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The consequences of ignoring measurement invariance for path coefficients in structural equation models.

ABSTRACT: We report a Monte Carlo study examining the effects of two strategies for handling measurement non-invariance - modeling and ignoring non-invariant items - on structural regression coefficients between latent variables measured with item response theory models for categorical indicators. These strategies were examined across four levels and three types of non-invariance - non-invariant loadings, non-invariant thresholds, and combined non-invariance on loadings and thresholds - in simple, partial, mediated and moderated regression models where the non-invariant latent variable occupied predictor, mediator, and criterion positions in the structural regression models. When non-invariance is ignored in the latent predictor, the focal group regression parameters are biased in the opposite direction to the difference in loadings and thresholds relative to the referent group (i.e., lower loadings and thresholds for the focal group lead to overestimated regression parameters). With criterion non-invariance, the focal group regression parameters are biased in the same direction as the difference in loadings and thresholds relative to the referent group. While unacceptable levels of parameter bias were confined to the focal group, bias occurred at considerably lower levels of ignored non-invariance than was previously recognized in referent and focal groups.

SUBMITTER: Guenole N

PROVIDER: S-EPMC4166111 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

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The consequences of ignoring measurement invariance for path coefficients in structural equation models.

Guenole Nigel N Brown Anna A

Frontiers in psychology 20140917

We report a Monte Carlo study examining the effects of two strategies for handling measurement non-invariance - modeling and ignoring non-invariant items - on structural regression coefficients between latent variables measured with item response theory models for categorical indicators. These strategies were examined across four levels and three types of non-invariance - non-invariant loadings, non-invariant thresholds, and combined non-invariance on loadings and thresholds - in simple, partial ...[more]

PMID: 25278911

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Project description:BackgroundClustering of observations is a common phenomenon in epidemiological and clinical research. Previous studies have highlighted the importance of using multilevel analysis to account for such clustering, but in practice, methods ignoring clustering are often employed. We used simulated data to explore the circumstances in which failure to account for clustering in linear regression could lead to importantly erroneous conclusions.MethodsWe simulated data following the random-intercept model specification under different scenarios of clustering of a continuous outcome and a single continuous or binary explanatory variable. We fitted random-intercept (RI) and ordinary least squares (OLS) models and compared effect estimates with the "true" value that had been used in simulation. We also assessed the relative precision of effect estimates, and explored the extent to which coverage by 95% confidence intervals and Type I error rates were appropriate.ResultsWe found that effect estimates from both types of regression model were on average unbiased. However, deviations from the "true" value were greater when the outcome variable was more clustered. For a continuous explanatory variable, they tended also to be greater for the OLS than the RI model, and when the explanatory variable was less clustered. The precision of effect estimates from the OLS model was overestimated when the explanatory variable varied more between than within clusters, and was somewhat underestimated when the explanatory variable was less clustered. The cluster-unadjusted model gave poor coverage rates by 95% confidence intervals and high Type I error rates when the explanatory variable was continuous. With a binary explanatory variable, coverage rates by 95% confidence intervals and Type I error rates deviated from nominal values when the outcome variable was more clustered, but the direction of the deviation varied according to the overall prevalence of the explanatory variable, and the extent to which it was clustered.ConclusionsIn this study we identified circumstances in which application of an OLS regression model to clustered data is more likely to mislead statistical inference. The potential for error is greatest when the explanatory variable is continuous, and the outcome variable more clustered (intraclass correlation coefficient is ≥ 0.01).

Dataset Information

The consequences of ignoring measurement invariance for path coefficients in structural equation models.

Publications

The consequences of ignoring measurement invariance for path coefficients in structural equation models.

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