> d4 <- d7[d7$x == 4,]
> table(d4$y)
0 1 2 3 4 5 6 7 8
3 1 4 2 1 1 2 3 3
> c(mean(d4$y), var(d4$y))
[1] 4.050000 8.365789
> library(glmmML)
> glmmML(cbind(y, N - y) ~ x, data = d7, family = binomial, cluster = id)
Call: glmmML(formula = cbind(y, N - y) ~ x, family = binomial, data = d7, cluster = id)
coef se(coef) z Pr(>|z|)
(Intercept) -4.190 0.8777 -4.774 1.81e-06
x 1.005 0.2075 4.843 1.28e-06
Scale parameter in mixing distribution: 2.408 gaussian
Std. Error: 0.2202
LR p-value for H_0: sigma = 0: 2.136e-55
Residual deviance: 269.4 on 97 degrees of freedom AIC: 275.4