This paper introduces generalized econometric models with selectivity, focusing on models with censored and discrete dependent variables. The author discusses the limitations of traditional models, such as the multinomial probit model, and proposes alternative approaches that allow for more flexible marginal distributions. The paper presents two main approaches: one based on bivariate normal distributions and another based on contingency-type distributions. Both approaches allow for tractable likelihood functions and are suitable for modeling selectivity in econometric models. The first approach involves transforming variables into standard normal variables and using a bivariate normal distribution with specified marginal distributions. This method allows for the derivation of likelihood functions and two-stage estimation procedures. The second approach uses contingency-type distributions, which also allow for tractable likelihood functions and can be used for modeling selectivity. The paper also discusses the two-stage estimation method, which can be applied to models with normal and non-normal marginal distributions. The method involves first estimating the parameters of the selection equation and then using these estimates to estimate the main equation. The paper provides formulas for the asymptotic covariance matrix of the estimates, which are important for inference. The paper also considers multiple-choice models with mixed continuous and discrete dependent variables. These models are more complex than traditional binary choice models and require more sophisticated estimation techniques. The paper discusses the use of the conditional multinomial logit model and the multinomial logit-OLS two-stage method for estimating these models. The paper concludes that the proposed generalized models are more flexible and can be applied to a wider range of econometric problems. The methods presented are computationally tractable and can be used for both binary and multiple-choice models. The paper also highlights the importance of correctly specifying the marginal distributions and the joint distributions of the variables in the model.This paper introduces generalized econometric models with selectivity, focusing on models with censored and discrete dependent variables. The author discusses the limitations of traditional models, such as the multinomial probit model, and proposes alternative approaches that allow for more flexible marginal distributions. The paper presents two main approaches: one based on bivariate normal distributions and another based on contingency-type distributions. Both approaches allow for tractable likelihood functions and are suitable for modeling selectivity in econometric models. The first approach involves transforming variables into standard normal variables and using a bivariate normal distribution with specified marginal distributions. This method allows for the derivation of likelihood functions and two-stage estimation procedures. The second approach uses contingency-type distributions, which also allow for tractable likelihood functions and can be used for modeling selectivity. The paper also discusses the two-stage estimation method, which can be applied to models with normal and non-normal marginal distributions. The method involves first estimating the parameters of the selection equation and then using these estimates to estimate the main equation. The paper provides formulas for the asymptotic covariance matrix of the estimates, which are important for inference. The paper also considers multiple-choice models with mixed continuous and discrete dependent variables. These models are more complex than traditional binary choice models and require more sophisticated estimation techniques. The paper discusses the use of the conditional multinomial logit model and the multinomial logit-OLS two-stage method for estimating these models. The paper concludes that the proposed generalized models are more flexible and can be applied to a wider range of econometric problems. The methods presented are computationally tractable and can be used for both binary and multiple-choice models. The paper also highlights the importance of correctly specifying the marginal distributions and the joint distributions of the variables in the model.