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Hello all, This is probably known, but it?s news to me: the standard errors printed for the lme model fit run under method=?ML? are in fact those computed under method=?REML?. Is this the expected behavior? And if...

John, this is indeed an unstructured variance-covariance matrix for the random effects. Not to be confused with the covariance matrix of the longitudinal vector of observations, which in the context of the general linear model can also be modeled...

One can figure out which likelihood version is correct (Laplace or nAGQ>1) by doing a simulation with random effects variance -> 0. I'll do that if I find time. Florin > On Apr 24, 2020, at 7:59 AM, Ben...

Interestingly (and reassuringly), Laplace and nAGQ give consistent results for binomial GLMM. Could there be a glitch for Poisson GLMM? #### Likelihood of Binomial GLMM Models # r-sig-mixed-models GLMM question* library(lme4) set.seed(51) # Simulate some random effect...

Thanks Ben, interesting! Any particular reason for this default choice? It sounds like separating parameter estimation (ML) from SE of the parameters (REML), but presumably when someone chooses ML for estimation they assume this goes to how the SE's...

Looks like you guys thought about deviance issues a lot: https://github.com/lme4/lme4/issues/375 Speaking about the principle of "least surprise", it is surprising to get completely different behaviors in deviance for nAGQ=1 vs nAGQ=2...

I modified Ben Goldstein's code slightly to show that it's indeed the nAGQ log-likelihood that's off by a constant, rather than the Laplace. While for model selection reasons one can argue that the constant doesn't...

No spoiler, I agree. When comparing across multiple models, each with their own "off by" constant, having the exact log-likelihood is important. > On Apr 25, 2020, at 5:33 AM, Martin Maechler <maechler at stat.math.ethz.ch> wrote...

Hi Dimitris, The point is that the ML standard errors reported by summary() do not match those computed under varFix. The reason for this is that indicated by Ben, which is that by default the varFix SE's get multiplied...

Hi John, Thanks for the Prentice reference. However, I just want to point out that the extended beta-binomial is proposed there as a marginal distribution for the observations. It could not arise from a mixed-effects model specification. This...

Hi Emmanuel, That's a good question. My guess is that the correlation is non-negative generally, but I wasn't able to prove it theoretically even in the simplest case when Y1, Y2 ~ Bernoulli(u) independent conditionally on u...

Hi Emmanuel, Your reasoning is correct. As a quibble, outside a simple repeated measures experiment setup, p(i,j) *does* depend on j. For example, if observations are collected over time, generally there is a time effect; if they are...

I forgot to mention that this proof works for any link function, any conditional distribution for the response, and any random effects distribution. In other words, it's not restricted to logit link, nor to binomial data, nor to normal...

Hi Emmanuel, So I can prove positive within-subject correlation for GLME logistic regression with random intercepts - assuming all observations have same mean! Let Yj ~ Bernoulli(mu), logit(mu) = beta + u, u ~ Normal(0, tau^2). Using the conditional covariance...