Within-Person Correlation with correlate_persons()

Analytic question

correlate_persons() estimates how two variables covary within each person. The function takes repeated measurements, a person identifier, and at least two variables. It returns one row per person and variable pair with the correlation, complete-pair count, confidence interval, and p-value.

correlate_persons() does not pool occasions across learners. A positive coefficient for one learner means that the learner tends to report higher values on both variables at the same occasions. It does not mean that learners with higher average values on one variable also have higher averages on the other variable.

Estimate the correlations

correlate_persons() computes confidence intervals with Fisher’s transformation. The time argument fixes row order for consistency with other person-level analyses, although contemporaneous correlation itself is unchanged by row order. Table 1 keeps two learners and three variable pairs.

correlations <- correlate_persons(analysis_data, id = "name", vars = c("efficacy", "monitoring", "effort"), time = "day", subject = c("Aisha", "Alice"))
correlations
#> PERSON-SPECIFIC CORRELATIONS
#>   Grouping   name
#>   People     2
#>   Pairs      3
#> 
#>   subject   x            y              n        r           95% CI          p
#> ------------------------------------------------------------------------------
#>   Aisha     efficacy     monitoring   156    0.394     [0.25, 0.52]    < 1e-04
#>   Aisha     efficacy     effort       156    0.352     [0.21, 0.48]    < 1e-04
#>   Aisha     monitoring   effort       156    0.284     [0.13, 0.42]   0.000325
#>   Alice     efficacy     monitoring   156   -0.231   [-0.37, -0.08]   0.003736
#>   Alice     efficacy     effort       156    0.491     [0.36, 0.60]    < 1e-04
#>   Alice     monitoring   effort       156   -0.352   [-0.48, -0.21]    < 1e-04

correlate_persons() finds positive associations among all three variables for Aisha in Table 1. Alice has a negative efficacy-monitoring association. The contrast shows why one pooled coefficient cannot represent every learner. The confidence intervals quantify sampling uncertainty for each person and pair.

Plot the person-specific coefficients

The coefficient-and-interval display preserves the sign, magnitude, and uncertainty of every association. Direct pair labels prevent the three correlations for a learner from being mistaken for repeated estimates of one quantity.

correlation_labels <- paste(correlations$subject,
                            paste(correlations$x, correlations$y, sep = " × "),
                            sep = " · ")
forest_plot(correlations$r, correlations$conf_low, correlations$conf_high,
            correlation_labels, xlab = "Within-person correlation (95% CI)")

Figure 1. Distribution of within-person correlations for two learners.

Figure 1 shows that all three displayed associations are positive for Aisha. Alice’s efficacy-effort association is positive, while both correlations involving monitoring are negative. The intervals make the disagreement between people visible; the figure does not identify a causal direction.

Assumptions and failure checks

correlate_persons() assumes paired numeric observations and an approximately linear association. The estimate can be unstable when the number of complete pairs is small. The min_n argument sets the minimum pair count. Constant variables return missing correlations because their standard deviations are zero.

correlate_persons() reports contemporaneous association. Serial dependence can make ordinary correlation intervals optimistic because adjacent observations may not be independent. Lagged prediction requires a temporal model such as fit_lm() with lagged predictors or one of the network estimators. Correlation alone does not adjust for other variables.

When to use which

correlate_persons() is appropriate for an initial pairwise account of within-person association. fit_lm() is appropriate when one outcome is conditional on several predictors. fit_within_between() is appropriate when within-person and between-person effects must be estimated separately. Dynamic-network models are appropriate when several variables act jointly as outcomes over time.

References