Probing Interactions in Multiple Linear

Regression, Latent Curve Analysis, and

Hierarchical Linear Modeling

Regression, Latent Curve Analysis, and

Hierarchical Linear Modeling

Interactive calculation tools for establishing simple intercepts, simple slopes, and regions of significance

© 2010-2023,

Kristopher J. Preacher

Kristopher J. Preacher

Probing interactions in multiple linear regression, latent curve analysis, and hierarchical linear modeling: Interactive calculation tools for establishing simple intercepts, simple slopes, and regions of significance

Kristopher J. Preacher (*Vanderbilt University*)

Patrick J. Curran (*University of North Carolina at Chapel Hill*)

Daniel J. Bauer (*University of North Carolina at Chapel Hill*)

The paper describing this web utility may be cited in APA style in the following manner:

Preacher, K. J., Curran, P. J., & Bauer, D. J. (2006). Computational tools for probing interaction effects in multiple linear regression, multilevel modeling, and latent curve analysis. *Journal of Educational and Behavioral Statistics*, *31*, 437-448.

These web pages provide tools for probing significant 2-way or 3-way interaction effects in multiple linear regression (MLR), latent curve analysis (LCA), and hierarchical linear modeling (HLM). It is necessary first to obtain output from an appropriately conducted analysis investigating an interaction effect using other software. General discussions on how to conduct these analyses can be found in the references listed at the bottom of each page.

The primer on interaction effects in multiple linear regression contains a review of key concepts related to interaction effects in MLR.

- Simple slopes and the region of significance for MLR 2-way interactions
- Simple slopes and the region of significance for MLR 3-way interactions

- Simple slopes and the region of significance for HLM 2-way interactions
- Simple slopes and the region of significance for HLM 3-way interactions

- Simple slopes and the region of significance for LCA 2-way interactions
- Simple slopes and the region of significance for LCA 3-way interactions

Software With Similar Capabilities

These web calculators are intended for use in conjunction with any regression / multilevel / growth curve modeling software that provides analysis results and asymptotic (co)variances for interaction (moderation) models. Other software may be more convenient for some users. For example:

- Andrew Hayes' MODPROBE and PROCESS macros for SPSS and SAS let users both fit a regression model with interactions and plot the results.
- Mplus users will find it convenient to use the LOOP option in Mplus 7, in conjunction with the PLOT option in the MODEL CONSTRAINT command, to create plots for interaction effects in single- and multilevel regression.
- Jeremy Dawson offers a number of Excel worksheets that automate many of the steps involved in plotting and probing interaction effects.

Original version posted May, 2006. Our thanks to the Carolina Structural Equation Modeling group (CSEM) for testing these pages.