[R-sig-ME] Distribution family for non-negative lower and upper bound values

[Steven J. Pierce]

Gitu,

Consider a mixed effects variant of the beta regression model, as discussed in the papers below.

Smithson, M., & Verkuilen, J. (2006). A better lemon squeezer? Maximum likelihood regression with beta-distributed dependent variables. Psychological Methods, 11(1), 54-71. doi:10.1037/1082-989X.11.1.54

Zimprich, D. (2010). Modeling change in skewed variables using mixed beta regression models. Research in Human Development, 7(1), 9-26. doi:10.1080/15427600903578136

Steven J. Pierce, Ph.D.
Associate Director
Center for Statistical Training & Consulting (CSTAT)
Michigan State University

-----Original Message-----
From: Gitu wa Mbui [mailto:gitumbui at gmail.com] 
Sent: Wednesday, December 23, 2015 8:54 PM
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] Distribution family for non-negative lower and upper bound values

I am running generalized additive mixed models on two response variables
separately. Values in response 1 are non-negative and bounded between 1-2,
while response 2 is also non- negative and bounded between 1-3.

In choosing the distribution for response 1, I have subtracted 1 (to
rescale to between 0-1) and logit transformed before fitting the models
with gaussian family.

As for response 2 (non-negative values between 1-3), I have divided the
values by 3 so as to rescale to between 0-1, before logit transforming and
fitting with gaussian family.

Does this sound like a good approach? if not what are the alternatives,
considering:
- responses 1&2 are not proportions
- I am using lme4 version (gamm4) which is limited on the number of
families that can be fit
- histograms of both responses are pretty flat (non skewed and don't look
anywhere near normal distribution

~ Gitu

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