Tobit Model And Its Application In Study Of The Influnce Of Medical Expenses

Because of the complexity of life phenomena, the dependent variable is partly continuous but has been limited or censored at one or more points in medical study. Thus the value of dependent variable is not right. The dependent variables come into being the censored distribution due to the continuous variable is censored in practice.Because the censored distribution is a mixed distribution of continuous and discrete distribution, those classical regression methods such as least square method can not work well while tobit model is a good alternative to solve this problem when modeling. When the underlying error term for tobit model is known to be normally distributed and homoskedasticity, maximum likelihood estimation is consistent and asymptotically normally distributed. However, it always appears non-normality especially heteroscedasticity in medical study and maximum likelihood estimation is incorrect in these conditions. Semiparametric estimators are hybrids of parametric and nonparametric approaches, more consistent than corresponding parametric models and typically more precise than their nonparametric counterparts. The merit of semiparametric estimation is no restrictions concerning the form of the error distribution or homoskedasticity of the residuals, so robust to heteroskedasticity of unknown form. In is paper, author mostly introduces two semiparametric estimations for tobit model: Symmetrically censored Least Squares and Censored Least Absolute Deviations. When the underlying error term for tobit model is known to be normally distributed and homoskedasticity, simulation study compares estimators for least square regression model, tobit model and truncated regression model and indicate that tobit model is the best as censoring. When heteroskedasticity, author compares maximum likelihood estimation, symmetrically censored least squares and censored least absolute deviations which indicate semiparametric estimation is better than parametric estimation. In medical example part, author analyse the influence of medical expenses on city inhabitants in Taiyuan Shanxi Province in 2004 using tobit model. In China, most researchers analyse the influence of clinical expenses and hospitalization expenses using multiple linear regression, logistic regression and factor analysis and so on.