1d:T792,# Likelihood-ratio test for variance components in `hglm` Likelihood-ratio test for the estimated variance components (or other dipersion parameters) in `hglm`. ```r lrt(hglm.obj1, hglm.obj2 = NULL) ``` ## Arguments - `hglm.obj1`: a fitted `hglm` object. - `hglm.obj2`: optional, another fitted `hglm` object to be tested against `hglm.obj1`. ## Details When `hglm.obj2 = NULL`, all the random effects variance components in `hglm.obj1` are tested against the null model with only fixed effects. The degree of freedom is determined by comparing the number of random effects terms in `hglm.obj1` and `hglm.obj2` or the null fixed-effects-only model. Note that the likelihood- ratio test statistic for variance estimates, which are bounded above zero, follows a 50:50 mixture distribution of chi-square with 0 and 1 degree of freedom (Self and Liang 1987 JASA). ## Returns Printout summary of the likelihood-ratio test results. Test statistic, p-value, etc. are returned. ## References Self, S. G., & Liang, K.-Y. (1987). Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard Conditions. **Journal of the American Statistical Association**, 82 (398), 605-610. ## Examples ```r require(hglm) ## Not run: set.seed(911) x1 <- rnorm(100) x2 <- rnorm(100) x3 <- rnorm(100) z1 <- factor(rep(LETTERS[1:10], rep(10, 10))) z2 <- factor(rep(letters[1:5], rep(20, 5))) Z1 <- model.matrix(~ 0 + z1) Z2 <- model.matrix(~ 0 + z2) u1 <- rnorm(10, 0, sqrt(2)) u2 <- rnorm(5, 0, sqrt(3)) y <- 1 + 2*x1 + 3*x2 + Z1%*%u1 + Z2%*%u2 + rnorm(100, 0, sqrt(exp(x3))) dd <- data.frame(x1 = x1, x2 = x2, x3 = x3, z1 = z1, z2 = z2, y = y) m20 <- hglm(X = cbind(rep(1, 100), x1, x2), y = y, Z = Z1, calc.like = TRUE) lrt(m20) m21 <- hglm(X = cbind(rep(1, 100), x1, x2), y = y, Z = cbind(Z1, Z2), RandC = c(10, 5), calc.like = TRUE) lrt(m20, m21) ## End(Not run) ```

lrt function