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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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Comparison of rmcorr and simple regression/correlation results for age and brain structure volume data. Each dot represents one of two separate observations of age and CBH for a participant. (A) Separate simple regressions/correlations by time: each observation is treated as independent, represented by shading all the data points black. The red line is the fit of the simple regression/correlation. (B) Rmcorr: observations from the same participant are given the same color, with corresponding lines to show the rmcorr fit for each participant. (C) Simple regression/correlation: averaged by participant. Note that the effect size is greater (stronger negative relationship) using rmcorr (B) than with either use of simple regression models (A) and (C). This figure was created using data from Raz et al. (2005).
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Figure 5: Comparison of rmcorr and simple regression/correlation results for age and brain structure volume data. Each dot represents one of two separate observations of age and CBH for a participant. (A) Separate simple regressions/correlations by time: each observation is treated as independent, represented by shading all the data points black. The red line is the fit of the simple regression/correlation. (B) Rmcorr: observations from the same participant are given the same color, with corresponding lines to show the rmcorr fit for each participant. (C) Simple regression/correlation: averaged by participant. Note that the effect size is greater (stronger negative relationship) using rmcorr (B) than with either use of simple regression models (A) and (C). This figure was created using data from Raz et al. (2005).

Mentions: First, we recreate the original cross-sectional (between-participants) analysis from the paper, where the relationship between age and CBH volume were assessed with separate simple regression/correlation models at Time 1 [r(70) = −0.36, 95% CI [−0.54, −0.14], p < 0.01] and Time 2 [r(70) = −0.40, 95% CI [−0.58, −0.19], p < 0.001; Figure 5A]. The interpretation of these results is cross-sectional: They indicate a moderately negative relationship between age and CBH volume across people, where older individuals tend to have a smaller volume and vice versa. If we instead analyze this data at the intra-individual level using rmcorr, we see a much stronger negative association between age and CBH volume, rrm (71) = −0.70, 95% CI [−0.81, −0.56], p < 0.001 (Figure 5B). These results are interpreted longitudinally, and indicate that as an individual ages, CBH volume tends to decrease. Finally, it is possible to analyze the relationship between age and CBH volume using each participant's data averaged across the two time periods and a simple regression/correlation. This model produces similar results to the original cross-sectional analysis: r(70) = −0.39, 95% CI [−0.57, −0.17], p < 0.01 (Figure 5C).


Repeated Measures Correlation
Comparison of rmcorr and simple regression/correlation results for age and brain structure volume data. Each dot represents one of two separate observations of age and CBH for a participant. (A) Separate simple regressions/correlations by time: each observation is treated as independent, represented by shading all the data points black. The red line is the fit of the simple regression/correlation. (B) Rmcorr: observations from the same participant are given the same color, with corresponding lines to show the rmcorr fit for each participant. (C) Simple regression/correlation: averaged by participant. Note that the effect size is greater (stronger negative relationship) using rmcorr (B) than with either use of simple regression models (A) and (C). This figure was created using data from Raz et al. (2005).
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Figure 5: Comparison of rmcorr and simple regression/correlation results for age and brain structure volume data. Each dot represents one of two separate observations of age and CBH for a participant. (A) Separate simple regressions/correlations by time: each observation is treated as independent, represented by shading all the data points black. The red line is the fit of the simple regression/correlation. (B) Rmcorr: observations from the same participant are given the same color, with corresponding lines to show the rmcorr fit for each participant. (C) Simple regression/correlation: averaged by participant. Note that the effect size is greater (stronger negative relationship) using rmcorr (B) than with either use of simple regression models (A) and (C). This figure was created using data from Raz et al. (2005).
Mentions: First, we recreate the original cross-sectional (between-participants) analysis from the paper, where the relationship between age and CBH volume were assessed with separate simple regression/correlation models at Time 1 [r(70) = −0.36, 95% CI [−0.54, −0.14], p < 0.01] and Time 2 [r(70) = −0.40, 95% CI [−0.58, −0.19], p < 0.001; Figure 5A]. The interpretation of these results is cross-sectional: They indicate a moderately negative relationship between age and CBH volume across people, where older individuals tend to have a smaller volume and vice versa. If we instead analyze this data at the intra-individual level using rmcorr, we see a much stronger negative association between age and CBH volume, rrm (71) = −0.70, 95% CI [−0.81, −0.56], p < 0.001 (Figure 5B). These results are interpreted longitudinally, and indicate that as an individual ages, CBH volume tends to decrease. Finally, it is possible to analyze the relationship between age and CBH volume using each participant's data averaged across the two time periods and a simple regression/correlation. This model produces similar results to the original cross-sectional analysis: r(70) = −0.39, 95% CI [−0.57, −0.17], p < 0.01 (Figure 5C).

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.


Related in: MedlinePlus