🛸 The Directed Prediction Index (DPI).
The Directed Prediction Index (DPI) is a simulation-based method for quantifying the relative endogeneity of outcome versus predictor variables in multiple linear regression models.
Han-Wu-Shuang (Bruce) Bao 包寒吴霜
- Bao, H.-W.-S. (2025). DPI: The Directed Prediction Index. https://CRAN.R-project.org/package=DPI
- Note: This is the original citation. Please refer to the information when you
library(DPI)for the APA-7 format of the version you installed.
- Note: This is the original citation. Please refer to the information when you
## Method 1: Install from CRAN
install.packages("DPI")
## Method 2: Install from GitHub
install.packages("devtools")
devtools::install_github("psychbruce/DPI", force=TRUE)$$ \begin{aligned} \text{DPI}{X \rightarrow Y} & = t^2 \cdot \Delta R^2 \ & = t{\beta_{XY|Covs}}^2 \cdot (R_{Y \sim X + Covs}^2 - R_{X \sim Y + Covs}^2) \ & = t_{partial.r_{XY|Covs}}^2 \cdot (R_{Y \sim X + Covs}^2 - R_{X \sim Y + Covs}^2) \end{aligned} $$
In econometrics and broader social sciences, an exogenous variable is assumed to have a unidirectional (causal or quasi-causal) influence on an endogenous variable (
- It uses
$\Delta R_{Y vs. X}^2$ to test whether$Y$ (outcome), compared to$X$ (predictor), can be more strongly predicted by$m$ observable control variables (included in a regression model) and$k$ unobservable random covariates (specified byk.cov; see theDPI()function). A higher$R^2$ indicates relatively higher dependence (i.e., relatively higher end 614D ogeneity) in a given variable set. - It also uses
$t_{partial.r}^2$ to penalize insignificant partial correlation ($r_{partial}$ , with equivalent$t$ test as$\beta_{partial}$ ) between$Y$ and$X$ , while ignoring the sign ($\pm$ ) of this correlation. A higher$t^2$ (equivalent to$F$ test value when$df = 1$ ) indicates a more robust (less spurious) partial relationship when controlling for other variables. - Simulation samples with
k.covrandom covariates are generated to test the statistical significance of DPI.