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Improving the convergence rate and speed of fisher-scoring algorithm: ridge and anti-ridge methods in structural equation modeling

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 2017年第3期69卷 571-597页

作者： Yuan, Ke-Hai Bentler, Peter M. Univ Notre Dame Dept Psychol Notre Dame IN 46556 USA Univ Calif Los Angeles Dept Psychol Los Angeles CA 90095 USA

In structural equation modeling (SEM), parameter estimates are typically computed by the fisher-scoring algorithm, which often has difficulty in obtaining converged solutions. Even for simulated data with a correctly specified model, non-converged replications have been repeatedly reported in the literature. In particular, in Monte Carlo studies it has been found that larger factor loadings or smaller error variances in a confirmatory factor model correspond to a higher rate of convergence. However, studies of a ridge method in SEM indicate that adding a diagonal matrix to the sample covariance matrix also increases the rate of convergence for the fisher-scoring algorithm. This article addresses these two seemingly contradictory phenomena. Using statistical and numerical analyses, the article clarifies why both approaches increase the rate of convergence in SEM. Monte Carlo results confirm the analytical results. Recommendations are provided on how to increase both the speed and rate of convergence in parameter estimation.

关键词： fisher-scoring algorithm Coefficient of variation Condition number Speed of convergence

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A comparison between penalized logistic regressions and classification tree approaches

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2025年

作者： Behzadi, Mostafa Yunus, Rossita Mohamad Mohamad, Saharuddin Bin Hamzah, Nor Aishah Univ Malaya Inst Math Sci Kuala Lumpur 50603 Malaysia Univ Malaya Inst Biol Sci Fac Sci Kuala Lumpur 50603 Malaysia

The penalized models have been established to be necessary for classifying the emerging complex, high-dimensional datasets. One of these penalized models is the "modified elastic-net" (M-Enet). The special cases of M-Enet (ridge, bridge, Lasso, and elastic-net) can be produced based on its penalty function. By using the fact that the fisher-scoring (FS) and Newton-Raphson (NR) algorithms use different approaches to solve numerical problems but are the same in the canonical link, in order to ease implementation, we developed an FS algorithm for the computation of the parameter estimates of the M-Enet. A simulation study of the microbiome as complex, high-dimensional data shows that each special case of the M-Enet penalty function has superiority in the sense of model accuracy, sensitivity, and feature selection technique. A comparison study is performed between the classification of binary responses using M-Enet as a parametric method and the classification tree via "GUIDE" as a non parametric method. The statistical analysis of the numerical results reveals that the special cases of M-Enet models outperform other M-Enet models and GUIDE in terms of average prediction accuracy and sensitivity, with p-values of 0. 0362 and 0. 0214, respectively. Consequently, these models exhibit superior classification performance compared to other classifier models.

关键词： Classification tree complex high-dimensional data fisher-scoring algorithm GUIDE Lasso modified elastic-net penalized models ridge method

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Testing for positive association in contingency tables with fixed margins

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2004年第1期47卷 195-210页

作者： Bartolucci, F Scaccia, L Univ Urbino Dipartimento Econ I-61029 Urbino Italy Univ Perugia Dipartimento Sci Stat I-06100 Perugia Italy Univ Urbino Dipartimento Econ I-61029 Urbino Italy

An exact conditional approach is developed to test for certain forms of positive association between two ordinal variables (e.g. positive quadrant dependence, total positivity of order 2). The approach is based on the use of a test statistic measuring the goodness-of-fit of the model formulated according to the type of positive association of interest. The nuisance parameters, corresponding to the marginal distributions of the two variables, are eliminated by conditioning the inference on the observed margins. This, in turn, allows to remove the uncertainty on the conclusion of the test, which typically arises in the unconditional context where the null distribution of the test statistic depends on such parameters. Since the multivariate generalized hypergeometric distribution, which results from conditioning, is normally intractable, Markov chain Monte Carlo methods are used to obtain maximum likelihood estimates of the parameters of the constrained model. The Pearson's chi-squared statistics is used as a test statistic;a p-value for this statistic is computed through simulation, when the data are sparse, or exploiting the asymptotic theory based on the chi-bar squared distribution. The extension of the present approach to deal with bivariate contingency tables, stratified according to one or more explanatory discrete variables, is also outlined. Finally, three applications based on real data are presented. (C) 2003 Elsevier B.V. All rights reserved.

关键词： chi-bar squared distribution conditional inference fisher-scoring algorithm fisher's exact test Markov chain Monte Carlo Pearson's chi-squared statistic

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Generalized estimating equations (GEE) for mixed logistic models

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2003年第4期32卷 851-874页

作者： Feddag, ML Grama, I Mesbah, M Univ S Brittany Dept Appl Stat SABRES F-5600 Vannes France Univ Sci & Technol Algiers Algeria

In this article, the problem of estimating the fixed effects parameters and the variance components in logistic mixed models, is considered. W is well known that estimating these parameters by the method of maximum likelihood faces computational difficulties. As an alternative, we propose the Generalized Estimating Equations approach (denoted, GEE) defined by Liang and Zeger. The estimators obtained are consistent and asymptotically normal. We illustrate this method with simulations and with an analysis of real data in quality of life.

关键词： generalized linear mixed model logistic model Generalized Estimating Equations fisher-scoring algorithm Rasch model

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Exponential progressive step-stress life-testing with link function based on Box-Cox transformation

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2008年第8期138卷 2340-2354页

作者： Fan, Tsai-Hung Wang, Wan-Lun Balakrishnan, N. Natl Cent Univ Grad Inst Stat Jhongli 32001 Taiwan McMaster Univ Dept Math & Stat Hamilton ON Canada

in order to quickly extract information on the life of a product, accelerated life-tests are usually employed. In this article, we discuss a k-stage step-stress accelerated life-test with M-stress variables when the underlying data are progressively Type-I group censored. The life-testing model assumed is an exponential distribution with a link function that relates the failure rate and the stress variables in a linear way under the Box-Cox transformation, and a cumulative exposure model for modelling the effect of stress changes. The classical maximum likelihood method as well as a fully Bayesian method based on the Markov chain Monte Carlo (MCMC) technique is developed for inference on all the parameters of this model. Numerical examples are presented to illustrate all the methods of inference developed here, and a comparison of the ML and Bayesian methods is also carried out. (C) 2007 Elsevier B.V. All rights reserved.

关键词： step-stress test accelerated life-testing maximum likelihood estimates Bayesian inference fisher-scoring algorithm Markov chain Monte Carlo cumulative exposure model Box-Cox transformation progressive censoring link function

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MODELLING ZERO-INFLATED COUNT DATA WITH A SPECIAL CASE OF THE GENERALISED POISSON DISTRIBUTION

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ASTIN BULLETIN 2019年第3期49卷 689-707页

作者： Calderin-Ojeda, Enrique Gomez-Deniz, Emilio Barranco-Chamorro, Inmaculada Univ Melbourne Ctr Actuarial Studies Dept Econ Melbourne Vic 3010 Australia Univ Las Palmas Gran Canaria Dept Quantitat Methods Las Palmas Gran Canaria 35017 Spain Univ Las Palmas Gran Canaria Inst Tourism & Sustainable Econ Dev TIDES Las Palmas Gran Canaria 35017 Spain Univ Seville Fac Matemat Dept Matemat & RO E-41012 Seville Spain

A one-parameter version of the generalised Poisson distribution provided by Consul and Jain (1973) is considered in this paper. The distribution is uni- modal with a zero vertex and over-dispersed. A generalised linear model related to this distribution is also presented. Its parameters can be estimated by using a fisher-scoring algorithm which is equivalent to iteratively reweighted least squares. Due to its flexibility and capacity to describe highly skewed data with an excessive number of zeros, the model is suitable to be applied in insurance settings as an alternative to the negative binomial and zero-inflated model.

关键词： Zero-inflated count data generalised linear models generalised Poisson distribution automobile insurance fisher-scoring algorithm randomised quantile residuals

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Generalized estimating equations for longitudinal mixed Rasch model

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2005年第1-2期129卷 159-179页

作者： Feddag, ML Mesbah, M Univ S Brittany Lab SABRES F-56000 Vannes France Univ S Brittany UFR SSI F-56000 Vannes France

In this paper, the problem of estimating the fixed effects parameters and the variance of the random effects (variance components) in longitudinal mixed Rasch model is considered. It is well known that estimating these parameters by the method of maximum likelihood faces computational difficulties. As an alternative, we propose the generalized estimating equations approach. Approximations of the joint moments of the variables are proposed. The estimators obtained are consistent and asymptotically normal. We illustrate the usefulness of the method with simulations and with an analysis of real data from quality of life. (C) 2004 Elsevier B.V. All rights reserved.

关键词： IRT models Rasch model generalized linear mixed model fixed effects random effects generalized estimating equations longitudinal data fisher-scoring algorithm quality of life

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Matrix-variate Lindley distributions and its applications

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BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS 2021年第4期35卷 721-748页

作者： Tounsi, Mariem Zitouni, Mouna Sfax Natl Engn Sch Comp Engn & Appl Math Dept BP 1173 Sfax 3038 Tunisia Sfax Fac Sci Appl Math Dept BP 802 Sfax 3038 Tunisia

Restring on the fact that the definition of multivariate analogs of the real gamma distribution is replaced by the Wishart distribution on symmetric matrices, and based on the notion of mixture models which is a flexible and powerful tool for treating data taken from multiple subpopulations, we set forward a multivariate analog of the real Lindley distributions of the first and second kinds on the modern framework of symmetric cones which can be used to model waiting and survival times matrix data. Within this framework, we first construct a new probability distributions, named the matrix-variate Lindley distributions. Some fundamental properties of these new distributions are established. Their statistical properties including moments, the coefficient of variation, skewness and the kurtosis are discussed. We then create an iterative hybrid Expectation-Maximization fisher-scoring (EM-FS) algorithm to estimate the parameters of the new class of probability distributions. Through simulation as well as comparative studies with respect to the Wishart distribution, the effectiveness and reliability of the proposed distributions are proved. Finally, the usefulness and the applicability of the new models are elaborated and illustrated by means of two real data sets from biological sciences and medical image segmentation which is one of the most important and popular tasks in medical image analysis.

关键词： Lindley probability distribution Wishart probability distribution mixture models Expectation-Maximization algorithm fisher-scoring algorithm

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Fast Calculation of Restricted Maximum Likelihood Methods for Unstructured High-throughput Data 2

Fast Calculation of Restricted Maximum Likelihood Methods fo...

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2017 IEEE 2nd International Conference on Big Data Analysis（ICBDA 2017）

作者： Shengxin Zhu Department of Mathematics Xi'an Jiaotong-Liverpool University Laboratory of Computational PhysicsInstitute of Applied Physics and Computational Mathematics

ISBN: (纸本)9781509036202

Linear mixed models are often used for analysing unbalanced data with certain missing values in a broad range of *** restricted maximum likelihood method is often preferred to estimate co-variance parameters in such models due to its unbiased estimation of the underlying variance *** restricted log-likelihood function involves log determinants of a complicated co-variance matrix which are computational *** efficient statistical estimate of the underlying model parameters and quantifying the accuracy of the estimation requires the observed or the fisher information *** approaches to compute the observed and fisher information matrix are computationally *** algorithms are of highly demand to keep the restricted log-likelihood method scalable for increasing high-throughput unbalanced data *** this paper,we explore how to leverage an information splitting technique and dedicate matrix transform to significantly reduce *** with a fill-in reducing multi-frontal sparse direct solvers,this approach improves performance of the computation process.

关键词： linear mixed model restricted log-likelihood unbalanced data fisher-scoring algorithm multi-frontal factorization fill-in reducing algorithm

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Factorial experimental designs and generalized linear models

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SORT 2005年第2期29卷 249-268页

作者： Dossou-Gbete, S. Tinsson, W. Université de Pau et des Pays de l'Adour France Université de Pau et des Pays de l'Adour Laboratoire de Mathématiques Appliquées avenue de 1'Université 64000 Pau France

This paper deals with experimental designs adapted to a generalized linear model. We introduce a special link function for which the orthogonality of design matrix obtained under Gaussian assumption is preserved. We i... 详细信息

关键词： Exponential family Factorial designs fisher-scoring algorithm Generalized linear model Regular fraction

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