PROC QLIM: Ordered Data Modeling :: SAS/ETS(R) 9.22 User's Guide

The QLIM Procedure

Example 21.1 Ordered Data Modeling

Cameron and Trivedi (1986) studied Australian Health Survey data. Variable definitions are given in Cameron and Trivedi (1998, p. 68).

The dependent variable, dvisits, has nine ordered values. The following SAS statements estimate the ordinal probit model:

/*-- Ordered Discrete Responses --*/
proc qlim data=docvisit;
   model dvisits = sex age agesq income levyplus
                   freepoor freerepa illness actdays hscore
                   chcond1 chcond2 / discrete;
run;

The output of the QLIM procedure for ordered data modeling is shown in Output 21.1.1.

Output 21.1.1 Ordered Data Modeling

Binary Data

The QLIM Procedure

Discrete Response Profile of dvisits
Index	Value	Total Frequency
1	0	4141
2	1	782
3	2	174
4	3	30
5	4	24
6	5	9
7	6	12
8	7	12
9	8	6

Model Fit Summary
Number of Endogenous Variables	1
Endogenous Variable	dvisits
Number of Observations	5190
Log Likelihood	-3138
Maximum Absolute Gradient	0.0003675
Number of Iterations	82
Optimization Method	Quasi-Newton
AIC	6316
Schwarz Criterion	6447

Goodness-of-Fit Measures
Measure	Value	Formula
Likelihood Ratio (R)	789.73	2 * (LogL - LogL0)
Upper Bound of R (U)	7065.9	- 2 * LogL0
Aldrich-Nelson	0.1321	R / (R+N)
Cragg-Uhler 1	0.1412	1 - exp(-R/N)
Cragg-Uhler 2	0.1898	(1-exp(-R/N)) / (1-exp(-U/N))
Estrella	0.149	1 - (1-R/U)^(U/N)
Adjusted Estrella	0.1416	1 - ((LogL-K)/LogL0)^(-2/N*LogL0)
McFadden's LRI	0.1118	R / U
Veall-Zimmermann	0.2291	(R * (U+N)) / (U * (R+N))
McKelvey-Zavoina	0.2036
N = # of observations, K = # of regressors

Parameter Estimates
Parameter	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|
Intercept	1	-1.378705	0.147413	-9.35	<.0001
sex	1	0.131885	0.043785	3.01	0.0026
age	1	-0.534190	0.815907	-0.65	0.5126
agesq	1	0.857308	0.898364	0.95	0.3399
income	1	-0.062211	0.068017	-0.91	0.3604
levyplus	1	0.137030	0.053262	2.57	0.0101
freepoor	1	-0.346045	0.129638	-2.67	0.0076
freerepa	1	0.178382	0.074348	2.40	0.0164
illness	1	0.150485	0.015747	9.56	<.0001
actdays	1	0.100575	0.005850	17.19	<.0001
hscore	1	0.031862	0.009201	3.46	0.0005
chcond1	1	0.061601	0.049024	1.26	0.2089
chcond2	1	0.135321	0.067711	2.00	0.0457
_Limit2	1	0.938884	0.031219	30.07	<.0001
_Limit3	1	1.514288	0.049329	30.70	<.0001
_Limit4	1	1.711660	0.058151	29.43	<.0001
_Limit5	1	1.952860	0.072014	27.12	<.0001
_Limit6	1	2.087422	0.081655	25.56	<.0001
_Limit7	1	2.333786	0.101760	22.93	<.0001
_Limit8	1	2.789796	0.156189	17.86	<.0001

By default, ordinal probit/logit models are estimated assuming that the first threshold or limit parameter ( $\text{[math]}$ ) is 0. However, this parameter can also be estimated when the LIMIT1=VARYING option is specified. The probability that $\text{[math]}$ belongs to the $\text{[math]}$ th category is defined as

$\text{[math]}$

where $\text{[math]}$ is the logistic or standard normal CDF, $\text{[math]}$ and $\text{[math]}$ . Output 21.1.2 lists ordinal probit estimates computed in the following program. Note that the intercept term is suppressed for model identification when $\text{[math]}$ is estimated.

/*-- Ordered Probit --*/
proc qlim data=docvisit;
   model dvisits = sex age agesq income levyplus
                   freepoor freerepa illness actdays hscore
                   chcond1 chcond2 / discrete(d=normal) limit1=varying;
run;

Output 21.1.2 Ordinal Probit Parameter Estimates with LIMIT1=VARYING

Binary Data

The QLIM Procedure

Parameter Estimates
Parameter	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|
sex	1	0.131885	0.043785	3.01	0.0026
age	1	-0.534181	0.815915	-0.65	0.5127
agesq	1	0.857298	0.898371	0.95	0.3399
income	1	-0.062211	0.068017	-0.91	0.3604
levyplus	1	0.137031	0.053262	2.57	0.0101
freepoor	1	-0.346045	0.129638	-2.67	0.0076
freerepa	1	0.178382	0.074348	2.40	0.0164
illness	1	0.150485	0.015747	9.56	<.0001
actdays	1	0.100575	0.005850	17.19	<.0001
hscore	1	0.031862	0.009201	3.46	0.0005
chcond1	1	0.061602	0.049024	1.26	0.2089
chcond2	1	0.135322	0.067711	2.00	0.0457
_Limit1	1	1.378706	0.147415	9.35	<.0001
_Limit2	1	2.317590	0.150206	15.43	<.0001
_Limit3	1	2.892994	0.155198	18.64	<.0001
_Limit4	1	3.090367	0.158263	19.53	<.0001
_Limit5	1	3.331566	0.164065	20.31	<.0001
_Limit6	1	3.466128	0.168799	20.53	<.0001
_Limit7	1	3.712493	0.179756	20.65	<.0001
_Limit8	1	4.168502	0.215738	19.32	<.0001

Top of Page