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Path Analysis and Structural Equation Models

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Modern Psychometrics with R

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Abstract

The first part of this chapter introduces simple path analysis structures, not involving any latent variables. Regression-based approaches such as multivariate regression, mediator models, moderator models, and extensions in terms of combined moderator-mediator path models are presented. The second part of this chapter is dedicated to path models with latent variables: structural equation models. This part builds heavily on elaborations on confirmatory factor analysis from the previous chapter. A special focus is on multigroup structural equation models which allow researchers to test hypotheses on group-specific parameters. Within this context non-nested model comparison is illustrated as well. Finally, latent growth models are introduced, an approach for studying changes over time.

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Notes

  1. 1.

    See https://socserv.socsci.mcmaster.ca/jfox/Books/Companion/appendix/Appendix-Multivariate- Linear-Models.pdf

  2. 2.

    We use a slightly nonstandard notation for the regression parameters in order to make it consistent with the symbols used in the moderator/mediator literature.

  3. 3.

    The packages mediation and lavaan treat missing values differently.

  4. 4.

    Note that in the syntax we use the symbol c instead of c′ as in Eq. (3.4).

  5. 5.

    Note that the authors obtained slightly different results since, apart from including covariates, they had special missing value treatments and did centering.

  6. 6.

    This notation is called “LISREL all-y” notation and is used by lavaan internally. There are several other options for SEM formulation (see Bollen, 1989; Kline, 2016).

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Authors and Affiliations

  1. Department of Psychology, Harvard University, Cambridge, MA, USA

    Patrick Mair

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  1. Patrick Mair
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Mair, P. (2018). Path Analysis and Structural Equation Models. In: Modern Psychometrics with R. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-319-93177-7_3

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