GLMM with time-series covariance and binary response variable?

Question

I have a binary response variable that was measured at irregular time intervals for a number of individuals. I want to fit a GLMM that accounts for the time-series covariance within individuals.

I know that this is possible for Gaussian response variables by using the corCAR1 autocorrelation structure in the nlme package, but it seems that nlme does not fit logistic GLMMs. On the other hand, I can fit a logistic GLMM in the other popular R package for multilevel models, lme4, but that package doesn't seem to allow for specifying a time-series covariance structure.

Does anyone know of a way to fit this model in R? I know this model would be useful for many researchers, because I have encountered several researchers working on various problems who also wanted to fit such a model, but couldn't find a way to do it in R, so they resorted to less than ideal models (e.g., simply fitting a logistic GLMM without accounting for the time series).

I would greatly appreciate any advice!!!

Answer 1

You can do this in the {mvgam} package, which fits dynamic regression models in State Space form for a fairly wide range of observation families. The bernoulli() family is what you would choose here, which fits a logistic regression but allows for latent dynamic processes to also be included, and you could use the CAR() trend model for specifying a continuous autoregressive process for irregularly-sampled data.