Using mixture models with known class membership to address incomplete covariance structures in multiple-group growth models

Su Young Kim, Eun-Young Mun, Stevens Smith

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

Multi-group latent growth modelling in the structural equation modelling framework has been widely utilized for examining differences in growth trajectories across multiple manifest groups. Despite its usefulness, the traditional maximum likelihood estimation for multi-group latent growth modelling is not feasible when one of the groups has no response at any given data collection point, or when all participants within a group have the same response at one of the time points. In other words, multi-group latent growth modelling requires a complete covariance structure for each observed group. The primary purpose of the present study is to show how to circumvent these data problems by developing a simple but creative approach using an existing estimation procedure for growth mixture modelling. A Monte Carlo simulation study was carried out to see whether the modified estimation approach provided tangible results and to see how these results were comparable to the standard multi-group results. The proposed approach produced results that were valid and reliable under the mentioned problematic data conditions. We also present a real data example and demonstrate that the proposed estimation approach can be used for the chi-square difference test to check various types of measurement invariance as conducted in a standard multi-group analysis.

Original languageEnglish
Pages (from-to)94-116
Number of pages23
JournalBritish Journal of Mathematical and Statistical Psychology
Volume67
Issue number1
DOIs
StatePublished - 1 Feb 2014

Fingerprint

Covariance Structure
Growth Model
Mixture Model
Growth
Chi-Square Distribution
Measurement Invariance
Modeling
Class
Incomplete
Mixture Modeling
Structural Equation Modeling
Chi-square
Maximum Likelihood Estimation
Monte Carlo Simulation
Simulation Study
Valid
Trajectory

Cite this

@article{1bf1208a39604f20b37d5377c73195bb,
title = "Using mixture models with known class membership to address incomplete covariance structures in multiple-group growth models",
abstract = "Multi-group latent growth modelling in the structural equation modelling framework has been widely utilized for examining differences in growth trajectories across multiple manifest groups. Despite its usefulness, the traditional maximum likelihood estimation for multi-group latent growth modelling is not feasible when one of the groups has no response at any given data collection point, or when all participants within a group have the same response at one of the time points. In other words, multi-group latent growth modelling requires a complete covariance structure for each observed group. The primary purpose of the present study is to show how to circumvent these data problems by developing a simple but creative approach using an existing estimation procedure for growth mixture modelling. A Monte Carlo simulation study was carried out to see whether the modified estimation approach provided tangible results and to see how these results were comparable to the standard multi-group results. The proposed approach produced results that were valid and reliable under the mentioned problematic data conditions. We also present a real data example and demonstrate that the proposed estimation approach can be used for the chi-square difference test to check various types of measurement invariance as conducted in a standard multi-group analysis.",
author = "Kim, {Su Young} and Eun-Young Mun and Stevens Smith",
year = "2014",
month = "2",
day = "1",
doi = "10.1111/bmsp.12008",
language = "English",
volume = "67",
pages = "94--116",
journal = "British Journal of Mathematical and Statistical Psychology",
issn = "0007-1102",
publisher = "Wiley-Blackwell",
number = "1",

}

Using mixture models with known class membership to address incomplete covariance structures in multiple-group growth models. / Kim, Su Young; Mun, Eun-Young; Smith, Stevens.

In: British Journal of Mathematical and Statistical Psychology, Vol. 67, No. 1, 01.02.2014, p. 94-116.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Using mixture models with known class membership to address incomplete covariance structures in multiple-group growth models

AU - Kim, Su Young

AU - Mun, Eun-Young

AU - Smith, Stevens

PY - 2014/2/1

Y1 - 2014/2/1

N2 - Multi-group latent growth modelling in the structural equation modelling framework has been widely utilized for examining differences in growth trajectories across multiple manifest groups. Despite its usefulness, the traditional maximum likelihood estimation for multi-group latent growth modelling is not feasible when one of the groups has no response at any given data collection point, or when all participants within a group have the same response at one of the time points. In other words, multi-group latent growth modelling requires a complete covariance structure for each observed group. The primary purpose of the present study is to show how to circumvent these data problems by developing a simple but creative approach using an existing estimation procedure for growth mixture modelling. A Monte Carlo simulation study was carried out to see whether the modified estimation approach provided tangible results and to see how these results were comparable to the standard multi-group results. The proposed approach produced results that were valid and reliable under the mentioned problematic data conditions. We also present a real data example and demonstrate that the proposed estimation approach can be used for the chi-square difference test to check various types of measurement invariance as conducted in a standard multi-group analysis.

AB - Multi-group latent growth modelling in the structural equation modelling framework has been widely utilized for examining differences in growth trajectories across multiple manifest groups. Despite its usefulness, the traditional maximum likelihood estimation for multi-group latent growth modelling is not feasible when one of the groups has no response at any given data collection point, or when all participants within a group have the same response at one of the time points. In other words, multi-group latent growth modelling requires a complete covariance structure for each observed group. The primary purpose of the present study is to show how to circumvent these data problems by developing a simple but creative approach using an existing estimation procedure for growth mixture modelling. A Monte Carlo simulation study was carried out to see whether the modified estimation approach provided tangible results and to see how these results were comparable to the standard multi-group results. The proposed approach produced results that were valid and reliable under the mentioned problematic data conditions. We also present a real data example and demonstrate that the proposed estimation approach can be used for the chi-square difference test to check various types of measurement invariance as conducted in a standard multi-group analysis.

UR - http://www.scopus.com/inward/record.url?scp=84892447011&partnerID=8YFLogxK

U2 - 10.1111/bmsp.12008

DO - 10.1111/bmsp.12008

M3 - Article

VL - 67

SP - 94

EP - 116

JO - British Journal of Mathematical and Statistical Psychology

JF - British Journal of Mathematical and Statistical Psychology

SN - 0007-1102

IS - 1

ER -