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.
Highlights
Correlation is a popular measure to quantify the association between two variables
Widely used techniques for correlation, such as simple regression/Pearson correlation, assume independence of error between observations (Howell, 1997; Johnston and DiNardo, 1997; Cohen et al, 2003). This assumption does not pose a problem if each participant or independent observation is a single data point of paired measures
The assumption of independence is violated in repeated measures, in which each participant provides more than one data point
Summary
Widely used techniques for correlation, such as simple (ordinary least squares with a single independent variable) regression/Pearson correlation, assume independence of error between observations (Howell, 1997; Johnston and DiNardo, 1997; Cohen et al, 2003) This assumption does not pose a problem if each participant or independent observation is a single data point of paired measures (i.e., two data points corresponding to the same individual such as height and weight). One common solution is to average the repeated measures data for each participant prior to performing the correlation This aggregation may resolve the issue of non-independence but can produce misleading results if there are meaningful individual differences (Estes, 1956; Myung et al, 2000). R packages used in the paper, but not cited in the references, are listed in Appendix A
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