[R-sig-ME] Mixed model correlation structure for unbalanced longitudinal data

[Andy Flies]

Dear R users,

I have data from a long-term study that has opportunistically collected 
samples over the past 10 years. My data set is highly unbalanced because 
of the opportunistic sample collection.I have a single sample from 19 
individuals, 2 samples from 4 individuals, and 3 samples from 2 
individuals.I know that lmer can accommodate unbalanced data sets, but I 
am unsure if my data set is too unbalanced.

I am testing if social rank, reproductive status, and age affect my 
response variables. I also need to determine if sample collection 
parameters such as sample date and the time from anesthetizing the 
animal to the time the sample was collected affects the response variables.
Here are what I see as potential options:

1)Use a mixed model with subject as random intercept and sample date as 
random slope to account for potential temporal autocorrelation within 
the repeat samples.
Lmer( y ~ 1 + x1 + x2 + x3 + … (1 + date | subject)

2)Use a mixed model with subject as random intercept. Initial data 
exploration does not show any obvious temporal autocorrelation.
Lmer( y ~ 1 + x1 + x2 + x3 + … (1 | subject)

3)Use a GEE and specify an autoregressive correlation structure. I think 
this would be a good option, but from what I have found in the 
literature, my sample size is too small for this.

4)Use the mean for each individual and use a standard linear model. This 
option is not good because it does not allow me to include reproductive 
status as a predictor because reproductive status changes between samples.

5)Use only a single sample from each individual in standard linear 
model. This option is not good because my already limited sample size 
would be further reduced.

Please let me know which of the above options would be best or if you 
can suggest a better option. Any advice or literature references are 
sincerely appreciated.

Thanks,
Andy

-- 
Andy Flies - Ph.D. Candidate
Zoology Department Ecology, Evolutionary Biology, and Behavior (EEBB) 
Program
Michigan State University