Applied Regression Models in the Social Sciences

Many dependent variables analyzed in the social sciences are not continuous, but are dichotomous, with a yes/no response. A dichotomous dependent variable takes on only two values; the value 1 represents yes, and the value 0, no. The independent variables in the regression model are then used to predict whether the subjects fall into one of the two dependent variable categories. In this chapter we discuss the modeling of a dichotomous dependent variable and show why ordinary least squares regression is not appropriate. We discuss the logistic regression model. We fit a logistic regression equation and address several statistical concepts and issues: log likelihoods, the likelihood ratio chi-squared statistic, Pseudo R2, model adequacy, and statistical significance. We then discuss the interpretation of logit coefficients, odds ratios, standardized logit coefficients, and standardized odds ratios. We show how to use “margins” in the interpretation of logit models with predicted probabilities. The last sections deal with testing and evaluating nested logit models, and with comparing logit models with probit models.