Discrete Latent Variable Models

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Francesco Bartolucci ◽  
Silvia Pandolfi ◽  
Fulvia Pennoni
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Latent Class ◽  
Data Augmentation ◽  
Expectation Maximization Algorithm ◽  
Latent Variable Models ◽  
Annual Review ◽  
Publication Date ◽  
Variable Approach ◽  
Block Models

We review the discrete latent variable approach, which is very popular in statistics and related fields. It allows us to formulate interpretable and flexible models that can be used to analyze complex datasets in the presence of articulated dependence structures among variables. Specific models including discrete latent variables are illustrated, such as finite mixture, latent class, hidden Markov, and stochastic block models. Algorithms for maximum likelihood and Bayesian estimation of these models are reviewed, focusing, in particular, on the expectation–maximization algorithm and the Markov chain Monte Carlo method with data augmentation. Model selection, particularly concerning the number of support points of the latent distribution, is discussed. The approach is illustrated by summarizing applications available in the literature; a brief review of the main software packages to handle discrete latent variable models is also provided. Finally, some possible developments in this literature are suggested. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Latent variable models are network models

2010 ◽  
Vol 33 (2-3) ◽  
pp. 166-166 ◽  
Author(s):  
Peter C. M. Molenaar
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Network Models ◽  
Latent Variable Models ◽  
Variable Theory ◽  
The Relationship

AbstractCramer et al. present an original and interesting network perspective on comorbidity and contrast this perspective with a more traditional interpretation of comorbidity in terms of latent variable theory. My commentary focuses on the relationship between the two perspectives; that is, it aims to qualify the presumed contrast between interpretations in terms of networks and latent variables.

scholarly journals Discrete-Time Survival Mixture Analysis

2005 ◽  
Vol 30 (1) ◽  
pp. 27-58 ◽  
Author(s):  
Bengt Muthén ◽  
Katherine Masyn
Keyword(s):  
Survival Analysis ◽  
Latent Class Analysis ◽  
Discrete Time ◽  
Latent Variables ◽  
Repeated Measures ◽  
Latent Variable ◽  
Latent Class ◽  
Class Analysis ◽  
Special Cases ◽  
Discrete Time Survival Analysis

This article proposes a general latent variable approach to discrete-time survival analysis of nonrepeatable events such as onset of drug use. It is shown how the survival analysis can be formulated as a generalized latent class analysis of event history indicators. The latent class analysis can use covariates and can be combined with the joint modeling of other outcomes such as repeated measures for a related process. It is shown that conventional discrete-time survival analysis corresponds to a single-class latent class analysis. Multiple-class extensions are proposed, including the special cases of a class of long-term survivors and classes defined by outcomes related to survival. The estimation uses a general latent variable framework, including both categorical and continuous latent variables and incorporated in the Mplus program. Estimation is carried out using maximum likelihood via the EM algorithm. Two examples serve as illustrations. The first example concerns recidivism after incarceration in a randomized field experiment. The second example concerns school removal related to the development of aggressive behavior in the classroom.

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

2019 ◽  
Vol 7 (1) ◽  
pp. 234-246 ◽  
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.

scholarly journals Creative Personal Identity and Creative Mindsets, and Their Implications for Creative Potential and Metacognition: A Latent Variable and a Latent Class Approach

2021 ◽  
Vol 8 (2) ◽  
pp. 20-31
Author(s):  
Rogelio Puente-Diaz ◽  
Judith Cavazos-Arroyo
Keyword(s):  
Personal Identity ◽  
Self Efficacy ◽  
Latent Variables ◽  
Latent Variable ◽  
Divergent Thinking ◽  
Latent Class ◽  
Business Students ◽  
Creative Self ◽  
Selection Of ◽  
Creative Mindsets

Abstract The amount of attention given to creative beliefs has increased in recent years. This article suggests that the selection of one´s best ideas from a set of self-generated alternatives should be included as an indicator of metacognition; something known as creative metacognition accuracy. The present investigation examined the role of creative mindsets and creative personal identity on the selection of one´s best idea, creative self-efficacy, and potential, under two conceptualizations of these beliefs: latent variables and latent classes. College business students completed a battery of questionnaires assessing creative mindsets, creative personal identity, and creative self-efficacy. In addition, participants completed a divergent thinking task involving improvement of smartphones an-d were asked to choose their best idea. Two independent judges also selected the best idea from participants’ set of self-generated ideas. Under the latent class conceptualization, a class with high levels of growth mindset and creative personal identity, and low levels of a fixed mindset showed higher levels of accurate idea selection and creative self-efficacy than the rest of the classes. Similarly, under the latent variable conceptualization, creative personal identity had a positive influence on accurate idea selection and creative self-efficacy.

scholarly journals On the curved exponential family in the Stochatic Approximation Expectation Maximization Algorithm

2021 ◽  
Author(s):  
Vianney Debavelaere ◽  
Stéphanie Allassonnière
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Latent Variables ◽  
Latent Variable ◽  
Exponential Family ◽  
Expectation Maximization Algorithm ◽  
Computation Time ◽  
Initial Model ◽  
Joint Likelihood ◽  
Curved Exponential Family

The Expectation-Maximization Algorithm (EM) is a widely used method allowing to estimate the maximum likelihood of  models involving latent variables. When the Expectation step cannot be computed easily, one can use stochastic versions of the EM such as the Stochastic Approximation EM. This algorithm, however, has the drawback to require the joint likelihood to belong to the curved exponential family. To overcome this problem, \cite{kuhn2005maximum} introduced a rewriting of the model which ``exponentializes'' it by considering the parameter as an additional latent variable following a Normal distribution centered on the newly defined parameters and with fixed variance. The likelihood of this new exponentialized model now belongs to the curved exponential family. Although often used, there is no guarantee that the estimated mean is close to the  maximum likelihood estimate of the initial model. In this paper, we quantify the error done in this estimation while considering the exponentialized model instead of the initial one. By verifying those results on an example, we see that a trade-off must be made between the speed of convergence and the tolerated error. Finally, we propose a new algorithm allowing a better estimation of the parameter in a reasonable computation time to reduce the bias.

scholarly journals Causal Effects Based on Latent Variable Models

2019 ◽  
Author(s):  
Axel Mayer
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Structural Equation ◽  
Stochastic Theory ◽  
Latent Variable Models ◽  
Causal Effects ◽  
Equation Modeling ◽  
Differential Effectiveness ◽  
Measurement Models ◽  
Effect Model

Building on the stochastic theory of causal effects and latent state-trait theory, this article shows how a comprehensive analysis of the effectiveness of interventions can be conducted based on latent variable models. The proposed approach offers new ways to evaluate the differential effectiveness of interventions for substantive researchers in experimental and observational studies while allowing for complex measurement models. The key definitions and assumptions of the stochastic theory of causal effects are first introduced and then four statistical models that can be used to estimate various types of causal effects with latent state-trait models are developed and illustrated: The multistate effect model with and without method factors, the true-change effect model, and the multitrait effect model. All effect models with latent variables are implemented based on multigroup structural equation modeling with the EffectLiteR approach. Particular emphasis is placed on the development of models with interactions that allow for interindividual differences in treatment effects based on latent variables. Open source software code is provided for all models.

Risks and Opportunities to Ensure Equity in the Application of Big Data Research in Public Health

2021 ◽  
Vol 43 (1) ◽  
Author(s):  
Paul Wesson ◽  
Yulin Hswen ◽  
Gilmer Valdez ◽  
Kristefer Stojanovski ◽  
Margaret A. Handley
Keyword(s):  
Public Health ◽  
Big Data ◽  
Data Augmentation ◽  
Public Health Research ◽  
Machine Learning Algorithms ◽  
Annual Review ◽  
Publication Date ◽  
Medical Claims ◽  
Marginalized Communities ◽  
Big Data Applications

The big data revolution presents an exciting frontier to expand public health research, broadening the scope of research and increasing the precision of answers. Despite these advances, scientists must be vigilant against also advancing potential harms toward marginalized communities. In this review, we provide examples in which big data applications have (unintentionally) perpetuated discriminatory practices, while also highlighting opportunities for big data applications to advance equity in public health. Here, big data is framed in the context of the five Vs (volume, velocity, veracity, variety, and value), and we propose a sixth V, virtuosity, which incorporates equity and justice frameworks. Analytic approaches to improving equity are presented using social computational big data, fairness in machine learning algorithms, medical claims data, and data augmentation as illustrations. Throughout, we emphasize the biasing influence of data absenteeism and positionality and conclude with recommendations for incorporating an equity lens into big data research. Expected final online publication date for the Annual Review of Public Health, Volume 43 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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