[R-sig-ME] LME - varComb and varIdent

[Friso Muijsers]

Hello,

I'm quite new to LMEs and have a question to which I did not find an 
answer in the archives or in the P&B chapter 5 (allthough I have 
problems undestanding the latter, fully).
Im trying to fit a linear mixed model to my data (DV = numerical, IV = 
numerical and factorial).
I have some issues with variance heterogeneity within two of my factors:

1) experimental type, two levels: "lab" and "field")
2) system, two levels: "marine" and "limnic"

When adding both variance structures to my models, my results differ 
slightly, depending on whether I use "weights = 
varIdent(form=~1|system*exp.type)" or "weights = 
varComb(varIdent(form=~1|exp.type), varIdent(form=~1|system))".
Which approach would be the better one? What does the " * " exactly do? 
It somehow uses one additional df.

                             Model     df      AIC BIC            
logLik               Test       L.Ratio p-value
lmaicresisa         1             14     127.1082     160.2804 -49.55408
lmaicresisb         2             15     128.8289     164.3707 -49.41447 
     1 vs 2      0.279231         0.5972


And a general question: I've seen (read) many people arguing that one 
should not use the varFunc too excessively. With only one varIdent 
Factor, my models have indeed much better p-values (all though I 
understand that those are less relevant in LME) but my AIC and LogLik 
increase. Should I use the more parsimonious model with both variance 
factors (as indicated by AIC) ? Are the low p-values with 2 
var-functions an indication of a bad model? QQ-Plots indicate a slightly 
better model fit with 2 var-functions.

It is difficult to add a nice example here, since my data are relatively 
complex (meta-analysis). If it is necessary, I can try to create a 
comparable dataset, allthough not sure how to.

This is my model:

lmresisc = 
lme(resis.log~evenness+exp.type+exp.type:evenness+org.type.merged+org.type.merged:evenness+system+log(exact.duration)+system2,
                        random =~1|authors.year,
                        data = 
data[(!is.na(data$evenness)&!is.na(data$resis.log)),], weights = 
varIdent(form=~1|system*exp.type), method = "ML")
         summary(lmresisc)
         lmaicresisc = stepAIC(lmresisc)
         summary(lmaicresisc)

This is the last step of the stepAIC:

Step:  AIC=128.83
resis.log ~ evenness + exp.type + org.type.merged + system +
     log(exact.duration) + evenness:exp.type + evenness:org.type.merged

                                                    Df    AIC
<none>                                               128.83
- evenness:exp.type                1       129.38
- system                                    1       132.48
- evenness:org.type.merged  2        133.55
- log(exact.duration)                1        134.20


and this is the summary of the final model

       Value                 Std.Error     DF    t-value p-value
(Intercept) -1.963651         0.6959103     62     -2.8217014  0.0064
evenness                                                   -2.231725     
     1.4724964     62     -1.5156064  0.1347
exp.typelab                                                -0.487326     
     0.9387122       7     -0.5191437  0.6197
org.type.mergedheterotroph                   -2.245062 1.3380510       7 
     -1.6778601  0.1373
org.type.mergedmixed                            -2.494429 1.1662591   
     7     -2.1388289  0.0698
systemmarine                                            0.505430     
0.2204285       7      2.2929430  0.0556
log(exact.duration)                                    0.406731     
0.1536198     62      2.6476456  0.0103
evenness:exp.typelab                               2.295373 1.4621236 
     62      1.5698901  0.1215
evenness:org.type.mergedheterotroph   3.686948         1.6697807 62      
2.2080430  0.0309
evenness:org.type.mergedmixed            5.930363         2.0642291     
62      2.8729191  0.0056


I hope I gave enough information, please forgive me, if not. This is my 
first question here, so i'm not sure about that.
Thanks in advance!

Friso

-- 
Friso Muijsers

Institute for Chemistry and Biology of the Marine Environment (ICBM)
Carl-von-Ossietzky University Oldenburg
Schleusenstrasse 1
26382 Wilhemshaven