| The study on relationship between binary response variable and some explanatory variables about re-sults is a main purpose of logistic regression model. There is no probability distribution can be considered about explanatory variable. And it can be considered for discrete type, continuous type or mixed type. The response variabley={0, 1}(success/failure) usually follows Bernoulli probability distribution, then E(Y)= P(Y=1)=π,0<π<1.The stationary distribution Markov chain to get the sample about π(x) is established by MCM-C(Monte Carlo Markov Chain), to conducted all kinds of statistical inference based of the sample. The Advantage of MCMC is appropriate for wide or difficult problems, and the convergence speed is not re-duced. First, the parameters of multivariate Logistic regression model was estimated by using MCMC method in this paper, and compared results with the estimated result of maximum likelihood estimation. The result showed that:the two methods of model had similar results for the parameter estimation, Max-imum likelihood estimation within MCMC 95% confidence interval for the parameter estimation. the MCMC method is feasible to estimate the parameters, the result is reliable.Second, the classical logistic regression model is appropriate for the problems of binary variable. Due to various nature of imprecise observations, the response variable is often between 0 and 1, no probability distribution can be considered for response variable, error can not be completely regarded as random as-pect. More natural and feasible measure is the response variable was described by some linguistic terms, the response categories is relatively fuzzy state, and bernoulli probability distribution can not be con-sidered for response variable. The probability of success P(Y=1) can not be calculated. Therefore, combined the classical logistic regression model with fuzzy sets theory, a fuzzy logistic regression model of crisp input and fuzzy output data is constructed, the coefficients and outputs are LR type fuzzy num-bers. Considering the possibilities of success instead of the probabilities, the possibilities of success are described by some linguistic terms. Then the distance between two fuzzy numbers is constructed by cut sets. The least squares estimation of fuzzy parameters are obtained in proposed model based on the dis-tance. Finally, application of model to three clinical cases, the capability index of three model estimation results are 0.54,0.46,0.32, showed that the proposed model is effective of an ordinary one. |
