### Abstract

Growth curve modeling provides a general framework for analyzing longitudinal data from social, behavioral, and educational sciences. Bayesian methods have been used to estimate growth curve models, in which priors need to be specified for unknown parameters. For the covariance parameter matrix, the inverse Wishart prior is most commonly used due to its proper and conjugate properties. However, many researchers have pointed out that the inverse Wishart prior might not work as expected. The purpose of this study is to investigate the influence of the inverse Wishart prior and compare it with a class of separation-strategy priors on the parameter estimates of growth curve models. In this article, we illustrate the use of different types of priors with 2 real data analyses, and then conduct simulation studies to evaluate and compare these priors in estimating both linear and nonlinear growth curve models. For the linear model, the simulation study shows that both the inverse Wishart and the separation-strategy priors work well for the fixed effects parameters. For the Level 1 residual variance estimate, the separation-strategy prior performs better than the inverse Wishart prior. For the covariance matrix, the results are mixed. Overall, the inverse Wishart prior is suggested if the population correlation coefficient and at least 1 of the 2 marginal variances are large. Otherwise, the separation-strategy prior is preferred. For the nonlinear growth curve model, the separation-strategy priors work better than the inverse Wishart prior.

Original language | English (US) |
---|---|

Journal | Structural Equation Modeling |

DOIs | |

State | Accepted/In press - Sep 20 2015 |

### Fingerprint

### Keywords

- Bayesian estimation
- covariance matrix
- growth curve models
- inverse Wishart prior
- separation-strategy prior

### ASJC Scopus subject areas

- Modeling and Simulation
- Decision Sciences(all)
- Economics, Econometrics and Finance(all)
- Sociology and Political Science

### Cite this

**Comparison of Inverse Wishart and Separation-Strategy Priors for Bayesian Estimation of Covariance Parameter Matrix in Growth Curve Analysis.** / Liu, Haiyan; Zhang, Zhiyong; Grimm, Kevin.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Comparison of Inverse Wishart and Separation-Strategy Priors for Bayesian Estimation of Covariance Parameter Matrix in Growth Curve Analysis

AU - Liu, Haiyan

AU - Zhang, Zhiyong

AU - Grimm, Kevin

PY - 2015/9/20

Y1 - 2015/9/20

N2 - Growth curve modeling provides a general framework for analyzing longitudinal data from social, behavioral, and educational sciences. Bayesian methods have been used to estimate growth curve models, in which priors need to be specified for unknown parameters. For the covariance parameter matrix, the inverse Wishart prior is most commonly used due to its proper and conjugate properties. However, many researchers have pointed out that the inverse Wishart prior might not work as expected. The purpose of this study is to investigate the influence of the inverse Wishart prior and compare it with a class of separation-strategy priors on the parameter estimates of growth curve models. In this article, we illustrate the use of different types of priors with 2 real data analyses, and then conduct simulation studies to evaluate and compare these priors in estimating both linear and nonlinear growth curve models. For the linear model, the simulation study shows that both the inverse Wishart and the separation-strategy priors work well for the fixed effects parameters. For the Level 1 residual variance estimate, the separation-strategy prior performs better than the inverse Wishart prior. For the covariance matrix, the results are mixed. Overall, the inverse Wishart prior is suggested if the population correlation coefficient and at least 1 of the 2 marginal variances are large. Otherwise, the separation-strategy prior is preferred. For the nonlinear growth curve model, the separation-strategy priors work better than the inverse Wishart prior.

AB - Growth curve modeling provides a general framework for analyzing longitudinal data from social, behavioral, and educational sciences. Bayesian methods have been used to estimate growth curve models, in which priors need to be specified for unknown parameters. For the covariance parameter matrix, the inverse Wishart prior is most commonly used due to its proper and conjugate properties. However, many researchers have pointed out that the inverse Wishart prior might not work as expected. The purpose of this study is to investigate the influence of the inverse Wishart prior and compare it with a class of separation-strategy priors on the parameter estimates of growth curve models. In this article, we illustrate the use of different types of priors with 2 real data analyses, and then conduct simulation studies to evaluate and compare these priors in estimating both linear and nonlinear growth curve models. For the linear model, the simulation study shows that both the inverse Wishart and the separation-strategy priors work well for the fixed effects parameters. For the Level 1 residual variance estimate, the separation-strategy prior performs better than the inverse Wishart prior. For the covariance matrix, the results are mixed. Overall, the inverse Wishart prior is suggested if the population correlation coefficient and at least 1 of the 2 marginal variances are large. Otherwise, the separation-strategy prior is preferred. For the nonlinear growth curve model, the separation-strategy priors work better than the inverse Wishart prior.

KW - Bayesian estimation

KW - covariance matrix

KW - growth curve models

KW - inverse Wishart prior

KW - separation-strategy prior

UR - http://www.scopus.com/inward/record.url?scp=84945232029&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84945232029&partnerID=8YFLogxK

U2 - 10.1080/10705511.2015.1057285

DO - 10.1080/10705511.2015.1057285

M3 - Article

AN - SCOPUS:84945232029

JO - Structural Equation Modeling

JF - Structural Equation Modeling

SN - 1070-5511

ER -