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      Repeated Measures Correlation

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          Abstract

          Repeated measures correlation (rmcorr) is a statistical technique for determining the common within-individual association for paired measures assessed on two or more occasions for multiple individuals. Simple regression/correlation is often applied to non-independent observations or aggregated data; this may produce biased, specious results due to violation of independence and/or differing patterns between-participants versus within-participants. Unlike simple regression/correlation, rmcorr does not violate the assumption of independence of observations. Also, rmcorr tends to have much greater statistical power because neither averaging nor aggregation is necessary for an intra-individual research question. Rmcorr estimates the common regression slope, the association shared among individuals. To make rmcorr accessible, we provide background information for its assumptions and equations, visualization, power, and tradeoffs with rmcorr compared to multilevel modeling. We introduce the R package (rmcorr) and demonstrate its use for inferential statistics and visualization with two example datasets. The examples are used to illustrate research questions at different levels of analysis, intra-individual, and inter-individual. Rmcorr is well-suited for research questions regarding the common linear association in paired repeated measures data. All results are fully reproducible.

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          Most cited references30

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          Using Mutivariate Statistics

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            Statistical methods in psychology journals: Guidelines and explanations.

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              Move over ANOVA: progress in analyzing repeated-measures data and its reflection in papers published in the Archives of General Psychiatry.

              The analysis of repeated-measures data presents challenges to investigators and is a topic for ongoing discussion in the Archives of General Psychiatry. Traditional methods of statistical analysis (end-point analysis and univariate and multivariate repeated-measures analysis of variance [rANOVA and rMANOVA, respectively]) have known disadvantages. More sophisticated mixed-effects models provide flexibility, and recently developed software makes them available to researchers. To review methods for repeated-measures analysis and discuss advantages and potential misuses of mixed-effects models. Also, to assess the extent of the shift from traditional to mixed-effects approaches in published reports in the Archives of General Psychiatry. The Archives of General Psychiatry from 1989 through 2001, and the Department of Veterans Affairs Cooperative Study 425. Studies with a repeated-measures design, at least 2 groups, and a continuous response variable. The first author ranked the studies according to the most advanced statistical method used in the following order: mixed-effects model, rMANOVA, rANOVA, and end-point analysis. The use of mixed-effects models has substantially increased during the last 10 years. In 2001, 30% of clinical trials reported in the Archives of General Psychiatry used mixed-effects analysis. Repeated-measures ANOVAs continue to be used widely for the analysis of repeated-measures data, despite risks to interpretation. Mixed-effects models use all available data, can properly account for correlation between repeated measurements on the same subject, have greater flexibility to model time effects, and can handle missing data more appropriately. Their flexibility makes them the preferred choice for the analysis of repeated-measures data.
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                Author and article information

                Contributors
                Journal
                Front Psychol
                Front Psychol
                Front. Psychol.
                Frontiers in Psychology
                Frontiers Media S.A.
                1664-1078
                07 April 2017
                2017
                : 8
                : 456
                Affiliations
                [1] 1US Army Research Laboratory, Human Research and Engineering Directorate Aberdeen Proving Ground, USA
                [2] 2US Army Laboratory South Field Element, Human Research and Engineering Directorate, University of Texas Arlington Arlington, TX, USA
                Author notes

                Edited by: Prathiba Natesan, University of North Texas, USA

                Reviewed by: Zhaohui Sheng, Western Illinois University, USA; Jocelyn Holden Bolin, Ball State University, USA

                *Correspondence: Jonathan Z. Bakdash jonathan.z.bakdash.civ@ 123456mail.mil

                This article was submitted to Quantitative Psychology and Measurement, a section of the journal Frontiers in Psychology

                Article
                10.3389/fpsyg.2017.00456
                5383908
                28439244
                95013894-24a8-4d42-89d3-41d03d35abc1
                Copyright © 2017 Bakdash and Marusich.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                History
                : 06 January 2017
                : 13 March 2017
                Page count
                Figures: 6, Tables: 3, Equations: 5, References: 44, Pages: 13, Words: 7879
                Categories
                Psychology
                Methods

                Clinical Psychology & Psychiatry
                correlation,repeated measures,individual differences,intra-individual,statistical power,multilevel modeling

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