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Parameter expansion to accelerate EM: The PXEM algorithm
, 1998
"... The EM algorithm and its extensions are popular tools for modal estimation but are often criticised for their slow convergence. We propose a new method that can often make EM much faster. The intuitive idea is to use a 'covariance adjustment ' to correct the analysis of the M step, capitalising on e ..."
Abstract

Cited by 35 (7 self)
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The EM algorithm and its extensions are popular tools for modal estimation but are often criticised for their slow convergence. We propose a new method that can often make EM much faster. The intuitive idea is to use a 'covariance adjustment ' to correct the analysis of the M step, capitalising on extra information captured in the imputed complete data. The way we accomplish this is by parameter expansion; we expand the completedata model while preserving the observeddata model and use the expanded completedata model to generate EM. This parameterexpanded EM, PXEM, algorithm shares the simplicity and stability of ordinary EM, but has a faster rate of convergence since its M step performs a more efficient analysis. The PXEM algorithm is illustrated for the multivariate t distribution, a random effects model, factor analysis, probit regression and a Poisson imaging model.
Some statistical models and computational methods that may be useful for cognitivelyrelevant assessment
, 1999
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Separable Factor Analysis with Applications to Mortality Data
, 2012
"... Human mortality datasets can be expressed as multiway data arrays, the dimensions of which correspond to categories by which mortality rates are reported, such as age, sex, country and year. Regression models for such data typically assume an independent error distribution, or an error model that al ..."
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Human mortality datasets can be expressed as multiway data arrays, the dimensions of which correspond to categories by which mortality rates are reported, such as age, sex, country and year. Regression models for such data typically assume an independent error distribution, or an error model that allows for dependence along at most one or two dimensions of the data array. However, failing to account for other dependencies can lead to inefficient estimates of regression parameters, inaccurate standard errors and poor predictions. An alternative to assuming independent errors is to allow for dependence along each dimension of the array using a separable covariance model. However, the number of parameters in this model increases rapidly with the dimensions of the array, and for many arrays, maximum likelihood estimates of the covariance parameters do not exist. In this paper, we propose a submodel of the separable covariance model that estimates the covariance matrix for each dimension as having factor analytic structure. This model can be viewed as an extension of factor analysis to arrayvalued data, as it uses a factor model to estimate the covariance along each dimension of the array. We discuss properties of this model as they relate to ordinary factor analysis, describe maximum likelihood and Bayesian estimation methods, and provide a likelihood ratio testing procedure for selecting the factor model ranks. We
Preprint 1 Robust Factor Analysis Using the Multivariate tDistribution
"... Abstract: Factor analysis is a standard method for multivariate analysis. The sampling model in the most popular factor analysis is Gaussian and has thus often been criticized for its lack of robustness. A simple robust extension of the Gaussian factor analysis model is obtained by replacing the mul ..."
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Abstract: Factor analysis is a standard method for multivariate analysis. The sampling model in the most popular factor analysis is Gaussian and has thus often been criticized for its lack of robustness. A simple robust extension of the Gaussian factor analysis model is obtained by replacing the multivariate Gaussian distribution with a multivariate tdistribution. We develop computational methods for both maximum likelihood estimation and Bayesian estimation of the factor analysis model. The proposed methods include the ECME and PXEM algorithms for maximum likelihood estimation and Gibbs sampling methods for Bayesian inference. Numerical examples show that use of multivariate tdistribution improves the robustness for the parameter estimation in factor analysis.