| The mixture regression model discussed in this paper is a situation with mixed data. Specifically, in the observations, some data is from a model, while others from other models. This kind of information is unknown.In the situation of mixture regression, data is from different models. For every linear model, estimating the parameters is essential. Mixture regression model can be treated as a regression and a clustering problem which is seem as model-based clustering. Mixture regression need estimate the parameters in the model when it is a regression problem. How-ever, classifying the observation suitably is also necessary in mixture regression model.Mixture regression model can be solved by EM Algorithm. In fact, when some variable cannot be observed, EM Algorithm is a statistical method for maximizing the likelihood function by iterative method. Classified information is considered as missing variables to use EM algorithm solve mixture regression problem. The EM algorithm for mixture regression model and mixture robust regression are discussed in this paper.We also propose a Fast Iteration Method for solving mixture regression model. Com-pared to the EM algorithm, the proposed method is faster, more flexible and can solve mixture regression model with different error distribution (i.e. Laplace and t distribution). Fast Iteration Method for mixture regression, robust mixture regression and logistic mixture regression are mentioned in this paper.Extensive numeric experiments show our proposed method has better performance on randomly simulations and real data. In the prior of randomly numeric simulation, the Fast Iteration Method for robust mixture regression performs better than EM algorithm when the model error ε obey a Laplace distribution. The real data experiment show the algorithm can solve the outlier problem. At last, we compared the Fast Iteration Method for logistic mixture regression and K-means.Another problem for mixture regression is confirming the quantity of the model. We define the information criterion (AIC and BIC) by treating the information of classifying observations as part of parameters. Compared to BIC, AIC performs better to confirm the quantity of regression model. |
