Example of Ordinal Logistic Regression

The manager of a physician's office wants to know which factors influence patient satisfaction. Patients are asked whether they are unlikely, somewhat likely, or very likely to return for follow-up care. Relevant predictors include employment status, age, and proximity to office.

The manager uses how likely a patient is to return as a response variable. The categories in the response variable have a natural order from unlikely to very likely, so the response variable is ordinal. Because the response variable is ordinal, the manager uses ordinal logistic regression to model the relationship between the predictors and the response variable. The manager uses a significance level of 0.05 to assess the statistical significance of the model and the goodness-of-fit of the model.

Open the sample data, PatientSatisfaction.MTW.
Select any cell in the Return Appointment column.
Right-click the worksheet and choose Column Properties > Value Order.
Select User-specified order and arrange the values in this order:
- Very Likely
- Somewhat Likely
- Unlikely
Choose Stat > Regression > Ordinal Logistic Regression.
In Response, enter 'Return Appointment'.
In Model, enter Distance Distance*Distance.
Click OK.

Interpret the results

The p-value for the test that all slopes are zero is less than 0.05. The low p-value indicates that the relationship between the response variable and the predictors is statistically significant. The p-value for both goodness-of-fit tests is greater than 0.05. These high p-values do not provide evidence that the model is inadequate.

In the Logistic regression table, the p-values for Distance and Distance*Distance are both less than the significance level of 0.05. The coefficient for Distance is negative which indicates that generally, patients who live farther from the office are less likely to return for follow-up care. The coefficient for Distance*Distance is positive, which indicates that after a certain distance, patients become more likely to return. Based on these results, the manager theorizes that patients that live close to the office are more to schedule follow-up care because of the convenient office location. Patients who are willing to travel a long distance for an initial appointment are also more likely to return for follow-up care. The manager plans to add new questions to the survey to investigate these ideas. The manager also plans to study the predictions from the model to determine the distance at which patients become more likely to return.

Ordinal Logistic Regression: Return Appointment versus Distance

Link Function: Logit

Response Information

Variable	Value	Count
Return Appointment	Very Likely	19
	Somewhat Likely	43
	Unlikely	11
	Total	73

Logistic Regression Table

						95% CI
Predictor	Coef	SE Coef	Z	P	Odds Ratio	Lower	Upper
Const(1)	6.38671	3.06110	2.09	0.037
Const(2)	9.31883	3.15929	2.95	0.003
Distance	-1.25608	0.523879	-2.40	0.017	0.28	0.10	0.80
Distance*Distance	0.0495427	0.0214636	2.31	0.021	1.05	1.01	1.10

Log-Likelihood = -66.118

Test of All Slopes Equal to Zero

DF	G	P-Value
2	6.066	0.048

Goodness-of-Fit Tests

Method	Chi-Square	DF	P
Pearson	114.903	100	0.146
Deviance	94.779	100	0.629

Measures of Association:

(Between the Response Variable and Predicted Probabilities)

Pairs	Number	Percent	Summary Measures	Value
Concordant	938	62.6	Somers’ D	0.29
Discordant	505	33.7	Goodman-Kruskal Gamma	0.30
Ties	56	3.7	Kendall’s Tau-a	0.16
Total	1499	100.0