

### Value

By default, a vector of (2-sided test) p-values. If the model is intercept-only then a `NULL` is returned by default.

### Warning

This function has not yet been thoroughly tested. Convergence failure is possible for some models applied to certain data sets; it is a good idea to set `trace = TRUE` to monitor convergence.

### Note

Only models with a full-likelihood are handled, so that quasi-type models such as `quasipoissonff` should not be fed in. One day this function might allow for terms, such as arising from `poly` and `bs`.

### Author(s)

T. W. Yee.

### See Also

`hdeff`, `summaryvglm`, `vglm`, `confintvglm`, `pchisq`, `profilevglm`.

### Examples

    pneumo <- transform(pneumo, let = log(exposure.time))
    fit <- vglm(cbind(normal, mild, severe) ~ let, propodds, data = pneumo)
    cbind(coef(summary(fit)),
          "LRT pvalue" = lrp(fit, omit1s = FALSE))

[Package VGAM version 1.0-4 Index]