Compute intervenor-adjusted partial correlation matrix

Computes the partial correlation between Y[i] and Y[j] adjusting for the "intervenor" variables Y[i+1], ..., Y[j-1]. Under an antedependence model of order p, partial correlations for |i-j| > p should be approximately zero.

Usage

partial_corr(y, test = FALSE, n_digits = 3)

Arguments

y

Numeric matrix with n_subjects rows and n_time columns.

test

Logical; if TRUE, returns significance flags based on approximate threshold 2/sqrt(n_eff) where n_eff = n_subjects - (lag - 1). Default FALSE.

n_digits

Integer; number of decimal places for rounding. Default 3.

Value

A list with components:

correlation

Matrix with correlations (upper triangle) and variances (diagonal)

partial_correlation

Matrix with partial correlations (lower triangle) and variances (diagonal)

significant

(If test=TRUE) Matrix flagging significant partial correlations (1 = significant)

n_subjects

Number of subjects

n_time

Number of time points

Details

The intervenor-adjusted partial correlation between Y[i] and Y[j] (i < j) is computed as the correlation between the residuals from regressing Y[i] and Y[j] on the intervenor set Y[i+1], ..., Y[j-1].

For adjacent time points (|i-j| = 1), the partial correlation equals the ordinary correlation since there are no intervenors.

The diagonal of both returned matrices contains variances (not correlations). This keeps scale information available alongside correlation structure.

The significance test uses an approximate threshold of 2/sqrt(n_eff), which corresponds roughly to a 95% confidence bound under normality. This is a rough screening tool, not a formal hypothesis test.

References

Zimmerman, D. L. and Nunez-Anton, V. (2009). Antedependence Models for Longitudinal Data. CRC Press.

See also

plot_prism for visual diagnostics

Examples

if (FALSE) { # \dontrun{
data("bolus_inad")
pc <- partial_corr(bolus_inad$y, test = TRUE)

# View partial correlations (lower triangle)
pc$partial_correlation

# Extract variances from the diagonal
variances <- diag(pc$partial_correlation)

# Check which are "significant" (rough screen for AD order)
pc$significant
} # }