A fast Monte Carlo expectation–maximization algorithm for estimation in latent class model analysis with an application to assess diagnostic accuracy for cervical neoplasia in women with atypical glandular cells

The expectation–maximization algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The expectation–maximization is best suited for situations where the expectation in each E-step and the maximization in each M-step are straightforward. A difficulty with the implementation of the expectation–maximization algorithm is that each E-step requires the integration of the log-likelihood function in closed form. The explicit integration can be avoided by using what is known as the Monte Carlo expectation–maximization algorithm. The Monte Carlo expectation–maximization uses a random sample to estimate the integral at each E-step. But the problem with the Monte Carlo expectation–maximization is that it often converges to the integral quite slowly and the convergence behavior can also be unstable, which causes computational burden. In this paper, we propose what we refer to as the quantile variant of the expectation–maximization algorithm. We prove that the proposed method has an accuracy of [Formula: see text], while the Monte Carlo expectation–maximization method has an accuracy of [Formula: see text]. Thus, the proposed method possesses faster and more stable convergence properties when compared with the Monte Carlo expectation–maximization algorithm. The improved performance is illustrated through the numerical studies. Several practical examples illustrating its use in interval-censored data problems are also provided.

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A latent class analysis towards stability and changes in breadwinning patterns among coupled households

Dependence Modeling ◽

10.1515/demo-2019-0012 ◽

2019 ◽

Vol 7 (1) ◽

pp. 234-246 ◽

Cited By ~ 2

Author(s):

Fulvia Pennoni ◽

Miki Nakai

Keyword(s):

Latent Variable ◽

Latent Class ◽

Wage Gap ◽

Latent Class Model ◽

Expectation Maximization Algorithm ◽

Information Criteria ◽

Class Model ◽

Missing Responses ◽

Concomitant Variables ◽

Ordinal Variable

AbstractA latent class model is proposed to examine couples’ breadwinning typologies and explain the wage differentials according to the socio-demographic characteristics of the society with data collected through surveys. We derive an ordinal variable indicating the couple’s income provision-role type and suppose the existence of an underlying discrete latent variable to model the effect of covariates. We use a two-step maximum likelihood inference conducted to account for concomitant variables, informative sampling scheme and missing responses. The weighted log-likelihood is maximised through the Expectation-Maximization algorithm and information criteria are used to develop the model selection. Predictions are made on the basis of the maximum posterior probabilities. Disposing of data collected in Japan over thirty years we compare couples’ breadwinning patterns across time. We provide some evidence of the gender wage-gap and we show that it can be attributed to the fact that, especially in Japan, duties and responsibilities for the child care are supported exclusively by women.

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Exact and Monte Carlo calculations of integrated likelihoods for the latent class model

Journal of Statistical Planning and Inference ◽

10.1016/j.jspi.2010.03.042 ◽

2010 ◽

Vol 140 (11) ◽

pp. 2991-3002 ◽

Cited By ~ 16

Author(s):

C. Biernacki ◽

G. Celeux ◽

G. Govaert

Keyword(s):

Monte Carlo ◽

Latent Class ◽

Latent Class Model ◽

Class Model ◽

Monte Carlo Calculations

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Guessing and Forgetting: A Latent Class Model for Measuring Learning

Political Analysis ◽

10.1093/pan/mpw010 ◽

2016 ◽

Vol 24 (2) ◽

pp. 226-242 ◽

Cited By ~ 1

Author(s):

M. Ken Cor ◽

Gaurav Sood

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Gender Gap ◽

Latent Class ◽

Latent Class Model ◽

Political Knowledge ◽

Difference Score ◽

Class Model ◽

Mild Assumption ◽

Simple Difference

Guessing on closed-ended knowledge items is common. Under likely-to-hold assumptions, in the presence of guessing, the most common estimator of learning, difference between pre- and postprocess scores, is negatively biased. To account for guessing-related error, we develop a latent class model of how people respond to knowledge questions and identify the model with the mild assumption that people do not lose knowledge over short periods of time. A Monte Carlo simulation over a broad range of informative processes and knowledge items shows that the simple difference score is negatively biased and the method we develop here is unbiased. To demonstrate its use, we apply our model to data from Deliberative Polls. We find that estimates of learning, once adjusted for guessing, are about 13% higher. Adjusting for guessing also eliminates the gender gap in learning, and halves the pre-deliberation gender gap on political knowledge.

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