[R-sig-ME] Setting Theta for NB models

[Dan Smith]

Hello,

I've been working on some data that has a negative binomial distribution
(seed count data) and have a question regarding how lme4 handles theta. I
have determined the data's theta value using the equation (mean^theta =
var). I have to run a few models with different link functions to satisfy
co-author curiosity (even after having them read O'hara & Kotze 2010). My
question is, does lme4 make a transformation to the theta value concordant
with the link function? My assumption is that it does not, and I need to
adjust the theta in accordance with any transformations applied within the
model.

wagr1 <- glmer(WAGRcount ~ treatment + (1|treatment:plot), family =
negative.binomial(*link = "identity", theta = 2.25232*), data = wagrcores)
summary(wagr1)

wagr2 <- glmer(WAGRcount ~ treatment + (1|treatment:plot), family =
negative.binomial(*link = "log", theta = 1.8173*), data = wagrcores,control
= glmerControl(optimizer = "nloptwrap", calc.derivs = FALSE))
summary(wagr2)

Thank you,
 -Dan

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