Dewey & Lu Path Coefficient Analysis

Partition correlation coefficients between multiple predictor variables and a primary target response variable into direct effects, indirect effects, and unexplained residual variation.

What is Path Analysis?

Path Analysis applies Dewey and Lu's path coefficient technique to standard linear correlation matrices. While standard correlation coefficients measure overall linear association between variables, they do not distinguish between direct causal contributions and indirect associations routed through correlated intermediate traits.

Path analysis solves a system of standardized linear regression equations to partition correlation coefficients into direct path coefficients (direct impact) and indirect path coefficients (impact mediated through intermediate traits), along with calculating a residual effect (unexplained variance).

Key Concept

Direct effects measure pure causal impact of a predictor trait holding all other predictor traits constant. Indirect effects quantify contributions routed through correlated intermediate predictor traits.

Data Layout Requirements

Data must be provided in tabular format containing multiple continuous predictor metric columns and one target outcome response column.

Sample_Entity	Predictor_Metric_1	Predictor_Metric_2	Predictor_Metric_3	Target_Response_Y
Entity_01	18.20	45.80	8.50	124.50
Entity_02	23.40	56.10	11.20	145.80
Entity_03	15.50	38.90	7.10	112.90
Entity_04	18.90	47.20	8.80	126.80

Example structure for predictor variables (X) and target response outcome (Y).

Statistical Principles & Metrics

Path coefficient equations partition total correlation (r) into direct and indirect paths:

Direct Path Coefficient: Standardized partial regression coefficient measuring direct effect of a predictor trait on Target Y, holding all other traits constant.
Indirect Path Coefficient: Simple correlation between Predictor A and Predictor B multiplied by the direct path coefficient of Predictor B on Target Y.
Residual Path Effect (R): Square root of (1 - sum of products of simple correlation coefficients and direct path coefficients), representing unexplained target variance.

Multicollinearity Warning

If two predictor traits are highly correlated (r > 0.95), path matrix inversion can become unstable, inflating direct path coefficients. Check for collinearity prior to path estimation.

Key Features of the DATES Module

Dual Correlation Drivers

Supports path decomposition using either phenotypic correlation matrices (rp) or genotypic correlation matrices (rg).

Comprehensive Table

Outputs direct effects (diagonal) and indirect effects (off-diagonal) alongside total correlation values.

Residual Calculation

Provides exact residual path effect (R) indicating goodness of fit and missing causal factors.

References & Citation

If you use DATES for Path Coefficient Analysis in your research, please cite:

@article{dewey1959correlation, title={A correlation and path-coefficient analysis of components of crested wheatgrass seed production}, author={Dewey, DR and Lu, KH}, journal={Agronomy Journal}, volume={51}, number={9}, pages={515--518}, year={1959} }