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I'd like to fit a Poisson-Tweedie model with random effects. I'm wondering if it is possible to do it with the mcglm package. I'm following the work of Bonat et al (2017): "Extended Poisson-Tweedie: properties and regression models for count data".

In particular, I`m working with a count response variable measured in the same subject in 4 different moments. The predictor includes a factor (the treatment applied to the subjects) and the log of the time (the time refers to the number of days elapsed betwwen the administration of the treatment and the measurement). I need to include the patient as a random effect.

I'd appreciate any help. Thanks in advance.

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Random effects models are in general used to deal with dependent data as you described. However, it is not the unique way. The mcglm package provides marginal models for dealing with dependent data and it already implements the Poisson-Tweedie distribution for dealing with counting data. Of course, you can specify a random effect model on top of the Poisson-Tweedie distribution, but the fitting process will be extreme challenging. The probability mass function of the Poisson-Tweedie distribution is not available in closed-form, which implies that the likelihood function is defined as an intractable integral. Thus, the standard method of maximum likelihood for fitting random effects models is extremely challenging to implement in practice. You can have more details about mcglm's in my papers https://www.jstatsoft.org/article/view/v084i04 and https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/rssc.12145.

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