CHAPTER 10 ORDINAL REGRESSION MODELS Damodar Gujarati Econometrics

CHAPTER 10 ORDINAL REGRESSION MODELS Damodar Gujarati Econometrics by Example

ORDINAL REGRESSION MODELS Ø In many applications in the social and medical sciences the discrete response categories are ordered or ranked. Ø In labor market studies, workers can work full time, part time, or not be in the workforce. Ø Corporate bonds are rated as B, B+, A, A++, each higher rating denoting higher credit worthiness. Ø Cannot be treated as interval-scale or ratio-scale variables Ø Cannot say that the difference between full time work and part time work or between part time work and no work is the same. Ø The ratio between any two categories here may not be practically meaningful. Damodar Gujarati Econometrics by Example

ORDERED LOGIT MODEL (OLM) Ø Estimate where there are J ordered alternatives, and a 1 – a(J-1) represent cutoffs or threshold parameters. Ø Gives the (cumulative) probability that Yi falls in a category j and below. Ø The slope coefficients of the X regressors are the same in each category; only their intercepts (cutoffs) differ. That is why OLM are also known as proportional-odds models. Damodar Gujarati Econometrics by Example

ORDERED LOGIT MODEL (CONT. ) Ø The cumulative probabilities are shown as: Ø And the odds ratio is defined as: Ø We end up with the following ordered logit function: Damodar Gujarati Econometrics by Example

ALTERNATIVES TO PROPORTIONAL ODDS MODEL Ø Formal Test of Parallel Regression Lines: Ø The tests, omodel and Brant, developed by Long and Freese, can be used to test the assumption of parallel regression lines (easily downloaded in Stata). Ø If the assumption of parallel regression lines is violated, one alternative is to use the multinomial logit model (MLM) discussed in the previous chapter or other alternatives. Damodar Gujarati Econometrics by Example