I have an experimental treatment at 15 sites and would like to build models to associate usage rates of 4 species with a set of 6 explanatory variables. In the end, I would like to rank the importance of these variable for each species.
Ordinarily, I would simply fit the models and then standardize the beta coefficient by dividing by the standard error and ordering by absolute value.
However, in this case, I need to model a random effect of site and my response variable must be modeled as zero-inflated Poisson, which takes me outside of the realm in which I've seen this comparative analysis performed.
Is there an analogous procedure to ranking standardized beta coefficients for generalized linear mixed models?
Much thanks in advance!
You could also rank by the absolute value of the wald statistics, since it is unitless. Another advantage of the wald statistics is that it takes the uncertainty of the estimates into consideration.
You may consider the R-packages "betareg" (Cribari-Neto and Zeileis, 2010) or "simplexreg" (Zhang, Qiu and Shi, 2016) to do regression analysis and select the site with median "average rate" (sandwich way) as the reference if the within-site correlation can be ignored. Currently I didn't see any work on mixed-effects model based on beta distribution, noting that beta distribution does not belong to exponential family, nor dispersion models, although one can transform the \alpha and \beta to the mean parameter \mu = \alpha / (\alpha + \beta) . You may refer to Qiu et al (2008) work on the topic of mixed-effects model for longitudinal proportional data.
Cribari-Neto F and Zeileis A (2010). betareg: Beta Regression in R. Journal of Statistical Software, 34(2), 1–24.
Zhang P, Qiu Z and Shi C (2016). simplexreg: An R Package for Regression Analysis of Proportional Data Using the Simplex Distribution. Journal of Statistical Software, 71(11), 1–21.
Qiu, Z., Song, P.X.-K. and Tan, M., Simplex mixed-effects models for longitudinal proportional data, Scandinavian Journal of Statistics, 2008, 35(4): 577-96.
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