Can someone point me to a reference that will explain why, when using mixed models (glmer and lmer) adding explanatory variables decreases the log likelihood? This makes no sense to me, as adding explanatory power should make the model fit the data worse. I've attached the data I am using, which contains no missing values, and here are the models I am running, and the results:
Any help is appreciated. Thanks!
#note, models do not fully converge, but examination of estimates using verbose=T suggests they are resonable
mod.null = glmer(res.lifesat.last5 ~ 1 + (1|hhidpn) + (1|hhid), data=data.nomiss, family=binomial(link="probit"))
mod1 = glmer(res.lifesat.last5 ~ networth2.gmc + (1|hhidpn) + (1|hhid), data=data.nomiss, family=binomial(link="probit"))
mod2 = glmer(res.lifesat.last5 ~ networth2.gmc + married + (1|hhidpn) + (1|hhid), data=data.nomiss, family=binomial(link="probit"))
mod3 = glmer(res.lifesat.last5 ~ networth2.gmc + married + depscore + selfhealth + (1|hhidpn) + (1|hhid), data=data.nomiss, family=binomial(link="probit"))
#note that mod2 and mod3 have lower log-likelihoods than mod1, and mod3 has a lower LL than the null model
anova(mod.null, mod1, mod2, mod3)
Andrew Miles