# Likelihood Ratio Test of Nested Models `lrtest` is a generic function for carrying out likelihood ratio tests. The default method can be employed for comparing nested VGLMs (see details below). ```r lrtest(object, ...) lrtest_vglm(object, ..., no.warning = FALSE, name = NULL) ``` ## Arguments - `object`: a `vglm` object. See below for details. - ``...``: further object specifications passed to methods. See below for details. - `no.warning`: logical; if `TRUE` then no warning is issued. For example, setting `TRUE` might be a good idea when testing for linearity of a variable for a `"pvgam"` object. - `name`: a function for extracting a suitable name/description from a fitted model object. By default the name is queried by calling `formula`. ## Details `lrtest` is intended to be a generic function for comparisons of models via asymptotic likelihood ratio tests. The default method consecutively compares the fitted model object `object` with the models passed in `...`. Instead of passing the fitted model objects in `...`, several other specifications are possible. The updating mechanism is the same as for `waldtest()` in `lmtest`: the models in `...` can be specified as integers, characters (both for terms that should be eliminated from the previous model), update formulas or fitted model objects. Except for the last case, the existence of an `update` method is assumed. See `waldtest()` in `lmtest` for details. Subsequently, an asymptotic likelihood ratio test for each two consecutive models is carried out: Twice the difference in log-likelihoods (as derived by the `logLik` methods) is compared with a Chi-squared distribution. ## Note The code was adapted directly from `lmtest` (written by T. Hothorn, A. Zeileis, G. Millo, D. Mitchell) and made to work for VGLMs and S4. This help file also was adapted from `lmtest`. **Approximate** LRTs might be applied to VGAMs, as produced by `vgam`, but it is probably better in inference to use `vglm` with regression splines (`bs` and `ns`). This methods function should not be applied to other models such as those produced by `rrvglm`, by `cqo`, by `cao`. ## Warning Several `VGAM` family functions implement distributions which do not satisfying the usual regularity conditions needed for the LRT to work. No checking or warning is given for these. ## Returns An object of class `"VGAManova"` which contains a slot with the log-likelihood, degrees of freedom, the difference in degrees of freedom, likelihood ratio Chi-squared statistic and corresponding p value. These are printed by `stats:::print.anova()`; see `anova`. ## See Also `lmtest`, `vglm`, `lrt.stat.vlm`, `score.stat.vlm`, `wald.stat.vlm`, `anova.vglm`. ## Examples ```r set.seed(1) pneumo <- transform(pneumo, let = log(exposure.time), x3 = runif(nrow(pneumo))) fit1 <- vglm(cbind(normal, mild, severe) ~ let , propodds, pneumo) fit2 <- vglm(cbind(normal, mild, severe) ~ let + x3, propodds, pneumo) fit3 <- vglm(cbind(normal, mild, severe) ~ let , cumulative, pneumo) # Various equivalent specifications of the LR test for testing x3 (ans1 <- lrtest(fit2, fit1)) ans2 <- lrtest(fit2, 2) ans3 <- lrtest(fit2, "x3") ans4 <- lrtest(fit2, . ~ . - x3) c(all.equal(ans1, ans2), all.equal(ans1, ans3), all.equal(ans1, ans4)) # Doing it manually (testStatistic <- 2 * (logLik(fit2) - logLik(fit1))) (pval <- pchisq(testStatistic, df = df.residual(fit1) - df.residual(fit2), lower.tail = FALSE)) (ans4 <- lrtest(fit3, fit1)) # Test PO (parallelism) assumption ```

lrtest function