Logistic and Probit Models

Abstract

In demographic research, we often face situations where the dependent variable of interest is a dichotomy, such as dead or alive, divorced or still in marriage, accept or reject contraception, and so forth. In recent years, logistic regression has been used to study topics as diverse as marital formation and dissolution (Abdelrahman and Morgan, 1987; White, 1987; Trussell and Rao, 1989), contraceptive use (Studer and Thornton, 1987), premarital sexual experience (Newcomer and Udry, 1987), premarital pregnancy (Robbins et al. 1985), childlessness (Rao, 1987a), and spouse abuse (Kalmuss and Seltzer, 1986). These and other studies that have employed logistic regression analysis have something in common—the dichotomous dependent variable. It is relatively easy to create dummy explanatory variables whenever we consider nominal scale variables in the regression model and employ the linear regression procedure available in many standard statistical packages. However, when the dependent variable of consideration is dichotomous, the usual assumptions underlying the linear model are rarely satisfied. The most serious problem arises because predictions may lie outside the (0,1) interval. To circumvent this problem, we have to consider alternative distributional assumptions for which all predictions must lie within the appropriate interval. One immediate solution is to transform the original model so that prediction will be in the (0,1) interval for all X. In attempting transformation, we would like to maintain the property that increases in X are associated with increases (or decreases) in the dependent variable for all values of X (i.e., monotonic transformation). Several cumulative probability functions are possible, but we will consider only two, the logistic and the normal (probit model). Like in any other model fitting, the goal of our analysis using logistic or normal distribution is to find a best-fitting and most parsimonious model that describes the relation between the dependent variable and a set of predictors.