Multinomial Regression Models: An Econometrics Approach

1. CHAPTER 9 MULTINOMIAL REGRESSION MODELS Damodar Gujarati Econometrics by Example

2. MULTINOMIAL REGRESSION MODELS (MRM) • When the individual has to choose among several discrete alternatives, use multinomial regression models (MRM), which assume independence of irrelevant alternatives (IIA). Some examples are: • 1. Transportation choices: Car, bus, railroad, bicycle • 2. Choice of Presidential candidate: Democrat, Republican, or Independent • 3. Choice of education: High school, college, post-graduate • 4. Choice of Job: Do not work, work part time, or work full time • 5. Buying a car: American, Japanese, European Damodar Gujarati Econometrics by Example

3. MULTINOMIAL REGRESSION MODELS (MRM) • Consider the nominal or unordered MRM. • For transportation choice, use the nominal MRM because there is no particular (natural) order among the various options. • Three types of models: • 1. Nominal MRM for chooser-specific data • 2. Nominal MRM for choice-specific data • 3. Nominal MRM for chooser-specific and choice-specific data, or mixed nominal MRM • Chooser represents an individual who has to choose among several alternatives. • Choice represents the alternatives or options that face an individual. Damodar Gujarati Econometrics by Example

4. MULTINOMIAL LOGIT (MLM) OR MULTINOMIAL PROBIT MODELS (MPM) • These models are used for chooser-specific data. • These models answer: How do the choosers’ characteristics affect their choosing a particular alternative among a set of alternatives? • MLM or MPM is suitable when regressors vary across individuals. Damodar Gujarati Econometrics by Example

5. MULTINOMIAL LOGIT (MLM) • Generalize logit model as follows: • Choose a base category and set the coefficients equal to zero. Damodar Gujarati Econometrics by Example

6. MULTINOMIAL LOGIT (CONT.) • Take log of odds ratios and estimate equations simultaneously using maximum likelihood (ML): Damodar Gujarati Econometrics by Example

7. CONDITIONAL LOGIT (CLM) OR CONDITIONAL PROBIT (CPM) MODELS • These models are used for choice-specific data. • These models answer: How do the characteristics or features of various alternatives affect individuals’ choice among them? • CLM or CPM is appropriate when regressors vary across alternatives. Damodar Gujarati Econometrics by Example

8. CONDITIONAL LOGIT MODEL (CLM) • Generalize the logit model as follows: • Unlike with MLM, the coefficients α and β do not vary across choices, yet the added subscript j for an individual varies across the alternatives. • Estimated using maximum likelihood. Damodar Gujarati Econometrics by Example

9. MIXED MRM • Models used when we have data on both chooser-specific and choice-specific characteristics. • Such models can also be estimated by the conditional logit model by adding appropriate dummy variables. • For example, in choosing cars, features of the cars as well as income and age of individuals may affect their choice of car. Damodar Gujarati Econometrics by Example

10. MIXED LOGIT (MXL) • To incorporate subject-specific characteristics in the analysis, MXL proceeds as follows: • Interact the subject-specific variables with the choice-specific characteristics. • Estimate model using CLM. Damodar Gujarati Econometrics by Example