scholarly journals Efficient maximum likelihood estimation of multiple membership linear mixed models, with an application to educational value-added assessments

2013 ◽  
Vol 59 ◽  
pp. 13-27 ◽  
Author(s):  
Andrew T. Karl ◽  
Yan Yang ◽  
Sharon L. Lohr
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Mixed Models ◽  
Linear Mixed Models ◽  
Value Added ◽  
Likelihood Estimation ◽  
Educational Value ◽  
Multiple Membership

MAXIMUM LIKELIHOOD ESTIMATION FOR SIMPLEX DISTRIBUTION NONLINEAR MIXED MODELS VIA AN EM ALGORITHM

2009 ◽  
Vol 02 (01) ◽  
pp. 9-17
Author(s):  
HONGJIE WEI ◽  
WENZHUAN ZHANG
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Em Algorithm ◽  
Random Effects ◽  
Mixed Models ◽  
Likelihood Estimation ◽  
Psychological Research ◽  
Nonlinear Mixed Models ◽  
Simplex Distribution ◽  
Intraocular Gas

Longitudinal continuous proportional data is common in many fields such as biomedical research, psychological research and so on. As shown in [16], such data can be fitted with simplex models. Based on the original models of [16] which assumed a fixed effect for every subject, this paper extends the models by adding random effects and proposes simplex distribution nonlinear mixed models which are one kind of nonlinear reproductive dispersion mixed models. By treating the random effects in the models as hypothetical missing data and applying Metropolis–Hastings (M–H) algorithm, this paper develops an EM algorithm with Markov chain Monte–Carlo method for maximum likelihood estimation in the models. The method is illustrated with the same data from an ophthalmology study on the use of intraocular gas in retinal surgeries in [16] for ease of comparison.

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