Bayesian Analysis of a Growth Curve Model with a General Autoregressive Covariance Structure

Lee, J. C.; Chang, C. H.

doi:10.1111/1467-9469.00217

Cited by 10 publications

(6 citation statements)

References 24 publications

(28 reference statements)

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“…MLE for growth curve models is embedded in commercial statistical packages, such as SAS PROC MIXED and PROC NLMIXED and Splus LME and NLME. Recently, Bayesian methods have received more attention as useful tools for estimating a variety of models including growth curve models, in particular complex growth curve models which can be difficult or impossible to estimate in the current MLE-based software (Lee & Chang, 2000;Lee & Liu, 2000;McArdle & Wang, in press;Menzefricke, 1998;Pettitt, Tran, Haynes, & Hay, 2006;Seltzer, Wong, & Bryk, 1996).…”

Section: Introductionmentioning

confidence: 99%

Bayesian analysis of longitudinal data using growth curve models

Zhang

Hamagami

Wang

et al. 2007

International Journal of Behavioral Development

117

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Bayesian methods for analyzing longitudinal data in social and behavioral research are recommended for their ability to incorporate prior information in estimating simple and complex models. We first summarize the basics of Bayesian methods before presenting an empirical example in which we fit a latent basis growth curve model to achievement data from the National Longitudinal Survey of Youth. This step-by-step example illustrates how to analyze data using both noninformative and informative priors. The results show that in addition to being an alternative to the maximum likelihood estimation (MLE) method, Bayesian methods also have unique strengths, such as the systematic incorporation of prior information from previous studies. These methods are more plausible ways to analyze small sample data compared with the MLE method.

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Section: Introductionmentioning

confidence: 99%

Bayesian analysis of longitudinal data using growth curve models

Zhang

Hamagami

Wang

et al. 2007

International Journal of Behavioral Development

117

View full text Add to dashboard Cite

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“…More specifically, Scheines et al (1999) showed that Bayesian estimation outperforms ML estimation when sample size is small. Lee and Chang (2000) demonstrated that the MCMC algorithm provides a smaller prediction error such as the mean squared deviation and is slightly more efficient with small sample growth data.…”

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confidence: 99%

The Impact of Prior Information on Bayesian Latent Basis Growth Model Estimation

Shi

Tong

2017

SAGE Open

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Latent basis growth modeling is a flexible version of the growth curve modeling, in which it allows the basis coefficients of the model to be freely estimated, and thus the optimal growth trajectories can be determined from the observed data. In this article, Bayesian estimation methods are applied for latent basis growth modeling. Because the latent basis coefficients are important parameters that determine the growth pattern in latent basis growth models, we evaluate the impact of different priors for the basis coefficients on parameter recovery and model estimation. Noninformative priors, informative priors with varying levels of accuracy and precision, and data-dependent priors are considered. In addition, the issue of model specification is treated as a prior selection procedure. The impact of model misspecification and priors for model parameters are investigated simultaneously. A Monte Carlo simulation study is conducted and suggests that misspecified models adversely affect the parameter estimation much more than inaccurate priors. Recommendations on prior selection in latent basis growth models are given based on the simulation results. A real data example on the development of schoolchildren's reading ability is also provided to illustrate the comparison among different sets of priors.

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“…SAS NLMIXED uses maximum likelihood estimation (MLE) and is limited to handling two-level data; Mplus uses MLE, robust weighted least squares, and other methods; and WinBUGS uses Bayesian methods. In particular, complex growth curve models can be difficult or impossible to estimate using current MLE-based software (J. C. Lee & Chang, 2000; J. C. Lee & Liu, 2000;McArdle & Wang, 2006;Menzefricke, 1999;Pettitt, Tran, Haynes, & Hay, 2006;. Bayesian methods have been widely applied in time series contexts and have played a significant role in recent developments in error correction and stochastic volatility models (Congdon, 2003).…”

Section: Level 2 Modelmentioning

confidence: 99%

The Multigroup Multilevel Categorical Latent Growth Curve Models

Hung

2010

Multivariate Behavioral Research

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Longitudinal data describe developmental patterns and enable predictions of individual changes beyond sampled time points. Major methodological issues in longitudinal data include modeling random effects, subject effects, growth curve parameters, and autoregressive residuals. This study embedded the longitudinal model within a multigroup multilevel framework and allowed for autoregressive residuals. The parameter in the new model can be estimated using the computer program WinBUGS, which adopts Markov Chain Monte Carlo algorithms. Two simulation studies were conducted. An empirical example was raised and established based on models generated by the results of empirical data, which have been fitted and compared.

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Bayesian Analysis of a Growth Curve Model with a General Autoregressive Covariance Structure

Cited by 10 publications

References 24 publications

Bayesian analysis of longitudinal data using growth curve models

Bayesian analysis of longitudinal data using growth curve models

The Impact of Prior Information on Bayesian Latent Basis Growth Model Estimation

The Multigroup Multilevel Categorical Latent Growth Curve Models

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