scholarly journals A comparison of Bayesian to maximum likelihood estimation for latent growth models in the presence of a binary outcome

2020 ◽  
Vol 44 (5) ◽  
pp. 447-457
Author(s):  
Su-Young Kim ◽  
David Huh ◽  
Zhengyang Zhou ◽  
Eun-Young Mun
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Structural Equation ◽  
Growth Models ◽  
Likelihood Estimation ◽  
Equation Modeling ◽  
Latent Growth ◽  
Ml Estimation ◽  
Parameter Recovery ◽  
Latent Growth Models

Latent growth models (LGMs) are an application of structural equation modeling and frequently used in developmental and clinical research to analyze change over time in longitudinal outcomes. Maximum likelihood (ML), the most common approach for estimating LGMs, can fail to converge or may produce biased estimates in complex LGMs especially in studies with modest samples. Bayesian estimation is a logical alternative to ML for LGMs, but there is a lack of research providing guidance on when Bayesian estimation may be preferable to ML or vice versa. This study compared the performance of Bayesian versus ML estimators for LGMs by evaluating their accuracy via Monte Carlo (MC) simulations. For the MC study, longitudinal data sets were generated and estimated using LGM via both ML and Bayesian estimation with three different priors, and parameter recovery across the two estimators was evaluated to determine their relative performance. The findings suggest that ML estimation is a reasonable choice for most LGMs, unless it fails to converge, which can occur with limiting data situations (i.e., just a few time points, no covariate or outcome, modest sample sizes). When models do not converge using ML, we recommend Bayesian estimation with one caveat that the influence of the priors on estimation may have to be carefully examined, per recent recommendations on Bayesian modeling for applied researchers.

Bayesian Structural Equation Modeling in Sport and Exercise Psychology

2015 ◽  
Vol 37 (4) ◽  
pp. 410-420 ◽  
Author(s):  
Andreas Stenling ◽  
Andreas Ivarsson ◽  
Urban Johnson ◽  
Magnus Lindwall
Keyword(s):  
Structural Equation Modeling ◽  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Bayesian Approach ◽  
Structural Equation ◽  
Equation Modeling ◽  
Exercise Psychology ◽  
Informative Priors ◽  
Sport And Exercise ◽  
Bayesian Structural Equation Modeling

Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.

scholarly journals Study length, change process separability, parameter estimation, and model evaluation in hybrid autoregressive-latent growth structural equation models for longitudinal data

2021 ◽  
pp. 016502542110228
Author(s):  
D. Angus Clark ◽  
Amy K. Nuttall ◽  
Ryan P. Bowles
Keyword(s):  
Longitudinal Data ◽  
Change Process ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Growth Models ◽  
Parameter Estimates ◽  
Latent Growth ◽  
Additional Time ◽  
Latent Growth Models ◽  
Time Points

Hybrid autoregressive-latent growth structural equation models for longitudinal data represent a synthesis of the autoregressive and latent growth modeling frameworks. Although these models are conceptually powerful, in practice they may struggle to separate autoregressive and growth-related processes during estimation. This confounding of change processes may, in turn, increase the risk of the models producing deceptively compelling results (i.e., models that fit excellently by conventional standards despite highly biased parameter estimates). Including additional time points provides models with more raw information about change, which could help improve process separability and the accuracy of parameter estimates to a degree. This study thus used Monte Carlo simulation methods to examine associations between change process separability, the number of time points in a model, and the consequences of misspecification, across three prominent hybrid autoregressive-latent growth models: the Latent Change Score model (LCS), the Autoregressive Latent Trajectory Model (ALT), and the Latent Growth Model with Structured Residuals (LGM-SR). Results showed that including more time points increased process separability and robustness to misspecification in the LCS and ALT, but typically not at a rate that would be practically feasible for most developmental researchers. Alternatively, regardless of how many time points were in the model process separability was high in the LGM-SR, as was robustness to misspecification. Overall, results suggest that the LGM-SR is the most effective of the three hybrid autoregressive-latent growth models considered here.

scholarly journals Pushing the Limits

Methodology ◽  
2019 ◽  
Vol 15 (1) ◽  
pp. 31-43 ◽  
Author(s):  
Mariëlle Zondervan-Zwijnenburg ◽  
Sarah Depaoli ◽  
Margot Peeters ◽  
Rens van de Schoot
Keyword(s):  
Statistical Analysis ◽  
Maximum Likelihood ◽  
Lower Bound ◽  
Bayesian Estimation ◽  
Prior Information ◽  
Latent Growth Modeling ◽  
Effect Sizes ◽  
Latent Growth ◽  
Ml Estimation ◽  
Multiple Group

Abstract. Longitudinal developmental research is often focused on patterns of change or growth across different (sub)groups of individuals. Particular to some research contexts, developmental inquiries may involve one or more (sub)groups that are small in nature and therefore difficult to properly capture through statistical analysis. The current study explores the lower-bound limits of subsample sizes in a multiple group latent growth modeling by means of a simulation study. We particularly focus on how the maximum likelihood (ML) and Bayesian estimation approaches differ when (sub)sample sizes are small. The results show that Bayesian estimation resolves computational issues that occur with ML estimation and that the addition of prior information can be the key to detect a difference between groups when sample and effect sizes are expected to be limited. The acquisition of prior information with respect to the smaller group is especially influential in this context.

Maximum Likelihood Estimation of Nonlinear Structural Equation Models with Ignorable Missing Data

2003 ◽  
Vol 28 (2) ◽  
pp. 111-134 ◽  
Author(s):  
Sik-Yum Lee ◽  
Xin-Yuan Song ◽  
John C. K. Lee
Keyword(s):  
Missing Data ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Latent Variables ◽  
Structural Equation ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Equation Modeling ◽  
Nonlinear Structural ◽  
Nonlinear Structural Equation

The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models and it is very common to encounter missing data. In this article, an EM type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model with ignorable missing data, which are missing at random with an ignorable mechanism. To avoid computation of the complicated multiple integrals involved in the conditional expectations, the E-step is completed by a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm; while the M-step is completed efficiently by conditional maximization. Standard errors of the maximum likelihood estimates are obtained via Louis’s formula. The methodology is illustrated with results obtained from a simulation study and a real data set with rather complicated missing patterns and a large number of missing entries.

Consumer Perceptions of Interpersonal Equity and Satisfaction in Transactions: A Field Survey Approach

1989 ◽  
Vol 53 (2) ◽  
pp. 21-35 ◽  
Author(s):  
Richard L. Oliver ◽  
John E. Swan
Keyword(s):  
Maximum Likelihood ◽  
Structural Equation ◽  
Field Survey ◽  
Likelihood Estimation ◽  
Consumer Perceptions ◽  
Mediating Effect ◽  
Equation Modeling ◽  
Managerial Implications ◽  
The Subject ◽  
Survey Approach

Automobile purchasers were surveyed about feelings toward their inputs to and outcomes from the sales transaction, as well as their perceptions of the inputs and outcomes of the salesperson. Structural equation modeling with maximum likelihood estimation shows two concepts advanced in the equity literature, fairness and preference (advantageous inequity), to be related differentially to input and outcome judgments. No necessary symmetry is observed between the weights attached to inputs and outcomes or between those attached to self and salesperson. When framed in a larger perspective involving satisfaction with the salesperson, the fairness dimension mediates the effect of inputs and outcomes on satisfaction whereas preference does not. The fairness influence is robust against the simultaneous inclusion of disconfirmation in the satisfaction equation. Satisfaction, in turn, is related strongly to the consumer's intention cognitions. The findings suggest that the retail sales transaction may differ in substantive ways from the subject-peer and worker-coworker comparisons in other disciplines and that models of interpersonal satisfaction in the sales transaction should include the mediating effect of the fairness dimension of equity. The managerial implications of these findings are discussed.

scholarly journals APPLICATION OF LATENT GROWTH MODELING ON MOTHER-REPORTED MONITORING

2019 ◽  
Vol 3 (2) ◽  
pp. 1-8
Author(s):  
Ahmad Farooqi
Keyword(s):  
Longitudinal Data ◽  
Growth Model ◽  
Structural Equation ◽  
Growth Models ◽  
Moving Average ◽  
Equation Modeling ◽  
Fit Indices ◽  
Linear Quadratic ◽  
Latent Growth ◽  
Chi Square

One of the basic observation in the social and behavioral sciences is that things are changed over the time. Longitudinal data analysis can yield valuable information about this change. Although many techniques have been developed to capitalize on these desirable features of longitudinal data, the structural equation modeling approach of building latent growth models (LGMs) has become one of the commonly used statistical models. A subset of data is taken from the National Longitudinal Survey 97, prepared by the Bureau of Labor Statistics, U.S. Four waves of mother monitoring reported by youth in the year 1997 to the year 2000 are used for the analysis. A total of 2675 adult respondents are used in our analysis. Mother monitoring scores reported by youth are used as a dependent variable. There are 52% male and 48% female in the data. Different linear, quadratic, autoregressive and moving average LGMs with gender as a covariate are used and compared to study the effects of mother monitoring over a 4 year period of time. It is found mom monitoring is increasing slowly over the period of time. An association was found between slop and intercept of fitted latent growth model and female has a significant effect on slop but not on the intercept of the fitted growth model. Five fit indices Chi-square, GFI, CFI, RMSEA, and AIC are used to select an appropriate model.

scholarly journals Maximum Likelihood for Cross-lagged Panel Models with Fixed Effects

2017 ◽  
Vol 3 ◽  
pp. 237802311771057 ◽  
Author(s):  
Paul D. Allison ◽  
Richard Williams ◽  
Enrique Moral-Benito
Keyword(s):  
Maximum Likelihood ◽  
Fixed Effects ◽  
Structural Equation ◽  
Generalized Method Of Moments ◽  
Equation Modeling ◽  
Ml Estimation ◽  
Panel Models ◽  
Software Packages ◽  
Wide Range ◽  
Dynamic Panel Models

Panel data make it possible both to control for unobserved confounders and allow for lagged, reciprocal causation. Trying to do both at the same time, however, leads to serious estimation difficulties. In the econometric literature, these problems have been solved by using lagged instrumental variables together with the generalized method of moments (GMM). Here we show that the same problems can be solved by maximum likelihood (ML) estimation implemented with standard software packages for structural equation modeling (SEM). Monte Carlo simulations show that the ML-SEM method is less biased and more efficient than the GMM method under a wide range of conditions. ML-SEM also makes it possible to test and relax many of the constraints that are typically embodied in dynamic panel models.

Sign in / Sign up

Export Citation Format

Share Document