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I am assessing the effect of 5 predictor variables on species abundance. I have created 12 generalized linear models in R that have the same response and five predictors. Rather than run a complex model with one response, five predictors and a 12 way interaction, I opted to subset the dataset out and run each group separately (resulting in 12 models). Each model was run using package glmmtmb in R because my count data had high dispersion. All of my models are negative binomials, but they differ in the dispersion parameter used: NB1 or NB2.

Does anyone have a sense on whether it is appropriate to visualizing these models together in one plot? I am envisioning plotting my model results in coefficient estimate plot. I normally would think that this is OK if all 12 models utilized the same model family and structure, but this is not the case. Because dispersion parameter choice can change confidence intervals, coefficient estimates, and p values, I am more hesitant to quantitatively compare or visualize these models together.

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As long as you're using the same link function in every case, the coefficients should be comparable — they represent the expected change in the location (mean in this case) of the response, on the link-function (log) scale, regardless of the assumptions about the likelihood/variance-mean scaling. (In the specific case of a log link, you can also exponentiate the coefficients and the endpoints of the confidence intervals [not the standard errors!] to get numbers you can interpret as the expected proportional change in the mean, rather than the expected change in the log of the mean.

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