Please check the latest news (change log) and keep this package updated.

To-do list:

• Allow for specification of exogenous variables in DPI_dag().
• Support non-linear and multilevel models.

DPI 2026.2

• Minor changes and improvements.

DPI 2025.11

• Improved DPI_dag() and plot.dpi.dag(). Also forced the plot to strictly show a DAG while changing edge color of insignificant DPI into faded grey.
• (Fixed in patch version 2025.10-1) Fixed DPI_curve() for wrong (reverse) direction of DPI caused by the change of parameter order of x and y in version 2025.10.
• (Fixed in patch version 2025.10-1) Fixed a bug caused by dpi parameter-object name conflict (internally) when saving DPI() results into a file.

DPI 2025.10

This version contains breaking changes to function names and visualization methods.

• Added DPI_dag(): Directed acyclic graphs (DAGs) via DPI exploratory analysis (causal discovery) for all significant partial correlations.
• Added bonf and pseudoBF parameters to DPI(), DPI_curve(), and DPI_dag().
  • bonf: Bonferroni correction to control for false positive rates among multiple pairwise DPI tests.
  • pseudoBF: Use normalized pseudo Bayes Factors sigmoid(log(PseudoBF10)) as the Significance score (0~1). Pseudo Bayes Factors are computed using the transformation rules proposed by Wagenmakers (2022) https://doi.org/10.31234/osf.io/egydq.
• Added S3 methods plot.cor.net(), plot.bns.dag(), and plot.dpi.dag() that can transform qgraph base-plot objects into ggplot objects for more stable and flexible visualization.
• Added p_to_bf(): Convert p values to pseudo Bayes Factors (\(\text{PseudoBF}_{10}\)).
• Renamed cor_network() to cor_net(), dag_network() to BNs_dag(), and matrix_cor() to cor_matrix().
• Fixed cor_net() to return the exactly correct p values of (partial) correlation coefficients.
• Improved output information in console and plot.

DPI 2025.9

This version contains breaking changes to both algorithm and functionality.

• Refined DPI() algorithm to limit \(\text{DPI} \in (-1, 1)\) and also simplified its output information. \[ \begin{aligned} \text{DPI}_{X \rightarrow Y} & = \text{Direction}_{X \rightarrow Y} \cdot \text{Significance}_{X \rightarrow Y} \\ & = \text{Delta}(R^2) \cdot \text{Sigmoid}(\frac{p}{\alpha}) \\ & = \left( R_{Y \sim X + Covs}^2 - R_{X \sim Y + Covs}^2 \right) \cdot \left( 1 - \tanh \frac{p_{XY|Covs}}{2\alpha} \right) \\ & \in (-1, 1) \end{aligned} \]
  • In an earlier version of algorithm, the strength score was computed as \(t_{\beta_{XY|Covs}}^2 = t_{r.partial_{XY|Covs}}^2 \in [0, +\infty)\). While this algorithm performs as well as the new \(\text{Sigmoid}(\frac{p}{\alpha})\) approach (e.g., both have low false positive and false negative rates), \(t^2\) has a major flaw that its values cannot converge to a limited range so that the final DPI values would be heavily determined by \(t^2\), which is not a desired attribute. In contrast, the new algorithm can make the significance score more likely to be an “on-off switch”, with values more likely approximating 0 or 1, thereby minimizing its impact on the interpretation of final DPI values.
• Renamed data_random() to sim_data() with enhanced functionality that supports data simulation from a multivariate normal distribution, using MASS::mvrnorm().
• Added sim_data_exp(): Simulate experiment-like data with independent binary Xs.
• Used gc() in DPI(), DPI_curve(), and dag_network() for memory garbage collection.
• Provided a better example in dag_network() for arranging multiple base-R-style plots using aplot::plot_list().

DPI 2025.8

• Added dag_network(): Directed acyclic graphs (DAGs) via causal Bayesian networks (BNs).
• Improved cor_network(): Correlation and partial correlation networks.
• Moved help pages of all S3 method functions to S3method.dpi and S3method.network and made them as internal topics.

DPI 2025.6

• CRAN package publication.
• Initial public release on GitHub.
• Developed core functions and package logo.