Expectation–maximization algorithm

About: Expectation–maximization algorithm is a research topic. Over the lifetime, 11823 publications have been published within this topic receiving 528693 citations. The topic is also known as: EM algorithm & Expectation Maximization.

Using EM to Obtain Asymptotic Variance-Covariance Matrices: The SEM Algorithm

Abstract: The expectation maximization (EM) algorithm is a popular, and often remarkably simple, method for maximum likelihood estimation in incomplete-data problems. One criticism of EM in practice is that asymptotic variance–covariance matrices for parameters (e.g., standard errors) are not automatic byproducts, as they are when using some other methods, such as Newton–Raphson. In this article we define and illustrate a procedure that obtains numerically stable asymptotic variance–covariance matrices using only the code for computing the complete-data variance–covariance matrix, the code for EM itself, and code for standard matrix operations. The basic idea is to use the fact that the rate of convergence of EM is governed by the fractions of missing information to find the increased variability due to missing information to add to the complete-data variance–covariance matrix. We call this supplemented EM algorithm the SEM algorithm. Theory and particular examples reinforce the conclusion that the SEM alg...

A counting process approach to maximum likelihood estimation in frailty models

Abstract: We study counting process models for event history data where the intensities depend on unobservable quantities ("frailties"). Examples include models for dependent failure times and regression models with unobservable covariates. Estimation in both parametric and nonor semi-parametric models is performed by maximum likelihood methods using the EM algorithm. Simulations and practical examples are presented.

Maximum Likelihood Estimates for a Multivariate Normal Distribution when Some Observations are Missing

Abstract: S EVERAL authors recently have derived maximum likelihood estimates of parameters of multivariate normal distributions in cases where some observations are missing (Edgett [2] and Lord [3], [4]). The purpose of this note is to give an approach to these problems that indicates the estimates with a minimum of mathematical manipulation; this approach can easily be applied to other cases. (The technique bears some resemblance to that of Cochran and Bliss in a dierent problem [1].) The method will be indicated by treating the simplest case involving a bivariate normal distribution. Suppose x and y have a bivariate normal distribution with means P, and m,u variances ,2 and UY2 and correlation coefficient p. We shall indicate the density by n(x, y|,ux, p,u; 2 a2; p). Suppose n observations are made on the pair (x, y) and N-n observations are made on x; that is, N-n observations on y are missing. The data are

Full-information item bi-factor analysis

Abstract: A plausibles-factor solution for many types of psychological and educational tests is one that exhibits a general factor ands − 1 group or method related factors. The bi-factor solution results from the constraint that each item has a nonzero loading on the primary dimension and at most one of thes − 1 group factors. This paper derives a bi-factor item-response model for binary response data. In marginal maximum likelihood estimation of item parameters, the bi-factor restriction leads to a major simplification of likelihood equations and (a) permits analysis of models with large numbers of group factors; (b) permits conditional dependence within identified subsets of items; and (c) provides more parsimonious factor solutions than an unrestricted full-information item factor analysis in some cases.

Longitudinal Modeling with Randomly and Systematically Missing Data: A Simulation of Ad Hoc, Maximum Likelihood, and Multiple Imputation Techniques

Abstract: For organizational research on individual change, missing data can greatly reduce longitudinal sample size and potentially bias parameter estimates. Within the structural equation modeling framework, this article compares six missing data techniques (MDTs): listwise deletion, pairwise deletion, stochastic regression imputation, the expectation-maximization (EM) algorithm, full information maximization likelihood (FIML), and multiple imputation (MI). The rationale for each technique is reviewed, followed by Monte Carlo analysis based on a threewave simulation of organizational commitment and turnover intentions. Parameter estimates and standard errors for each MDT are contrasted with complete-data estimates, under three mechanisms of missingness (completely random, random, and nonrandom) and three levels of missingness (25%, 50%, and 75%; all monotone missing). Results support maximum likelihood and MI approaches, which particularly outperform listwise deletion for parameters involving many recouped cases....