Tuesday, September 08, 2009

StereoTypes

"There must be more to life...
Than stereotypes"
So goes the famous song by Blur, but this doesn't ring true for those of us with a keen interest in analysing ordinal outcome variables. According to Mark Lunt (writing for Stata.com), one common approach, known as the Proportional Odds (PO) Model, is implemented in Stata as ordered logit.

If the assumptions of the PO model are not satisfied, an alternative is to treat the outcome as categorical, rather than ordinal, and use multinomial logistic regression in Stata. It is also possible to use Anderson's "Stereotype Ordinal Regression (SOR) Model", which according to Lunt, "can be thought of as imposing ordering constraints on a multinomial model. The multinomial model provides the best possible fit to the data, at the cost of a large number of parameters which can be difficult to interpret. Stereotype regression aims to reduce the number of parameters by imposing constraints, without reducing the adequacy of the fit."

The stereotype approach is also discussed in Scott Long's book on "Regression Models for Categorical Dependent Variables using Stata" (exact page opens up), and in an epidemiology review article by Annath and Kleinbaum which takes a broad look at regression models for ordinal responses. A relevant publication by Mark Lunt (in 'Statistics in Medicine'; 2005) is available here: "Prediction of ordinal outcomes when the association between predictors and outcome differs between outcome levels".

Finally, those with an interest in anchoring vignettes may be interested in this work by Johnson that was published in Psychomatrika less than two years ago: "Discrete Choice Models for Ordinal Response Variables - A Generalization of the Stereotype Model". Johnson discusses the case of the generalized stereotype model, which includes category-specific random effects due to individual differences in response style. "...Unlike standard random utility models the generalized stereotype model is better suited for ordinal response variables and can be interpreted as a kind of unidimensional unfolding model".

2 comments:

Kevin Denny said...

At first glance, it seemed this post was a tribute to wife-swapping. Glad it turned out to be a little more mundane though nonetheless interesting. Its good to have alternatives to the usual multinomial & ordered choice models.

Martin Ryan said...

I'll have to blame Blur for that one Kevin. It's ironic that in this (ordinal outcome) scenario, it's the "stereotype" that is more unusual...