Damodar Gujarati

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CHAPTER 9

• MULTINOMIAL REGRESSION MODELS

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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

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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.

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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.

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MULTINOMIAL LOGIT (MLM)

• Generalize logit model as follows
• Choose a base category and set the coefficients
  equal to zero.

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MULTINOMIAL LOGIT (CONT.)

• Take log of odds ratios and estimate equations
  simultaneously using maximum likelihood (ML)

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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.

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CONDITIONAL LOGIT MODEL (CLM)

• Generalize the logit model as follows
• Unlike with MLM, the coefficients a and ß do not
  vary across choices, yet the added subscript j
  for an individual varies across the alternatives.
• Estimated using maximum likelihood.

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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.

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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.