1. Discrete Choice Modeling William Greene Stern School of Business New York University Lab Sessions

2. Lab Session 6 Ordered Choice Models

3. Data Set Data for this session are healthcare.lpj Refer to healthcare.lim for full list of the variables. This is an unbalanced panel. The group counter is already in the data set. Use ;PDS=_Groupti for panel models

4. Binary Dependent Variables DOCTOR = visited the doctor at least once HOSPITAL = went to the hospital at least once. PUBLIC = has public health insurance (1=YES) ADDON = additional health insurance.(1=Yes) ADDON is extremely unbalanced.

5. Dependent Variables: Ordered HSAT = ordered reported health satisfaction, coded 0,1,…,10. Use with ORDERED or ORDERED ; Logit Request marginal effects with ; Marginal as usual.

6. Ordered Choice Models Ordered ; Lhs = dependent variable ; Rhs = One, … independent variables $ Remember to include the constant term For ordered logit in stead of ordered probit, use Ordered ; Logit ; Lhs = dependent variable ; Rhs = One, … independent variables $ To get marginal effects, use ; Margin as usual. There are fixed and random effects estimators for this model: ; FEM ; PDS = _Groupti ; Random ; PDS = _Groupti

7. Sample Selection in Ordered Choice

8. Sample Selection Ordered Probit PROBIT ; Lhs = … ; Rhs = … ; HOLD $ ORDERED ; Lhs = … ; Rhs = … ; Selection $ This is a maximum likelihood estimator, not a least squares estimator. There is no ‘lambda’ variable. The various parameters are present in the likelihood function.

9. Zero Inflated Ordered Probit

10. Zero Inflated Ordered Probit Model Zero inflated ordered probit model with correlation: A probit model for the zero cell (E.g., You can use DOCTOR for a model.) Create ; y1 = y > 0 $ Probit ; … ; HOLD $ Ordered probit with excess zeros Orde ; Lhs … ; Rhs … ; ZIOP$ Correlation between w (in probit) and ε in ordered probit model ; CORRELATION is optional. Rho=0 is the default.

11. Hierarchical Ordered Probit Hierarchical ordered probit. Ordered probit in which threshold parameters depend on variables. Two forms: HO1: μ(i,j) = exp[θ(j) + δ ’ z(i)]. HO2, different δ vector for each j. Use ORDERED ; … ; HO1 = list of variables or ORDERED ; … ; HO2 = list of variables. Can combine with SELECTION models and zero inflation models. This is also the Pudney and Shields generalized ordered probit from Journal of Applied Econometrics, August 2000, with the modification of using exp( … ) and internally, a way to make sure that the thresholds are ordered..