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Chapter 26 Anderson, C.J, & Rutkowski, L. (2006, accepted). Multinomial logistic regression models. In J. Osborne (ed) Best Practices in Quantitative Methods. Thousand Oaks, CA: Sage.

This work was supported by NSF Grant #0351175 awarded to Anderson, and by the National Center for Supercomputing Applications and the University of Illinois under the auspices of the NCSA/UIUC Faculty Fellows Program and the Bureau of Educational Research in the College of Education at the University of Illinois.

Overview of Chapter:

Chapter 24 presented logistic regression models for dichotomous response variables; however, many discrete response variables have three or more categories (e.g., political view, candidate voted for in an election, preferred mode of transportation, or response options on survey items). Multicategory response variables are found in a wide range of experiments and studies in a variety of different fields. A detailed example presented in this chapter uses data from 600 students from the High School and Beyond study (Tatsuoka & Lohnes, 1988) to look at the differences among high school students who attended academic, general, or vocational programs. The students’ socioeconomic status (ordinal), achievement test scores (numerical), and type of school (nominal) are all examined as possible explanatory variables. An example left to the interested reader using the same data set is to model the students’ intended career where the possibilities consist of 15 general job types (e.g., school, manager, clerical, sales, military, service, etc.). Possible explanatory variables include gender, achievement test scores, and other variables in the data set.

SAS Files for Analyses in the Chapter:

Description of variables in the High School and Beyond data set.

HSB data set with SAS code to create SAS data set.

Simple Models (Table 26.1). Baseline model where mean achievement is the explanatory variable and the separately fit models.

All Main effects with nominal SES (Table 26.2). Baseline model with mean achievement, SES (nominal), and school type as explanatory variables.

Plot fitted probabilities and odds (Figures 26.2 and 26.1)...and a few extra. Baseline model with mean achievement, SES (nominal), and school type as explanatory variables.

All Main effects with ordinal SES (Table 26.3). Baseline model with mean achievement, SES (ordinal), and school type as explanatory variables.

Conditional Multinominal Models (Table 26.4, 26.5, 26.6). This SAS input files shows you how to
- Expand the data files into one with 3 lines of data per student.
- Create indicator variables needed.
- Fit models already fit but fit them as Poisson log-linear models (not reported in the paper).
- Fit the baseline models as conditional multinomial models using PROC MDC (Multionmial Discrete Choice models) to a check that the data set is properly set-up (i.e., get the same results as PROC LOGISTIC).
- Fit model with restrictions on parameters (our "final" model).
- Fit model needed to test whether general and vocational programs are indistinguishable./li>

Hosmer-Lemeshow statistic & regression diagnoistic from PROC LOGISTIC. Briefly mentioned and references given in the chapter. See also SAS documentation to PROC LOGISTIC.

Range of Influence SAS module. Mentioned in the chapter, but not discussed or illustrated. For more information, see Fay, M.P. (2002). Measuring a binary response's range of influence in logistic regression. American Statistican, 56, 5-9.

Problems & solutions (multicolinearity and separation).

Data for Exercises at the End of the Chapter:

Exercise 1:
- Description of variables in the HSB data set.
- HSB data set with SAS code to create SAS data set.
Exercise 2:
- English placement test data. The data are from Lee, H.K. & Anderson, C.J. (2006). Validity and topic generality of a writing performance test. Language Testing, 23, xx-xx.