[R-sig-ME] Comparing linear and ordinal model random effects

[Stuart Luppescu]

Hello, I have a dataset with outcomes (student grades, A, B, C, D, F)
coded as 4, 3, 2, 1, 0. I did a linear mixed model, and a non-linear
model with ordered categorical outcomes (using MCMCglmm), with teacher
as the random effect.

For the linear model, the random effects were:

Random effects:
 Formula: ~1 | tid
        (Intercept) Residual
StdDev:   0.5644021 1.215661

(or 0.3185 and 1.4778 in squared units)

For the model with ordered categories, the variances were:

G-structure:  ~tid

    post.mean l-95% CI u-95% CI eff.samp
tid    0.4597   0.4426   0.4754     7732

 R-structure:  ~units

      post.mean l-95% CI u-95% CI eff.samp
units         1        1        1        0

The thresholds are:

 Cutpoints: 
                             post.mean l-95% CI u-95% CI eff.samp
cutpoint.traitfinal.points.1    0.9506   0.9459   0.9552     1458
cutpoint.traitfinal.points.2    1.9154   1.9097   1.9216     1092
cutpoint.traitfinal.points.3    2.9882   2.9807   2.9956     1096

It is much more convenient to use the linear model. (I can't even get
MCMCglmm to run with the complete dataset - 2.4 million observations.)
For the linear model the variances are in original score points; the
ordinal model the variances are in probits. I don't know how to convert
from probits to original score points.

Do I have any justification to say that both models result in similar
values for the variances and so it's OK to use the linear model?

-- 
Stuart Luppescu <slu at ccsr.uchicago.edu>
University of Chicago