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4 A binomial dependent variable. In this chapter we focus on the Logit model and the Probit model for binary choice, yielding a binomial dependent variable. In section 4.1 we discuss the model representations and ways to arrive at these specifications. | 4 A binomial dependent variable In this chapter we focus on the Logit model and the Probit model for binary choice yielding a binomial dependent variable. In section 4.1 we discuss the model representations and ways to arrive at these specifications. We show that parameter interpretation is not straightforward because the parameters enter the model in a nonlinear way. We give alternative approaches to interpreting the parameters and hence the models. In section 4.2 we discuss ML estimation in substantial detail. In section 4.3 diagnostic measures model selection and forecasting are considered. Model selection concerns the choice of regressors and the comparison of non-nested models. Forecasting deals with within-sample or out-of-sample prediction. In section 4.4 we illustrate the models for a data set on the choice between two brands of tomato ketchup. Finally in section 4.5 we discuss issues such as unobserved heterogeneity dynamics and sample selection. 4.1 Representation and interpretation In chapter 3 we discussed the standard Linear Regression model where a continuously measured variable such as sales was correlated with for example price and promotion variables. These promotion variables typically appear as 0 1 dummy explanatory variables in regression models. As long as such dummy variables are on the right-hand side of the regression model standard modeling and estimation techniques can be used. However when 0 1 dummy variables appear on the left-hand side the analysis changes and alternative models and inference methods need to be considered. In this chapter the focus is on models for dependent variables that concern such binomial data. Examples of binomial dependent variables are the choice between two brands made by a household on the basis of for example brand-specific characteristics and the decision whether or not to donate to charity. In this chapter we assume that the data correspond to a single crosssection that is a sample of N individuals has .