Limits...
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.


Related in: MedlinePlus

These notional plots illustrate the range of potential similarities and differences in the intra-individual association assessed by rmcorr and the inter-individual association assessed by ordinary least squares (OLS) regression. Rmcorr-values depend only on the intra-individual association between variables and will be the same across different patterns of inter-individual variability. (A)rrm = −1: depicts notional data with a perfect negative intra-individual association between variables, (B)rrm = 0: depicts data with no intra-individual association, and (C)rrm = 1: depicts data with a perfect positive intra-individual association. In each column, the relationship between subjects (inter-individual variability) is different, which does not change the rmcorr-values within a column. However, this does change the association that would be predicted by OLS regression (black lines) if the data were treated as IID or averaged by participant.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5383908&req=5

Figure 2: These notional plots illustrate the range of potential similarities and differences in the intra-individual association assessed by rmcorr and the inter-individual association assessed by ordinary least squares (OLS) regression. Rmcorr-values depend only on the intra-individual association between variables and will be the same across different patterns of inter-individual variability. (A)rrm = −1: depicts notional data with a perfect negative intra-individual association between variables, (B)rrm = 0: depicts data with no intra-individual association, and (C)rrm = 1: depicts data with a perfect positive intra-individual association. In each column, the relationship between subjects (inter-individual variability) is different, which does not change the rmcorr-values within a column. However, this does change the association that would be predicted by OLS regression (black lines) if the data were treated as IID or averaged by participant.

Mentions: Note that rmcorr can reveal very different within-participant associations among similar patterns of aggregated data, as depicted with notional data in Figure 2. All the data in a given row exhibit the same relationship when treated (incorrectly) as IID, indicated by the black simple regression line in each cell. However, across columns the intra-individual association is quite different. This phenomenon is why generating an rmcorr plot can be helpful for understanding a given dataset. As with other statistical techniques, visualization is key for interpreting results (Tukey, 1977).


Repeated Measures Correlation
These notional plots illustrate the range of potential similarities and differences in the intra-individual association assessed by rmcorr and the inter-individual association assessed by ordinary least squares (OLS) regression. Rmcorr-values depend only on the intra-individual association between variables and will be the same across different patterns of inter-individual variability. (A)rrm = −1: depicts notional data with a perfect negative intra-individual association between variables, (B)rrm = 0: depicts data with no intra-individual association, and (C)rrm = 1: depicts data with a perfect positive intra-individual association. In each column, the relationship between subjects (inter-individual variability) is different, which does not change the rmcorr-values within a column. However, this does change the association that would be predicted by OLS regression (black lines) if the data were treated as IID or averaged by participant.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 2: These notional plots illustrate the range of potential similarities and differences in the intra-individual association assessed by rmcorr and the inter-individual association assessed by ordinary least squares (OLS) regression. Rmcorr-values depend only on the intra-individual association between variables and will be the same across different patterns of inter-individual variability. (A)rrm = −1: depicts notional data with a perfect negative intra-individual association between variables, (B)rrm = 0: depicts data with no intra-individual association, and (C)rrm = 1: depicts data with a perfect positive intra-individual association. In each column, the relationship between subjects (inter-individual variability) is different, which does not change the rmcorr-values within a column. However, this does change the association that would be predicted by OLS regression (black lines) if the data were treated as IID or averaged by participant.
Mentions: Note that rmcorr can reveal very different within-participant associations among similar patterns of aggregated data, as depicted with notional data in Figure 2. All the data in a given row exhibit the same relationship when treated (incorrectly) as IID, indicated by the black simple regression line in each cell. However, across columns the intra-individual association is quite different. This phenomenon is why generating an rmcorr plot can be helpful for understanding a given dataset. As with other statistical techniques, visualization is key for interpreting results (Tukey, 1977).

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