Missing the Random Effect : When the Parameter Space Is Expanding

Ru Chen

ISBN 10: 3836434571 / ISBN 13: 9783836434577

Published by VDM Verlag Dr. Müller Feb 2008, 2008

About this Item

Neuware - In this project we look at the case when two of fundamental assumptions in the method of Maximum Likelihood are violated. In particular, we study a special class of misspecified models, where the true modelis a mixed effect model but the working model is a fixed effect model with parameters of dimension increasing with sample size. We provide a sufficient condition under which the MLE derived from the working model converges to a well-defined and asymptotically normally-distributed limit. In linear models, the sample variance is biased; but there exists a robust variance estimator of the MLE that converges to the true variance in probability. We also study the Criterion-based automatic model selection methods and find that they may select a linear model that contains spurious variables, but this can be avoided by using the robust variance estimator for the MLE in Bonferroni-adjusted model section or by choosing lamdan that grows fast enough in Shao`s GIC. In generalized linear models, general results are given and computational and simulation studies are carried out to corroborate asymptotic theoretical results as well as to calculate quantities that are not available in theoretical calculation. We find that when the link function in generalized linear mixed models is correctly specified, the estimated parameters have entries that are close to zero except for those corresponding to the fixed effects in the true model. The estimated variance of the MLE is always smaller than the true variance of the MLE, but the robust `sandwich` variance estimator can estimate the true variance very well, and extra significant variables will appear only when the link function is not correctly specified.

Seller Inventory # 9783836434577

Bibliographic Details

• Title: Missing the Random Effect : When the Parameter Space Is Expanding
• Publisher: VDM Verlag Dr. Müller Feb 2008
• Publication Date: 2008
• Language: English
• ISBN 10: 3836434571
• ISBN 13: 9783836434577
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 24W x 0H x 0D centimeters 24 centimeters width by 0 centimeters height by 0 centimeters depth
• Weight: 1050 grams

About this title

Synopsis

In this project we look at the case when two of fundamental assumptions in the method of Maximum Likelihood are violated. In particular, we study a special class of misspecified models, where the true model is a mixed effect model but the working model is a fixed effect model with parameters of dimension increasing with sample size. We provide a sufficient condition under which the MLE derived from the working model converges to a well-defined and asymptotically normally-distributed limit. In linear models, the sample variance is biased; but there exists a robust variance estimator of the MLE that converges to the true variance in probability. We also study the Criterion-based automatic model selection methods and find that they may select a linear model that contains spurious variables, but this can be avoided by using the robust variance estimator for the MLE in Bonferroni-adjusted model section or by choosing ?n that grows fast enough in Shao's GIC. In generalized linear models, general results are given and computational and simulation studies are carried out to corroborate asymptotic theoretical results as well as to calculate quantities that are not available in theoretical calculation. We find that when the link function in generalized linear mixed models is correctly specified, the estimated parameters have entries that are close to zero except for those corresponding to the fixed effects in the true model. The estimated variance of the MLE is always smaller than the true variance of the MLE, but the robust "sandwich" variance estimator can estimate the true variance very well, and extra significant variables will appear only when the link function is not correctly specified.

About the Author

Ph.D in mathematical statistics fromUnviersity of Maryland at College Park.Lead biostatistician at MannkindCorporation, New Jersey.