In this chapter, we will survey the elements of estimation, inference, and analysis with the ordered choice model. It will prove useful to develop an application as part of the discussion.

Application of the ordered choice model to self-assessed health status

Riphahn et al. (2003) analyzed individual data on health care utilization (doctor visits and hospital visits) using various models for counts. The data set is an unbalanced panel of 7,293 German households observed from one to seven times for a total of 27,326 observations, extracted from the German Socioeconomic Panel (GSOEP). (See Riphahn et al. (2003) and Greene (2008a) for discussion of the data set in detail.) Among the variables in this data set is HSAT, a self-reported health assessment that is recorded with values 0,1,…,10 (so, J = 10). Figure 5.1 shows the distribution of outcomes for the full sample: The figure reports the variable NewHSAT, not the original variable. Forty of the 27,326 observations on HSAT in the original data were coded with noninteger values between 6.5 and 6.95. We have changed these forty observations to sevens. In order to construct a compact example that is sufficiently general to illustrate the technique, we will aggregate the categories shown as follows: (0–2) = 0, (3–5) = 1, (6–8) = 2, (9) = 3, (10) = 4. (One might expect collapsing the data in this fashion to sacrifice some information and, in turn, produce a less efficient estimator of the model parameters. See Murad et al. (2003) for some analysis of this issue.)