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Repeated Measures Correlation

View Article: PubMed Central - PubMed

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.

No MeSH data available.


Power curves for (A) small, rrm, and r = 0.10, (B) medium, rrm, and r = 0.3, and (C) large effect sizes, rrm, and r = 0.50. X-axis is sample size. Note the sample size range differs among the panels. Y-axis is power. k denotes the number of repeated paired measures. Eighty percent power is indicated by the dotted black line. For rmcorr, the power of k = 2 is asymptotically equivalent to k = 1. A comparison to the power for a Pearson correlation with one data point per participant (k = 1) is also shown.
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Figure 4: Power curves for (A) small, rrm, and r = 0.10, (B) medium, rrm, and r = 0.3, and (C) large effect sizes, rrm, and r = 0.50. X-axis is sample size. Note the sample size range differs among the panels. Y-axis is power. k denotes the number of repeated paired measures. Eighty percent power is indicated by the dotted black line. For rmcorr, the power of k = 2 is asymptotically equivalent to k = 1. A comparison to the power for a Pearson correlation with one data point per participant (k = 1) is also shown.

Mentions: Because rmcorr is able to take advantage of multiple data points per participant, it generally has much greater statistical power than a standard Pearson correlation using averaged data. Low power typically overestimates effect sizes (e.g., Button et al., 2013). Power for rmcorr increases exponentially when either the value of k (the number of repeated observations) or the value of N (the total number of unique participants) increases. Figure 4 illustrates the power curves over different values of k and N for small, medium, and large effect sizes.


Repeated Measures Correlation
Power curves for (A) small, rrm, and r = 0.10, (B) medium, rrm, and r = 0.3, and (C) large effect sizes, rrm, and r = 0.50. X-axis is sample size. Note the sample size range differs among the panels. Y-axis is power. k denotes the number of repeated paired measures. Eighty percent power is indicated by the dotted black line. For rmcorr, the power of k = 2 is asymptotically equivalent to k = 1. A comparison to the power for a Pearson correlation with one data point per participant (k = 1) is also shown.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5383908&req=5

Figure 4: Power curves for (A) small, rrm, and r = 0.10, (B) medium, rrm, and r = 0.3, and (C) large effect sizes, rrm, and r = 0.50. X-axis is sample size. Note the sample size range differs among the panels. Y-axis is power. k denotes the number of repeated paired measures. Eighty percent power is indicated by the dotted black line. For rmcorr, the power of k = 2 is asymptotically equivalent to k = 1. A comparison to the power for a Pearson correlation with one data point per participant (k = 1) is also shown.
Mentions: Because rmcorr is able to take advantage of multiple data points per participant, it generally has much greater statistical power than a standard Pearson correlation using averaged data. Low power typically overestimates effect sizes (e.g., Button et al., 2013). Power for rmcorr increases exponentially when either the value of k (the number of repeated observations) or the value of N (the total number of unique participants) increases. Figure 4 illustrates the power curves over different values of k and N for small, medium, and large effect sizes.

View Article: PubMed Central - PubMed

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.

No MeSH data available.