[R-sig-ME] Nested subject-longitudinal logit design

[arun]

Dear R mixed group,

I posted recently regarding inputs for a longitudinal logit model using lme4.  I got some valuable comments from the group.  Still, I have some doubts regarding the random effects in the model.  For e.g., in the model below, I am measuring the binary response (1- insect present in light area, 0- insect present in dark area) as dependent variable, with fixed effects of Wavelength (3 levels) of light applied on insect in a petridish (half-covered with aluminium foil) for a period starting from 1 min to 20 min.  Depending on the starting response (animal present in dark or light zone of petridish at 0 min), there is another factor (Start_Resp - 2 levels - L starting in light zone, D- starting in dark zone).  It was really important to introduce this factor, as the response is drastically different in both levels of the factor for each of the wavelengths.  Since, we are measuring the response every 1 min (0 or 1), for 20 min, time is also a factor with
 20 levels or a covariate.   In the present model, I introduce time as a covariate and extracted deviations for individual measurements as a random effect in "resid".  
BehavdatOrig$resid<-as.factor(1:dim(BehavdatOrig)[1])

(fm<-lmer(Response~Wavelength*Start_Resp*time+(1|resid)+(1+time|Subject), family=binomial,data=BehavdatOrig)

If Wavelength, starting response are fixed effects and time as covariate, I think I can have an interaction term as Wavelength*Start_Resp*time.  But, subjects are not repeated for the experiment.  If I have column called "Rep" (replication) in the dataset for each treatment (another column - Treatment = Combination of Wavelength*Strain*Start_Resp) does it make sense to introduce Subject as nested within Treatment using the  


BehavdatOrig <- within(BehavdatOrig, Subject <- factor(Treatment:Rep)) 


It is an unbalanced dataset with respect to number of replications.  I made a mistake in my previous analysis as I used Subject as replicates which gave me completely different results.  The shrink fit model graph for each subject looks to have small deviations from the population.  In this scenario, should I have to replace this model with quasibinomial model.


 Quasibinomial model with cbind( sum of response for every 5 minute, and 5-response) with this new settings.  For one thing, there is no quasibinomial link function in lmer, still I used binomial link to get results.  Another problem with quasibinomial is that I am not able to get the shrink fit graph with quasibinomal response.  Should be a problem with lattice graph plots.  Any advice on this direction will be appreicated.    


Thanking you,

A.K.


The above fm model provides output as:
Formula: Response ~ Wavelength * Start_Resp * time + (1 | resid) + (1 +      time | Subject) 
   Data: BehavdatOrig 
  AIC  BIC logLik deviance
 1323 1413 -645.7     1291
Random effects:
 Groups  Name        Variance   Std.Dev.   Corr   
 resid   (Intercept) 8.3103e-12 2.8828e-06        
 Subject (Intercept) 1.6026e+01 4.0033e+00        
         time        1.2760e-01 3.5722e-01 -0.552 
Number of obs: 1960, groups: resid, 1960; Subject, 98



I also tried uncorrelated model fma. 


Formula: Response ~ Wavelength * Start_Resp * time + (1 | resid) + (1 |      Subject) + (0 + time | Subject) 
   Data: BehavdatOrig 
  AIC  BIC logLik deviance
 1333 1417 -651.6     1303
Random effects:
 Groups  Name        Variance   Std.Dev.  
 resid   (Intercept) 6.9660e-14 2.6393e-07
 Subject time        1.0964e-01 3.3112e-01
 Subject (Intercept) 1.1732e+01 3.4252e+00
et results:

Anova comparison favors the correlated model:
> anova(fma,fm)
Data: BehavdatOrig
Models:
fma: Response ~ Wavelength * Start_Resp * time + (1 | resid) + (1 | 
fma:     Subject) + (0 + time | Subject)
fm: Response ~ Wavelength * Start_Resp * time + (1 | resid) + (1 + 
fm:     time | Subject)
    Df    AIC    BIC  logLik  Chisq Chi Df Pr(>Chisq)    
fma 15 1333.2 1416.9 -651.57                             
fm  16 1323.4 1412.7 -645.69 11.767      1  0.0006031 ***