Residual analysis in regression mixture model

Miroshnychenko, V. O. (2019). Residual analysis in regression mixture model. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(3), 8–16. https://doi.org/10.17721/1812-5409.2019/3.1

We consider data in which each observed subject belongs to one of different subpopulations (components). The true number of component which a subject belongs to is unknown, but the researcher knows the probabilities that a subject belongs to a given component (concentration of the component in the mixture). The concentrations are different for different observations. So the distribution of the observed data is a mixture of components’ distributions with varying concentrations. A set of variables is observed for each subject. Dependence between these variables is described by a nonlinear regression model. The coefficients of this model are different for different components. An estimator is proposed for these regression coefficients estimation based on the least squares and generalized estimating equations. Consistency of this estimator is demonstrated under general assumptions. A mixture of logistic regression models with continuous response is considered as an example. It is shown that the general consistency conditions are satisfied for this model under very mild assumptions. Performance of the estimator is assessed by simulations and applied for sociological data analysis. Q-Q diagrams are built for visual comparison of residuals’ distributions.Key words: asymptotic behavior, generalized estimation equations, mixture model, non-linear regression, minimax weights, variance estimator.Pages of the article in the issue: 8 - 16Language of the article: Ukrainian