# Confidence Intervals for Parameters of VGLMs Computes confidence intervals (CIs) for one or more parameters in a fitted model. Currently the object must be a `"vglm"` object. ```r 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. ## Returns Same as `confint`. ## 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`. ## 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. ## See Also `vcovvlm`, `summaryvglm`, `confint`, `profile.glm`, `lrt.stat.vlm`, `wald.stat`, `plot.profile.glm`, `pairs.profile.glm`. ## Examples ```r # 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) ```

confintvglm function