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      The Effects of Misspecifying the Random Part of Multilevel Models

      research-article
      * , a , , a , b , b , b
      Methodology
      PsychOpen
      multilevel, random effects, fixed effects, Monte Carlo

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          Abstract

          This paper examined the amount bias in standard errors for fixed effects when the random part of a multilevel model is misspecified. Study 1 examined the effects of misspecification for a model with one Level 1 predictor. Results indicated that misspecifying random slope variance as fixed had a moderate effect size on the standard errors of the fixed effects and had a greater effect than misspecifying fixed slopes as random. In Study 2, a second Level 1 predictor was added and allowed for the examination of the effects of misspecifying the slope variance of one predictor on the standard errors for the fixed effects of the other predictor. Results indicated that only the standard errors of coefficient relevant to that predictor were impacted and that the effect size for the bias could be considered moderate to large. These results suggest that researchers can use a piecemeal approach to testing multilevel models with random effects.

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          Most cited references17

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          Fitting Linear Mixed-Effects Models Usinglme4

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            Multilevel Analysis: Techniques and Applications

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              Statistical power and optimal design for multisite randomized trials.

              The multisite trial, widely used in mental health research and education, enables experimenters to assess the average impact of a treatment across sites, the variance of treatment impact across sites, and the moderating effect of site characteristics on treatment efficacy. Key design decisions include the sample size per site and the number of sites. To consider power implications, this article proposes a standardized hierarchical linear model and uses rules of thumb similar to those proposed by J. Cohen (1988) for small, medium, and large effect sizes and for small, medium, and large treatment-by-site variance. Optimal allocation of resources within and between sites as a function of variance components and costs at each level are also considered. The approach generalizes to quasiexperiments with a similar structure. These ideas are illustrated with newly developed software.
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                Author and article information

                Journal
                METH
                Methodology
                Methodology
                Methodology
                PsychOpen
                1614-1881
                1614-2241
                30 September 2020
                2020
                : 16
                : 3
                : 224-240
                Affiliations
                [a ]Department of Psychology, Wright State University , Dayton, OH, USA
                [b ]Infor, Dallas, TX, USA
                Author notes
                [* ]Department of Psychology, Wright State University, Dayton, OH 45435-0001, USA. Tel. +1 937 775 3818, david.lahuis@ 123456wright.edu
                Article
                meth.2799
                10.5964/meth.2799
                de22abc6-f64a-4646-9d8e-f67d4fe1cad9

                This is an open-access article distributed under the terms of the Creative Commons Attribution (CC BY) 4.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 26 March 2019
                : 16 October 2019
                Product
                Self URI (journal-page): https://journals.psychopen.eu/
                Categories
                Original Article

                Psychology
                Monte Carlo,multilevel,random effects,fixed effects
                Psychology
                Monte Carlo, multilevel, random effects, fixed effects

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