[R] Optimisation and NaN Errors using clm() and clmm()

[Thomas]

Dear List,

I am using both the clm() and clmm() functions from the R package 
'ordinal'.

I am fitting an ordinal dependent variable with 5 categories to 9 
continuous predictors, all of which have been normalised (mean 
subtracted then divided by standard deviation), using a probit link 
function. From this global model I am generating a confidence set of 200 
models using clm() and the 'glmulti' R package. This produces these errors:

/> model.2.10 <- glmulti(as.factor(dependent) ~ 
predictor_1*predictor_2*predictor_3*predictor_4*predictor_5*predictor_6*predictor_7*predictor_8*predictor_9, 
data = database, fitfunc = clm, link = "probit", method = "g", crit = 
aicc, confsetsize = 200, marginality = TRUE)
...
After 670 generations:
Best model: 
as.factor(dependent)~1+predictor_1+predictor_2+predictor_3+predictor_4+predictor_5+predictor_6+predictor_8+predictor_9+predictor_4:predictor_3+predictor_6:predictor_2+predictor_8:predictor_5+predictor_9:predictor_1+predictor_9:predictor_4+predictor_9:predictor_5+predictor_9:predictor_6
Crit= 183.716706496392
Mean crit= 202.022138576506
Improvements in best and average IC have bebingo en below the specified 
goals.
Algorithm is declared to have converged.
Completed.
There were 24 warnings (use warnings() to see them)
 > warnings()
Warning messages:
1: optimization failed: step factor reduced below minimum
2: optimization failed: step factor reduced below minimum
3: optimization failed: step factor reduced below minimum/
etc.


I am then re-fitting each of the 200 models with the clmm() function, 
with 2 random factors (family nested within order). I get this error in 
a few of the re-fitted models:

/> model.2.glmm.2 <- clmm(as.factor(dependent) ~ 1 + predictor_1 + 
predictor_2 + predictor_3 + predictor_6 + predictor_7 + predictor_8 + 
predictor_9 + predictor_6:predictor_2 + predictor_7:predictor_2 + 
predictor_7:predictor_3 + predictor_8:predictor_2 + 
predictor_9:predictor_1 + predictor_9:predictor_2 + 
predictor_9:predictor_3 + predictor_9:predictor_6 + 
predictor_9:predictor_7 + predictor_9:predictor_8+ (1|order/family), 
link = "probit", data = database)
 > summary(model.2.glmm.2)
 >
Cumulative Link Mixed Model fitted with the Laplace approximation

formula: as.factor(dependent) ~ 1 + predictor_1 + predictor_2 + 
predictor_3 + predictor_6 + predictor_7 + predictor_8 + predictor_9 + 
predictor_6:predictor_2 + predictor_7:predictor_2 +
predictor_7:predictor_3 + predictor_8:predictor_2 + 
predictor_9:predictor_1 + predictor_9:predictor_2 +
predictor_9:predictor_3 + predictor_9:predictor_6 + 
predictor_9:predictor_7 + predictor_9:predictor_8 + (1 | order/family)
data: database

link threshold nobs logLik AIC niter max.grad cond.H
probit flexible 103 -65.56 173.13 58(3225) 8.13e-06 4.3e+03

Random effects:
Var Std.Dev
family:order 7.493e-11 8.656e-06
order 1.917e-12 1.385e-06
Number of groups: family:order 12, order 4

Coefficients:
Estimate Std. Error z value Pr(>|z|)
predictor_1 0.40802 0.78685 0.519 0.6041
predictor_2 0.02431 0.26570 0.092 0.9271
predictor_3 -0.84486 0.32056 -2.636 0.0084 **
predictor_6 0.65392 0.34348 1.904 0.0569 .
predictor_7 0.71730 0.29596 2.424 0.0154 *
predictor_8 -1.37692 0.75660 -1.820 0.0688 .
predictor_9 0.15642 0.28969 0.540 0.5892
predictor_2:predictor_6 -0.46880 0.18829 -2.490 0.0128 *
predictor_2:predictor_7 4.97365 0.82692 6.015 1.80e-09 ***
predictor_3:predictor_7 -1.13192 0.46639 -2.427 0.0152 *
predictor_2:predictor_8 -5.52913 0.88476 -6.249 4.12e-10 ***
predictor_1:predictor_9 4.28519 NA NA NA
predictor_2:predictor_9 -0.26558 0.10541 -2.520 0.0117 *
predictor_3:predictor_9 -1.49790 NA NA NA
predictor_6:predictor_9 -1.31538 NA NA NA
predictor_7:predictor_9 -4.41998 NA NA NA
predictor_8:predictor_9 3.99709 NA NA NA
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Threshold coefficients:
Estimate Std. Error z value
0|1 -0.2236 0.3072 -0.728
1|2 1.4229 0.3634 3.915
(211 observations deleted due to missingness)
Warning message:
In sqrt(diag(vc)[1:npar]) : NaNs produced/


I have tried a number of different approaches, each has its own 
problems. I have fixed these using various suggestions from online 
forums (eg 
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/015328.html, 
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q2/016165.html) 
and this is as good as I can get it.

After the first stage (generating the model set with glmulti) I tested 
every model in the confidence set individually - there were no errors - 
but there was clearly a problem during the model selection process. 
Should I be worried?

No errors appear in the top 5% of re-fitted models (which are the only 
ones I will be using) however I am concerned that errors may be 
indicative of a problem with my approach.

A further worry is that the errors might be removing models that could 
otherwise be included.

Any help would be much appreciated.

Tom