Trajectory Modeling of Longitudinal Binary Data: Application of the EM Algorithm for Mixture Models

2013 ◽  
Vol 43 (3) ◽  
pp. 495-519 ◽  
Author(s):  
Man-Kee M. Chu ◽  
John J. Koval
2000 ◽  
Vol 21 (8) ◽  
pp. 759-769 ◽  
Author(s):  
Aleix M. Martı́nez ◽  
Jordi Vitrià

2019 ◽  
Vol 8 (5) ◽  
pp. 66
Author(s):  
Balgobin Nandram ◽  
Yuan Yu

In sample surveys with sensitive items, sampled units may not respond or they respond untruthfully. Usually a negative answer is given when it is actually positive, thereby leading to an estimate of the population proportion of positives (sensitive proportion) that is too small. In our study, we have binary data obtained from the unrelated-question design, and both the sensitive proportion and the nonsensitive proportion are of interest. A respondent answers the sensitive item with a known probability, and to avoid non-identifiable parameters, at least two (not necessarily exactly two) different random mechanisms are used, but only one for each cluster of respondents. The key point here is that the counts are sparse (very small sample sizes), and we show how to overcome some of the problems associated with the unrelated question design. A standard approach to this problem is to use the expectation-maximization (EM) algorithm. However, because we consider only small sample sizes (sparse counts), the EM algorithm may not converge and asymptotic theory, which can permit normality assumptions for inference, is not appropriate; so we develop a Bayesian method. To compare the EM algorithm and the Bayesian method, we have presented an example with sparse data on college cheating and a simulation study to illustrate the properties of our procedure. Finally, we discuss two extensions to accommodate finite population sampling and optional responses.


2020 ◽  
Vol 41 ◽  
pp. 101073 ◽  
Author(s):  
Wentao Xiang ◽  
Ahmad Karfoul ◽  
Chunfeng Yang ◽  
Huazhong Shu ◽  
Régine Le Bouquin Jeannès

2021 ◽  
Author(s):  
◽  
Faezeh Frouzesh

<p>The use of mixture models in statistical analysis is increasing for datasets with heterogeneity and/or redundancy in the data. They are likelihood based models, and maximum likelihood estimates of parameters are obtained by the use of the expectation maximization (EM) algorithm. Multi-modality of the likelihood surface means that the EM algorithm is highly dependent on starting points and poorly chosen initial points for the optimization may lead to only a local maximum, not the global maximum. In this thesis, different methods of choosing initialising points in the EM algorithm will be evaluated and two procedures which make intelligent choices of possible starting points and fast evaluations of their usefulness will be presented. Furthermore, several approaches to measure the best model to fit from a set of models for a given dataset, will be investigated and some lemmas and theorems are presented to illustrate the information criterion. This work introduces two novel and heuristic methods to choose the best starting points for the EM algorithm that are named Combined method and Hybrid PSO (Particle Swarm Optimisation). Combined method is based on a combination of two clustering methods that leads to finding the best starting points in the EM algorithm in comparison with the different initialisation point methods. Hybrid PSO is a hybrid method of Particle Swarm Optimization (PSO) as a global optimization approach and the EM algorithm as a local search to overcome the EM algorithm’s problem that makes it independent to starting points. Finally it will be compared with different methods of choosing starting points in the EM algorithm.</p>


2021 ◽  
Author(s):  
Masahiro Kuroda

Mixture models become increasingly popular due to their modeling flexibility and are applied to the clustering and classification of heterogeneous data. The EM algorithm is largely used for the maximum likelihood estimation of mixture models because the algorithm is stable in convergence and simple in implementation. Despite such advantages, it is pointed out that the EM algorithm is local and has slow convergence as the main drawback. To avoid the local convergence of the EM algorithm, multiple runs from several different initial values are usually used. Then the algorithm may take a large number of iterations and long computation time to find the maximum likelihood estimates. The speedup of computation of the EM algorithm is available for these problems. We give the algorithms to accelerate the convergence of the EM algorithm and apply them to mixture model estimation. Numerical experiments examine the performance of the acceleration algorithms in terms of the number of iterations and computation time.


Biometrics ◽  
1988 ◽  
Vol 44 (2) ◽  
pp. 571 ◽  
Author(s):  
G. J. McLachlan ◽  
P. N. Jones

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