(Ordered) Category specific effects for cumulative ordinal model

[StaffanBetner]

In van der Ark (2001) it is stated that "Moreover, a GRM’s β_{jx} must satisfy the ordering β_{j1} < β_{j2} < ... < β_{jm}" (with reference to Samejima (1969, p. 23), which I think lays out the necessary conditions for category specific effects for a cumulative ordinal model (COM). I think it would be good to separate the current function cs and a function for category specific effects for COMs, since there is no necessary restriction of this type for sequential and adjacent-category models, maybe something like ocs (ordered category specific).

References:

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph Supplement.

Van Der Ark, L. A. (2001). Relationships and Properties of Polytomous Item Response Theory Models. Applied Psychological Measurement, 25(3), 273–282. https://doi.org/10.1177/01466210122032073

[paul-buerkner]

Fair, but how would you enfore this restriction in practice?

[StaffanBetner]

That's a good question. Something similar to monotonic effects maybe? But varying effects are tricky to combine with this restriction.

[StaffanBetner]

Peterson and Harrell (@harrelfe) (1990) calls it an unconstrained partial proportional odds model, see page 5 in the reference. Seems to be implemented in a Bayesian way in the package rmsb.

Peterson, B., & Harrell Jr, F. E. (1990). Partial proportional odds models for ordinal response variables. Journal of the Royal Statistical Society: Series C (Applied Statistics), 39(2), 205-217. http://hbiostat.org/papers/feh/pet90par.pdf
 

[paul-buerkner]

I checked the code of the rmsb package, and it doesn't seem to constrain the category specific effects at all.

I have decided to experimentally allow cs() for cumulative models (with a warning). It the few tests I have run, it seems to work well generally, but unsurprisingly some divergent transitions occur when the chain moves into an invalid space. How much that invalidates the results in this case, I cannot tell at this point.