# Mixed models and normally distributed random effects

I am attempting to analyze some data that includes 10 repeated measurements on 10 different samples. This would normally require using mixed models, and I have attempted to model these using lme in nlme and using glmer in lme4. The problem is that for the majority of these samples, the response curve is a flat line (i.e., slope is zero) due to several samples having all zero values. This means that the random effects are not going to be normally distributed, which is an assumption of mixed models.

I have considered using 0 inflated ZINB models. My understanding is these assume that some of the zeros are false zeros. In my case, all of the zeros are real zeros. Does this negate using ZINB models? Even if it doesn't, I'm not sure this takes care of the normal random effects issue. I tried using glmmadmb to model this data using family = nbinom and zeroInflated = TRUE, but I don't know if this is appropriate given the data. Any input would be greatly appreciated.

• Where did you get the idea that some of the zeroes had to be false? I have not heard this and I believe that it is incorrect. – Peter Flom Apr 10 '13 at 14:14
• Hi, from Zuur 'Mixed Effects Models and Extensions in Ecology with R'. He says... In the count process, the data are modelled with, for example a Poisson GLM... These are true zeros. But there is also a process that generates only false zeros, and these are modelled with a binomial model. Hence, the binomial GLM models the probability of measuring a false negative versus all other types of data (counts and true zeros). – Stephen 123 Apr 10 '13 at 14:29
• A negative binomial (or poisson) distribution can produce large sequences of zeros with a low enough rate parameter. How do you know all of your zeros are "real" (i.e. not the result of a Bernoulli trial prior to, say, a Poisson process)? – ndoogan Apr 10 '13 at 17:19
• I feel that the zeros I'm seeing are the result of processes I'm measuring and interested in as covariates. While it is possible a very small number are due to measurement error, the vast majority are important to understanding effects of the covariates. Getting a zero doesn't mean I've missed something, it means the covariates have acted to reduce the number present. To me, it doesn't seem like these are being determined by a Bernoulli process where chance is acting. However, I could certainly be wrong. – Stephen 123 Apr 10 '13 at 18:36