Visualizing Confidence Bands for Semiparametrically Estimated Nonlinear Relations Among Latent Variables

Jolynn Pek, R. Philip Chalmers, Bethany E. Kok and Diane Losardo
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Jolynn Pek: York University
R. Philip Chalmers: York University
Bethany E. Kok: Max Planck Institute for Human Cognitive and Brain Sciences
Diane Losardo: Amplify Education

Journal of Educational and Behavioral Statistics, 2015, vol. 40, issue 4, 402-423

Abstract: Structural equation mixture models (SEMMs), when applied as a semiparametric model (SPM), can adequately recover potentially nonlinear latent relationships without their specification. This SPM is useful for exploratory analysis when the form of the latent regression is unknown. The purpose of this article is to help users familiar with structural equation models to add SEMM to their toolkit of exploratory analytic options. We describe how the SEMM captures potential nonlinearity between latent variables, and how confidence bands (CBs; point wise and simultaneous) for the recovered latent function are constructed and interpreted. We then illustrate the usefulness of CBs for inference with an empirical example on the effect of emotions on cognitive processing. We also introduce a visualization tool that automatically generates plots of the latent regression and their CBs to promote user accessibility. Finally, we conclude with a discussion on the use of this SPM for exploratory research.

Keywords: exploratory; latent variables; point-wise confidence intervals; simultaneous confidence envelopes; structural equation mixture model (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:40:y:2015:i:4:p:402-423

DOI: 10.3102/1076998615589129

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