Longitudinal Measurement Non-Invariance with Ordered-Categorical Indicators: How are the Parameters in Second-Order Latent Linear Growth Models Affected?

Y. Liu, Stephen West

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Models of change typically assume longitudinal measurement invariance. Key constructs are often measured by ordered-categorical indicators (e.g., Likert scale items). If tests based on such indicators do not support longitudinal measurement invariance, it would be useful to gauge the practical significance of the detected non-invariance. The authors focus on the commonly used second-order latent growth curve model, proposing a sensitivity analysis that compares the growth parameter estimates from a model assuming the highest achieved level of measurement invariance to those from a model assuming a higher, incorrect level of measurement invariance as a measure of practical significance. A simulation study investigated the practical significance of non-invariance in different locations (loadings, thresholds, uniquenesses)  in second-order latent linear growth models. The mean linear slope was affected by non-invariance in the loadings and thresholds, the intercept variance was affected by non-invariance in the uniquenesses, and the linear slope variance and intercept–slope covariance were affected by non-invariance in all three locations.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalStructural Equation Modeling
DOIs
StateAccepted/In press - Jan 25 2018

Fingerprint

Measurement Invariance
Growth Model
Categorical
Linear Model
Invariance
Slope
Growth Curve Model
Intercept
Sensitivity Analysis
Gauge
Sensitivity analysis
Gages
Simulation Study
Model
Measurement invariance
Growth model
simulation
Estimate

Keywords

  • longitudinal measurement non-invariance
  • ordered-categorical indicators
  • second-order latent growth model
  • sensitivity analysis

ASJC Scopus subject areas

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

Cite this

@article{fe7540c683914827a288a2a6664cffae,
title = "Longitudinal Measurement Non-Invariance with Ordered-Categorical Indicators: How are the Parameters in Second-Order Latent Linear Growth Models Affected?",
abstract = "Models of change typically assume longitudinal measurement invariance. Key constructs are often measured by ordered-categorical indicators (e.g., Likert scale items). If tests based on such indicators do not support longitudinal measurement invariance, it would be useful to gauge the practical significance of the detected non-invariance. The authors focus on the commonly used second-order latent growth curve model, proposing a sensitivity analysis that compares the growth parameter estimates from a model assuming the highest achieved level of measurement invariance to those from a model assuming a higher, incorrect level of measurement invariance as a measure of practical significance. A simulation study investigated the practical significance of non-invariance in different locations (loadings, thresholds, uniquenesses)  in second-order latent linear growth models. The mean linear slope was affected by non-invariance in the loadings and thresholds, the intercept variance was affected by non-invariance in the uniquenesses, and the linear slope variance and intercept–slope covariance were affected by non-invariance in all three locations.",
keywords = "longitudinal measurement non-invariance, ordered-categorical indicators, second-order latent growth model, sensitivity analysis",
author = "Y. Liu and Stephen West",
year = "2018",
month = "1",
day = "25",
doi = "10.1080/10705511.2017.1419353",
language = "English (US)",
pages = "1--16",
journal = "Structural Equation Modeling",
issn = "1070-5511",
publisher = "Psychology Press Ltd",

}

TY - JOUR

T1 - Longitudinal Measurement Non-Invariance with Ordered-Categorical Indicators

T2 - How are the Parameters in Second-Order Latent Linear Growth Models Affected?

AU - Liu, Y.

AU - West, Stephen

PY - 2018/1/25

Y1 - 2018/1/25

N2 - Models of change typically assume longitudinal measurement invariance. Key constructs are often measured by ordered-categorical indicators (e.g., Likert scale items). If tests based on such indicators do not support longitudinal measurement invariance, it would be useful to gauge the practical significance of the detected non-invariance. The authors focus on the commonly used second-order latent growth curve model, proposing a sensitivity analysis that compares the growth parameter estimates from a model assuming the highest achieved level of measurement invariance to those from a model assuming a higher, incorrect level of measurement invariance as a measure of practical significance. A simulation study investigated the practical significance of non-invariance in different locations (loadings, thresholds, uniquenesses)  in second-order latent linear growth models. The mean linear slope was affected by non-invariance in the loadings and thresholds, the intercept variance was affected by non-invariance in the uniquenesses, and the linear slope variance and intercept–slope covariance were affected by non-invariance in all three locations.

AB - Models of change typically assume longitudinal measurement invariance. Key constructs are often measured by ordered-categorical indicators (e.g., Likert scale items). If tests based on such indicators do not support longitudinal measurement invariance, it would be useful to gauge the practical significance of the detected non-invariance. The authors focus on the commonly used second-order latent growth curve model, proposing a sensitivity analysis that compares the growth parameter estimates from a model assuming the highest achieved level of measurement invariance to those from a model assuming a higher, incorrect level of measurement invariance as a measure of practical significance. A simulation study investigated the practical significance of non-invariance in different locations (loadings, thresholds, uniquenesses)  in second-order latent linear growth models. The mean linear slope was affected by non-invariance in the loadings and thresholds, the intercept variance was affected by non-invariance in the uniquenesses, and the linear slope variance and intercept–slope covariance were affected by non-invariance in all three locations.

KW - longitudinal measurement non-invariance

KW - ordered-categorical indicators

KW - second-order latent growth model

KW - sensitivity analysis

UR - http://www.scopus.com/inward/record.url?scp=85041096308&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041096308&partnerID=8YFLogxK

U2 - 10.1080/10705511.2017.1419353

DO - 10.1080/10705511.2017.1419353

M3 - Article

AN - SCOPUS:85041096308

SP - 1

EP - 16

JO - Structural Equation Modeling

JF - Structural Equation Modeling

SN - 1070-5511

ER -