Abstract
In most regression models, readers have implicitly assumed that the dependent variable (regressand) Y is quantitative. On the contrary, explanatory variables could take the form of qualitative (or dummy), quantitative, or a triangulation thereof. This chapter discusses the observed fundamental differences between quantitative and qualitative models through a clear definition of their individual objectives. This chapter also considers many models in which the regressand is a qualitative variable, popularly called categorical variables, indicator variables, dummy variables, or qualitative variables. This chapter shows why it is not compulsory to restrict our dependent variable to dichotomous (yes/no) categories by establishing inherent benefits in estimating and interpreting trichotomous or polychotomous multiple category response variable. Relevant examples for developing, analyzing, and interpreting a probability model for a binary response variable using three known approaches (i.e. linear probability model, logit, and probit models) is also discussed.
TopLearning Objectives
Understand the differences between quantitative and qualitative regression models.
Understand how to develop, estimate and interpret qualitative response regression models.
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Comprehend the concept of linear probability models (LPM)? And what are its fundamental problems.
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Discuss alternatives to linear probability models.
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Does the conventionally computed R2 have any value in qualitative response regression models?
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Beyond the dichotomous (yes/no) regressand variable, how can researchers estimate and interpret polychotomous multiple regression models?
TopQualitative And Quantitative Dummy Models
Dependent variables in regression analysis is not only influenced by ratio scale constructs (e.g. temperature, height, income etc.) but can also be influenced by variables that are essentially qualitative in nature i.e. nominal scale such as religion, party affiliation, race, sex etc. A good practical example is workers in developed countries are found to earn more than workers in developing countries or educated citizens are found to earn more than the uneducated citizens. Arguably, this type of phenomena may result in discrimination based on nationality or level of education, hence qualitative variables such as nationality and level of education that can influence the regressand should be included among likely regressors.