We employ a variety of estimation methods as dictated by the type of outcome variables examined. For the continuous variable measuring the percent of time employed since leaving school, we are able to use ordinary least squares (OLS). For the dichotomous variables alcohol abuse or dependence, used drugs in the past month, ever in poverty between ages 25-29, and ever on welfare between ages 21-33, we employ logistic regressions. In the case of marriage and fertility outcomes, where there are multiple combinations of a single outcome variable, we estimate a multinomial logistic. The variables, "number of years in poverty" and "number of years on welfare," are count variables that are estimated using a negative binomial regression. Finally, to estimate the time since leaving school that is needed to acquire a steady job (lasting at least two years) requires estimating a survivor function which we approximate with the Weibull distribution.
A more detailed description of the estimation methods is included in Appendix A. What is important is the interpretation of the values reported from these regressions. They fall into two categories: marginal effects and odds ratios. We report marginal effects for OLS, negative binomial, and Weibull regressions. For each of these methods, the marginal effect measures the change in the outcome variable for a unit change in an explanatory variable. In the case of a categorical variable, each marginal effect is relative to the effect of an omitted category. For example, we divide age of initiation into four categories. In the regressions, initiation between ages 11-15 is omitted and serves as the reference category.
Odds ratios are reported for logistic and multinomial logistic regressions. Odds ratios measure the relative probability of the estimated outcome among one group relative to the reference group. The choice of reference group is the same across all types of estimations. Odds ratios for multinomial logistics are difficult to interpret because there are multiple equations. As an alternative we create predicted values for each outcome combination for each category of the relevant explanatory variable. Thus, we would have a predicted probability of observing each of the six adult family formation outcomes given each of the four age of initiation categories.