Briefly describe the difference between the following models: censored and truncated regression model, count data, ordered responses, and discrete choice data. Try to be specific in terms of describing the data involved

What will be an ideal response?

Answer: The answer should follow the discussion in Appendix 11.3. Briefly: censored regression models have a dependent variable that has been "censored" above or below a certain cutoff, such as in the case where some individuals actually spend different amounts of money on an item, but others do not spend any amount. An example is the tobit regression model. The difference to the truncated regression model is that data is available for both types of individuals, buyers and non-buyers in the case of the censored model, but only for buyers in the case of the truncated regression model. An example for these types of models are expenditures by individuals. There are other examples in economics where sample selection bias occurs, such as in the case of earnings functions (labor economics), industrial organization, and finance. Count data involves a discrete dependent variable, such as the number of times an activity is performed. Just as OLS does not perform well in the discrete dependent variable case, the same holds here, and special methods (Poisson and negative binomial regression models) have been developed to deal with the special format. Ordered response data resembles the count data situation, in that there is a natural ordering. The difference is that there are no natural numerical values attached, such as is the case when activity by individuals happens a discrete number of times during a certain period. The Federal Reserve may decide to lower the federal funds rate or not, and conditionally on lowering it, it may decide on a mild cut or a more severe cut. Ordered Probit Models have been developed for such situations. Finally, discrete choice data also allows for multiple responses, but these are not ordered, such as when the individual can decide on different modes of transportation. In addition to its use in transportation economics, multinomial probit and logit regression models have been developed and applied in labor economics and health economics.