PROC MIXED vs PROC GLIMMIX for REML and Distribution-Specific Model

[vitaaquaticus]

I have a dataset that contains three response variables (density of individuals in a 0.5 m^2 plot, length of the longest individual in the 0.5 m^2 plot, and percent cover of a 0.5 m^2 plot). The sample sizes are very small so I fitted a PROC MIXED statistical model for each response variable with REML and Kenward-Roger correction. I am having troubles finding a way to satisfy the model assumptions with respect to heteroscedasticity and normality. The residual vs predicted mean plot shows a diagonal shape (see photos below) with all of the transformations (log, sqrt, power, etc). I thought if I fit a beta distribution for percent cover and a poisson distribution for density, it might help solve the problem. But the issue is - PROC MIXED does not have the capability to specify a distribution. PROC GLIMMIX does but it does not appear to have the capability to specify REML and Kenward-Roger correction. I am a bit stumped at this point. I am hoping someone can help me on this. Thank you!

Sample Dataset:

data WORK.DATASET2;
  infile datalines dsd truncover;
  input F1:BEST4. Year:$4. Month:$5. Date:MMDDYY10. Cape:$2. Site:$2. Species:$19. Transect:$1. Quadrat:$2. Percent.Cover:BEST12. Density:BEST12. Frond.Length:BEST5. Length_75:32.;
  format F1 BEST4. Date MMDDYY10. Percent.Cover BEST12. Density BEST12. Frond.Length BEST5.;
datalines;
1 2016 May 05/06/2016 CF BB Saccharina sessilis 1 1 30 9 16.5 8.1867769506
2 2016 May 05/06/2016 CF BB Saccharina sessilis 1 2 51 11 26 11.514100371
3 2016 May 05/06/2016 CF BB Saccharina sessilis 1 3 14 5 13 6.846325042
4 2016 May 05/06/2016 CF BB Saccharina sessilis 1 4 3 1 8 4.75682846
5 2016 May 05/06/2016 CF BB Saccharina sessilis 1 5 4 1 2.1 1.7444738796
6 2016 May 05/06/2016 CF BB Saccharina sessilis 1 6 17 4 25.4 11.314237411
7 2016 May 05/06/2016 CF BB Saccharina sessilis 1 7 15 8 14 7.2376241554
8 2016 May 05/06/2016 CF BB Saccharina sessilis 1 8 21 4 23 10.502577066
9 2016 May 05/06/2016 CF BB Saccharina sessilis 1 9 16 5 9.5 5.4111890111
10 2016 May 05/06/2016 CF BB Saccharina sessilis 1 10 24 6 8.9 5.1527907317
11 2016 May 05/06/2016 CF BB Saccharina sessilis 1 11 17 5 2 1.6817928305
12 2016 May 05/06/2016 CF BB Saccharina sessilis 1 12 52 9 18.1 8.7752385459
13 2016 May 05/06/2016 CF BB Saccharina sessilis 1 13 17 2 13.8 7.1599388764
14 2016 May 05/06/2016 CF BB Saccharina sessilis 1 14 30 7 26 11.514100371
15 2016 May 05/06/2016 CF BB Saccharina sessilis 1 15 62 14 33.7 13.986930782
16 2016 May 05/06/2016 CF BB Saccharina sessilis 1 16 30 9 26 11.514100371
17 2016 May 05/06/2016 CF BB Saccharina sessilis 1 17 20 10 16.1 8.0374707792
18 2016 May 05/06/2016 CF BB Saccharina sessilis 1 18 6 3 8 4.75682846
19 2016 May 05/06/2016 CF BB Saccharina sessilis 1 19 10 3 11.1 6.0812412691
20 2016 May 05/06/2016 CF BB Saccharina sessilis 1 20 18 8 2.5 1.9881768219
;;;;

Sample code for Density:

ods graphics on;
PROC MIXED DATA = dataset2 plots(MAXPOINTS=none)=all;
	CLASS Year Month Cape Site Transect Quadrat;
	MODEL 'Density'n = Year Month(Year) Year|Cape/SOLUTION ddfm = KR CL ALPHA=0.05 INTERCEPT;
   RANDOM Quadrat(Transect) Transect(Site) Site(Cape) /CL ALPHA=0.05 TYPE=VC;
    LSMEANS Year|Cape / PDIFF CL ALPHA=0.05;
RUN;
ods graphics off;

[PGStats]

The pattern of residuals vs predicted is problematic. Fix that first. I think your model is overspecified.

Try

Month Year|Cape

instead of 

Year Month(Year) Year|Cape

[vitaaquaticus]

Thanks for the suggestion. I just tried it - it shows a very similar residual vs predicted plot.

[PGStats]

What is cape?

[vitaaquaticus]

Cape is a regional level. Site is a local level. It is like a city within a county. But in this case, a site within a cape.