Identifiability in Generalized Linear Models with Random Effects

Document Type : Original Paper


Department of Statistics , Shahid Beheshti University


Identifiablity is a necessary property for the adequacy of a statistical model‎. ‎When a model is not identifiable‎, ‎no amount of data cannot determine true parameter‎. ‎In this article‎, ‎well-known concept of identifiablity and it’s properties is reviewed‎. ‎Moreover‎, ‎since non-identifiablity problem in linear mixed effects models and generalized linear models with random effects is very common‎, ‎our main focus is on these models‎. ‎On the other hand‎, ‎statistical software‎, ‎after fitting non-identifiable models‎, ‎don’t usually indicate the problem and show invalid outputs‎. ‎Consequently‎, ‎it is useful to have a way to check model identifiability before fitting. In this regard‎, ‎some new theorems to check identifiability in generalized linear models with random effects are presented‎. ‎data from non-identifiable models are simulated and problems with model non-identifiablity are listed for showing advantages of the mentioned theorems.‎


Main Subjects

[1] Shao‎, ‎J‎. ‎(2003)‎. Mathematical Statistics (2nd ed.),. Springer‎.
‎[2] West‎, ‎B.‎, ‎Welch‎, K.B. ‎and ‎Galecki, A. T. (2007)‎. Linear Mixed Models: A Practical Guide Using StatisticalSoftware. NewYork‎: ‎Chapman & Hall‎, ‎CRC‎.
‎[3] Demidenko‎, ‎E‎. ‎(2004)‎. Mixed Models: Theory and Applications. John Wiley & Sons‎.
[4] Verbeke‎, ‎G‎. ‎and Molenberghs, G. (2009)‎. Linear Mixed Model for Longitudinal Data. Springer‎.
[5] Littell‎, ‎R. C.‎, ‎Henry‎, P. R. ‎and ‎Ammerman, C. B. (1998)‎. Statistical analysis of repeated measures data using sas procedures. Journal of Animal Science, 76, 1216-1231.
‎[6] Pinheiro‎, ‎J‎. ‎and Bates, D. (2009)‎. Mixed-Effects Models in S and S-PLUS. Springer‎.
‎[7] Wolfinger‎, ‎R‎. ‎(1993)‎. Covariance structure selection in general mixed models‎. Communications in Statistics: Simulation andComputation, 22(4)‎, ‎1079-1106‎.
‎[8] Wang‎, ‎W‎. ‎(2013)‎. Identifiability of linear mixed effects models. Electronic Journal of Statistics, 7, 244–263‎.
‎[9] San Martin‎, ‎E‎. ‎and Quintana, E. (2002)‎. Consistency and identifiability revisited‎. Brazilian Journal of Probability and Statistics, 16, ‎99–106‎.
[10] ‎Christensen‎, ‎R‎. ‎(2011).1‎ Plane Answers to Complex Questions‎: ‎The Theory of LinearModels (Fourth ed.)‎. Springer‎.
‎[11] Agresti‎, ‎A‎. ‎(2002)‎. Categorical Data Analysis‎, ‎p‎. ‎133‎. John Wiley & Sons‎.
[12] طهماسبی‌نژاد، ژاله (1390). ‌بررسی مدل‌های همبسته آمیخته با پاسخ‌های پیوسته و گسسته دودویی. پایان‌نامه کارشناسی ارشد, دانشگاه علم و صنعت ایران، تهران.
[13] قهرودی, زهرا رضایی (1387). کاربردهای مدل‌های انتقالی برای تحلیل داده‌های طولی با پاسخ رسته‌ای با و بدون مقادیر گم‌شده، پایان‌نامه دکترا، دانشگاه شهید بهشتی، تهران.
Volume 4, Issue 2 - Serial Number 2
October 2014
Pages 49-69
  • Receive Date: 09 October 2014
  • Revise Date: 01 July 2015
  • Accept Date: 13 October 2015
  • First Publish Date: 23 October 2015