Thesis
Interactions between level 1 predictors in multilevel models
University of Iowa
Master of Arts (MA), University of Iowa
Autumn 2025
DOI: 10.25820/etd.008220
Abstract
In multilevel models, interaction terms between two level 1 predictors have different methods of creation due to level 1 predictors containing both within and between variation (Loeys et al., 2018). Previous research on within-level interactions that consist of two level 1 predictors has different suggestions on how to correctly specify this interaction term. The purpose of the study is to understand how parameter estimates and standard errors in multilevel models are impacted by the different methods used to create this interaction term to determine which centering method results in the least amount of bias.
A Monte Carlo simulation with 1000 replications was conducted to assess the impacts of the interaction creation order (center first, product first, and double centering), the presence of a nonzero interaction effect, and model type (within-only or within and between). Cluster-mean centering was used for the level 1 predictors in random intercept models.
Results indicated that using the center first then product method to create the within-level interaction resulted in the least amount of bias in the parameter estimates. Bias was also found in cross-level interactions and cluster means. The bias in cross-level interaction parameter estimates was explained by both the within-level interaction creation method and the presence of a nonzero interaction effect. Bias in the standard errors for cluster means was not explained by the design conditions.
Details
- Title: Subtitle
- Interactions between level 1 predictors in multilevel models
- Creators
- Erica Dorman
- Contributors
- Lesa Hoffman (Advisor)Jonathan Templin (Committee Member)Ariel Aloe (Committee Member)
- Resource Type
- Thesis
- Degree Awarded
- Master of Arts (MA), University of Iowa
- Degree in
- Psychological and Quantitative Foundations (Educational Measurement and Statistics)
- Date degree season
- Autumn 2025
- DOI
- 10.25820/etd.008220
- Publisher
- University of Iowa
- Number of pages
- vi, 27 pages
- Copyright
- Copyright 2025 Erica Dorman
- Language
- English
- Date submitted
- 12/08/2025
- Description illustrations
- tables, graphs
- Description bibliographic
- Includes bibliographical references (page 27).
- Public Abstract (ETD)
- Statistical analyses that involve people clustered within groups such as students in universities require statistical methods to account for the dependency created by clusters. Multilevel models are commonly used for this purpose and allow researchers to examine differences within and between groups. Interaction terms in statistical models capture how the effect of one predictor changes depending on the value of another predictor. In multilevel models, person-specific (level 1) predictors require additional centering methods, such as cluster-mean centering. There is disagreement on how to create interaction terms between person-specific predictors in multilevel models (Loeys et al., 2018). This study used a Monte Carlo simulation to examine how different methods of creating an interaction term for two person-specific predictors (center first, product first, and double centering) affect the results. The effects of nonzero interactions (person-level, group-level, and cross-level) and of using within-only models were also evaluated. Results indicated that the center first method resulted in the least amount of bias for the within-level interaction. Bias in the cross-level interaction estimates was influenced by both the method used to create the person-level interaction and the presence of a nonzero true interaction effect. The standard errors for the group means also showed bias that was not explained by the design conditions.
- Academic Unit
- Psychological and Quantitative Foundations
- Record Identifier
- 9985134948902771
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