The Monte Carlo EM method for estimating multinomial probit latent variable models

Xingcai Zhou; Xinsheng Liu

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The Monte Carlo EM method for estimating multinomial probit latent variable models

机译：用于估计多项式概率潜在变量模型的Monte Carlo EM方法

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We propose a multinomial probit (MNP) model that is defined by a factor analysis model with covariates for analyzing unordered categorical data, and discuss its identification. Some useful MNP models are special cases of the proposed model. To obtain maximum likelihood estimates, we use the EM algorithm with its M-step greatly simplified under Conditional Maximization and its E-step made feasible by Monte Carlo simulation. Standard errors are calculated by inverting a Monte Carlo approximation of the information matrix using Louis’s method. The methodology is illustrated with a simulated data.

机译：我们提出了一种由因子分析模型定义的多项式概率模型（MNP），该模型具有用于分析无序分类数据的协变量，并讨论了其识别。一些有用的MNP模型是该模型的特例。为了获得最大似然估计，我们使用了EM算法，该算法的M步在条件最大化下得到了极大简化，而E步通过蒙特卡洛模拟得以实现。标准误差是通过使用路易斯方法对信息矩阵的蒙特卡洛近似求逆来计算的。用模拟数据说明了该方法。

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《Computational Statistics》 |2008年第2期|277-289|共13页
作者
Xingcai Zhou; Xinsheng Liu;
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作者单位

College of Science Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 210016 China;

College of Science Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 210016 China;

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正文语种 eng
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关键词
Multinomial probit model; Latent variable; Maximum likelihood estimates; Monte Carlo EM; Factor analysis;

机译：多项式概率模型;潜在变量;最大似然估计;Monte Carlo EM;因子分析;

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1. The Monte Carlo EM method for estimating multinomial probit latent variable models [J] . Xingcai Zhou, Xinsheng Liu Computational statistics . 2008,第2期

机译：估计多项式概率潜在变量模型的蒙特卡洛EM方法
2. A monte Carlo EM method for estimating multinomial probit models [J] . Ranjini Natarajan, Charles E. McCulloch, Nicholas M. Kiefer Computational statistics & data analysis . 2000,第1期

机译：用于估计多项式概率模型的蒙特卡洛EM方法
3. The Monte Carlo EM method for estimating multivariate tobit latent variable models [J] . X.C. Zhou, X.S. Liu Journal of statistical computation and simulation . 2009,第9a10期

机译：蒙特卡罗EM方法估计多元轨道潜在变量模型
4. W-BASED VS LATENT VARIABLES SPATIAL AUTOREGRESSIVE MODELS: EVIDENCE FROM MONTE CARLO SIMULATIONS [C] . An Liu, Henk Folmer, Han Oud International Society for Photogrammetry and Remote Sensing Commission Technical Commission Symposium . 2010

机译：基于W的VS潜在变量空间自回归模型：来自Monte Carlo模拟的证据
5. Guaranteed adaptive Monte Carlo methods for estimating means of random variables. [D] . Jiang, Lan. 2016

机译：确保随机变量均值的有保证的自适应蒙特卡洛方法。
6. SAF values for internal photon emitters calculated for the RPI-P pregnant-female models using Monte Carlo methods [O] . C. Y. Shi, X. George Xu, Michael G. Stabin -1

机译：使用Monte Carlo方法为RPI-P孕-雌模型计算的内部光子发射器的SAF值
7. Estimating regression coefficients by W-based and latent variables spatial autoregressive models in the presence of spillovers from hotspots: Evidence from Monte Carlo simulations [O] . Liu, A., Folmer, H., Oud, J.H.L. 2011

机译：在热点存在溢出的情况下，基于W和潜在变量的空间自回归模型估算回归系数：蒙特卡洛模拟的证据
8. Estimating System Reliability: Monte Carlo Methods, Sensitivity and Errors in Input Parameters [R] . Fishman, G. S. 1987

机译：估计系统可靠性：蒙特卡罗方法，灵敏度和输入参数误差

The Monte Carlo EM method for estimating multinomial probit latent variable models

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