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Sometimes we want to see how people change over time, as in studies of human development and lifespan. When we test the same group of individuals repeatedly over an extended period of time, we are conducting longitudinal research. Longitudinal research is a research design in which data-gathering is administered repeatedly over an extended period of time. For example, we may survey a group of individuals about their dietary habits at age 20, retest them a decade later at age 30, and then again...
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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Modeling construct change over time amidst potential changes in construct measurement: A longitudinal moderated

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  • 1Department of Psychology and Neuroscience, University of North Carolina at Chapel Hill.

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This study introduces a new Bayesian approach to analyze longitudinal data, improving upon traditional growth curve models by accurately distinguishing construct change from measurement changes over time. The method enhances the validity of research findings in developmental and psychological studies.

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Area of Science:

  • Psychometrics
  • Longitudinal Data Analysis
  • Developmental Psychology

Background:

  • Traditional growth curve models assume measurement invariance over time, which is often violated.
  • Using summed or averaged scale items can confound construct change with changes in measurement (differential item functioning [DIF]).
  • Second-order growth curve (SGC) models offer improvements but have limitations in handling time, DIF evaluation, and covariate incorporation.

Purpose of the Study:

  • To propose a novel, parsimonious framework for analyzing longitudinal data that accounts for differential item functioning (DIF).
  • To address limitations of existing second-order growth curve (SGC) models, particularly regarding time, DIF evaluation, and covariates.
  • To implement this new approach using Bayesian estimation for efficient DIF evaluation.

Main Methods:

  • Development of an alternative approach based on moderated nonlinear factor analysis.
  • Bayesian estimation with regularizing priors for efficient DIF evaluation.
  • A two-step workflow involving measurement evaluation followed by growth modeling.

Main Results:

  • The proposed model offers a parsimonious framework for incorporating multiple time points and DIF from various covariates.
  • Bayesian estimation facilitates efficient evaluation of DIF.
  • An empirical example demonstrated the model's utility in examining changes in adolescent delinquency over time.

Conclusions:

  • The proposed Bayesian moderated nonlinear factor analysis approach provides a valid and flexible alternative to traditional growth curve and SGC models.
  • This method enhances the accuracy of longitudinal data analysis by explicitly modeling and accounting for measurement changes (DIF).
  • The approach is particularly useful for complex longitudinal studies involving multiple time points, groups, and covariates.