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How Well Can Two-Wave Models Recover the Three-Wave Second Order Latent Model Parameters?

Although previous studies on structural equation modeling (SEM) have indicated that the second-order latent growth model (SOLGM) is a more appropriate approach to longitudinal intervention effects, its application still requires researchers to collect at least three-wave data (e.g. randomized pretest, posttest, and follow-up design). However, in some circumstances, researchers can only collect two-wave data for resource limitations. With only two-wave data, the SOLGM can not be identified and researchers often choose alternative SEM models to fit two-wave data. Recent studies show that the two-wave longitudinal common factor model (2W-LCFM) and latent change score model (2W-LCSM) can perform well for comparing latent change between groups. However, there still lacks empirical evidence about how accurately these two-wave models can estimate the group effects of latent change obtained by three-wave SOLGM (3W-SOLGM). The main purpose of this dissertation, therefore, is trying to examine to what extent the fixed effects of the tree-wave SOLGM can be recovered from the parameter estimates of the two-wave LCFM and LCSM given different simulation conditions.

Fundamentally, the supplementary study (study 2) using three-wave LCFM was established to help justify the logistics of different model comparisons in our main study (study 1). The data generating model in both studies is 3W-SOLGM and there are in total 5 simulation factors (sample size, group differences in intercept and slope, the covariance between the slope and intercept, size of time-specific residual, change the pattern of time-specific residual). Three main types of evaluation indices were used to assess the quality of estimation (bias/relative bias, standard error, and power/type I error rate). The results in the supplementary study show that the performance of 3W-LCFM and 3W-LCSM are equivalent, which further justifies the different models' comparison in the main study. The point estimates for the fixed effect parameters obtained from the two-wave models are unbiased or identical to the ones from the three-wave model. However, using two-wave models could reduce the estimation precision and statistical power when the time-specific residual variance is large and changing pattern is heteroscedastic (non-constant). Finally, two real datasets were used to illustrate the simulation results. / Doctor of Philosophy / To collect and analyze the longitudinal data is a very important approach to understand the phenomenon of development in the real world. Ideally, researchers who are interested in using a longitudinal framework would prefer collecting data at more than two points in time because it can provide a deeper understanding of the developmental processes. However, in real scenarios, data may only be collected at two-time points. With only two-wave data, the second-order latent growth model (SOLGM) could not be used. The current dissertation compared the performance of two-wave models (longitudinal common factor model and latent change score model) with the three-wave SOLGM in order to better understand how the estimation quality of two-wave models could be comparable to the tree-wave model. The results show that on average, the estimation from two-wave models is identical to the ones from the three-wave model. So in real data analysis with only one sample, the point estimate by two-wave models should be very closed to that of the three-wave model. But this estimation may not be as accurate as it is obtained by the three-wave model when the latent variable has large variability in the first or last time point. This latent variable is more likely to exist as a statelike construct in the real world. Therefore, the current study could provide a reference framework for substantial researchers who could only have access to two-wave data but are still interested in estimating the growth effect that supposed to obtain by three-wave SOLGM.

Identiferoai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/103856
Date14 June 2021
CreatorsDu, Chenguang
ContributorsCounselor Education, Miyazaki, Yasuo, Skaggs, Gary E., Gu, Fei, Kniola, David J.
PublisherVirginia Tech
Source SetsVirginia Tech Theses and Dissertation
Detected LanguageEnglish
TypeDissertation
FormatETD, application/pdf
RightsIn Copyright, http://rightsstatements.org/vocab/InC/1.0/

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