# Significance of effects in analysis of ordinal data with cumulative link models

I'm trying to analyse some repeatead measurements where the "dependent" variable is ordinal. As far as I've understood the literature I've read so far the correct way to go is cumulative link mixed models.

The data has independent variables with different lengths for each "session". I'm planning to

a) fit each variable with the ordinal variable with something like:

Y~ measurement value + 1|subject where Y is the ordinal value score, measurement values are continious numeric, Subject is self explainatory. From this I will try to see the dependance/effect between Y and measurement value .

b) After suitably aggregating the measurement variables I'll then try to make a bigger model containing more variables.

Is this a correct strategy? If yes: I plan to use package Ordinal in R. In step a) I've run some dummy models. The outputs from 'clmm()' are like this:

     link  threshold nobs logLik   AIC      niter      max.grad cond.H
logit flexible  4390 -6066.11 12156.21 1370(9263) 9.29e-04 2.9e+05
Random effects:
Groups  Name        Variance Std.Dev.
Period  (Intercept)  3.565   1.888
Subject (Intercept) 10.049   3.170
Number of groups:  Period 5,  Subject 4

Coefficients:
Estimate Std. Error z value Pr(>|z|)
value 0.017104   0.009952   1.719   0.0857 .


The authors of package ordinal state that: "The condition number of the Hessian measures the empirical identifiability of the model. High numbers, say larger than 10^4 or 10^6 indicate that the model is ill defined."clmm vignette

Should I interpret the above statement literaly, ie. a model with cond. Hessain < 10^4 is well defined? How do I evaluate this kind of models?

a) fit each variable with the ordinal variable with something like:

Y~ measurement value + 1|subject where Y is the ordinal value score, measurement values are continious numeric, Subject is self explainatory. From this I will try to see the dependance/effect between Y and measurement value.

b) After suitably aggregating the measurement variables I'll then try to make a bigger model containing more variables.

This seems like a stepwise procedure and would be best avoided. A better approach to variable selection, especially is to choose your variables of interest a priori, giving due consideration to confounding.

Why do you want to aggregate the measurement variables ?

clmm in the ordinal package would be a good place to start. You can also consider MCMCglmm pakcage for a fully Bayesian approach.

Regarding the condition number, if the model has converged without warnings, then everything should be OK, even with a high condition number. Even when it is ill-conditioned, a matrix can still be invertible. The problem is that very small changes to the matrix may make it non-invertible. If the model is taking a long time to converge, or generating warnings/errors and has a high condition number, then you may be able to overcome this by centering and/or rescaling some of the data.

• Thank you for your answer Robert! Unfortunately, I took no part in the experiment design and supposedly all the variables are variables of interest. About the aggregation part: My original post part of "The data has independent variables with different lengths for each "session" was a bit vague. I have variables with different length in each session,from 10 to 200 observations and different data length in each session. Aggregating the data will lead to a more "proper" dataset to work with less or no missing values or so I'm thinking. Jun 20, 2016 at 9:30