We consider finite mixtures of generalized linear models with binary output. We prove that cross moments (between the output and the regression variables) up to order three are sufficient to identify all parameters of the model. We propose a least-squares estimation method based on those moments and we prove the consistency and the Gaussian asymptotic behavior of the estimator. We provide simulation results and comparisons with likelihood methods. Numerical experiments were conducted using the R-package morpheus that we developed for our least-squares moment method and with the R-package flexmix for likelihood methods. We then give some possible extensions to finite mixtures of regressions with binary output including both continuous and categorical covariates, and possibly longitudinal data.

中文翻译：

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二元回归混合模型的最小二乘矩识别

我们考虑具有二进制输出的广义线性模型的有限混合。我们证明了高达三阶的交叉矩（输出变量和回归变量之间）足以识别模型的所有参数。我们提出了一种基于这些矩的最小二乘估计方法，并证明了估计器的一致性和高斯渐近行为。我们提供模拟结果并与似然方法进行比较。使用我们为最小二乘矩方法开发的 R-package morpheus 和用于似然方法的 R-package flexmix 进行了数值实验。然后，我们对具有二元输出的回归的有限混合给出了一些可能的扩展，包括连续和分类协变量，以及可能的纵向数据。