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

[Gitu wa Mbui]

Alain, Steven,

Thanks both for the lead and for the papers. A few clarifications:

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

I assume that you agree with the rescaling approach then? I should have
mentioned that I will be comparing several models  - the ideal package
would be gamm4, however it doesn't fit betar family. (gamm package does but
comparing models is compromised)

*2. AZ>>You could try a beta distribution, which can be used when your data
is between x1 and x2.*

Not sure I understand 'when your data is between x1 and x2'. What does x1
and x2 refer to?

In any case - as recommended in your book - beginners to GAMM, gamm4
package is ideal when comparing models (I have 500 models to compare). This
doesn't fit beta family - is there a workaround?

*3. AZ>>All in all this sounds like an MCMC job. I haven't tried
SabreR...maybe it can do a beta distribution.*

I haven't tried these two before

Kind regards,

Gitu











On Sat, Dec 26, 2015 at 1:57 AM, Steven J. Pierce <pierces1 at msu.edu> wrote:

> 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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