R: Confidence Intervals for Parameters of VGLMs

confintvglm {VGAM} | R Documentation

## Confidence Intervals for Parameters of VGLMs

### Description

Computes confidence intervals (CIs) for one or more parameters in a fitted model. Currently the object must be a `"vglm"` object.

### Usage

    confintvglm(object, parm, level = 0.95, method = c("wald", "profile"),
                trace = NULL, ...)

### Arguments

`object` | A fitted model object.
`parm, level, ...` | Same as `confint`.
`method` | Character. The default is the first method. Abbreviations are allowed. Currently `"profile"` is basically working; and it is likely to be more accurate especially for small samples, as it is based on a profile log likelihood, however it is computationally intensive.
`trace` | Logical. If `TRUE` then one can monitor the computation as it progresses (because it is expensive). The default is the orginal model's `trace` value (see `vglm.control`). Setting `FALSE` suppresses all intermediate output.

### Details

The default for this methods function is based on `confint.default` and assumes asymptotic normality. In particular, the `coef` and `vcov` methods functions are used for `vglm-class` objects.

When `method = "profile"` the function `profilevglm` is called to do the profiling. The code is very heavily based on `profile.glm` which was originally written by D. M. Bates and W. N. Venables (For S in 1996) and subsequently corrected by B. D. Ripley. Sometimes the profiling method can give problems, for example, `cumulative` requires the M linear predictors not to intersect in the data cloud. Such numerical problems are less common when `method = "wald"`, however, it is well-known that inference based on profile likelihoods is generally more accurate than Wald, especially when the sample size is small. The deviance (`deviance(object)`) is used if possible, else the difference `2 * (logLik(object) - ell)` is computed, where `ell` are the values of the loglikelihood on a grid.

For Wald CIs and `rrvglm-class` objects, currently an error message is produced because I haven't gotten around to write the methods function; it's not too hard, but am too busy! An interim measure is to coerce the object into a `"vglm"` object, but then the confidence intervals will tend to be too narrow because the estimated constraint matrices are treated as known.

For Wald CIs and `vgam-class` objects, currently an error message is produced because the theory is undeveloped.

### Value

Same as `confint`.

### Note

The order of the values of argument `method` may change in the future without notice. The functions `plot.profile.glm` and `pairs.profile.glm` from MASS appear to work with output from this function.

### Author(s)

Thomas Yee adapted `confint.lm` to handle `"vglm"` objects, for Wald-type confidence intervals. Also, `profile.glm` was originally written by D. M. Bates and W. N. Venables (For S in 1996) and subsequently corrected by B. D. Ripley. This function effectively calls `confint.profile.glm()` in MASS.

### See Also

`vcovvlm`, `summaryvglm`, `confint`, `profile.glm`, `lrt.stat.vlm`, `wald.stat`, `plot.profile.glm`, `pairs.profile.glm`.

### Examples

    # Example 1: this is based on a glm example
    counts <- c(18,17,15,20,10,20,25,13,12)
    outcome <- gl(3, 1, 9); treatment <- gl(3, 3)
     glm.D93 <-  glm(counts ~ outcome + treatment, family = poisson())
    vglm.D93 <- vglm(counts ~ outcome + treatment, family = poissonff)
    confint(glm.D93) # needs MASS to be present on the system
    confint.default(glm.D93)  # based on asymptotic normality
    confint(vglm.D93)
    confint(vglm.D93) - confint(glm.D93)    # Should be all 0s
    confint(vglm.D93) - confint.default(glm.D93)  # based on asympt. normality

    # Example 2: simulated negative binomial data with multiple responses
    ndata <- data.frame(x2 = runif(nn <- 100))
    ndata <- transform(ndata, y1 = rnbinom(nn, mu = exp(3+x2), size = exp(1)),
                              y2 = rnbinom(nn, mu = exp(2-x2), size = exp(0)))
    fit1 <- vglm(cbind(y1, y2) ~ x2, negbinomial, data = ndata, trace = TRUE)
    coef(fit1)
    coef(fit1, matrix = TRUE)
    confint(fit1)
    confint(fit1, "x2:1")  #  This might be improved to "x2" some day...
    ## Not run:
    confint(fit1, method = "profile")  # Computationally expensive
    confint(fit1, "x2:1", method = "profile", trace = FALSE)

    ## End(Not run)

    fit2 <- rrvglm(y1 ~ x2, negbinomial(zero = NULL), data = ndata)
    confint(as(fit2, "vglm"))  # Too narrow (SEs are biased downwards)

[Package VGAM version 1.1-3 Index]