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Title:

The Directed Prediction Index

Version:

2025.6

Date:

2025-06-17

Maintainer:

Han-Wu-Shuang Bao <baohws@foxmail.com>

Description:

The Directed Prediction Index ('DPI') is a simulation-based and conservative method for quantifying the relative endogeneity (relative dependence) of outcome (Y) versus predictor (X) variables in multiple linear regression models. By comparing the proportion of variance explained (R-squared) between the Y-as-outcome model and the X-as-outcome model while controlling for a sufficient number of potential confounding variables, it suggests a more plausible influence direction from a more exogenous variable (X) to a more endogenous variable (Y). Methodological details are provided at https://psychbruce.github.io/DPI/.

License:

GPL-3

Encoding:

UTF-8

URL:

https://psychbruce.github.io/DPI/

BugReports:

https://github.com/psychbruce/DPI/issues

Depends:

R (≥ 4.0.0)

Imports:

glue, crayon, cli, ggplot2, qgraph

Suggests:

bruceR

RoxygenNote:

7.3.2

NeedsCompilation:

Packaged:

2025-06-17 09:27:27 UTC; Bruce

Author:

Han-Wu-Shuang Bao

[aut, cre]

Repository:

CRAN

Date/Publication:

2025-06-18 08:50:05 UTC

The Directed Prediction Index (DPI).

Description

The Directed Prediction Index (DPI) is a simulation-based and conservative method for quantifying the relative endogeneity (relative dependence) of outcome (Y) vs. predictor (X) variables in multiple linear regression models. By comparing the proportion of variance explained (R-squared) between the Y-as-outcome model and the X-as-outcome model while controlling for a sufficient number of potential confounding variables, it suggests a more plausible influence direction from a more exogenous variable (X) to a more endogenous variable (Y). Methodological details are provided at https://psychbruce.github.io/DPI/.

Usage

DPI(
  model,
  y,
  x,
  data = NULL,
  k.cov = 1,
  n.sim = 1000,
  seed = NULL,
  progress,
  file = NULL,
  width = 6,
  height = 4,
  dpi = 500
)

Arguments

model

Model object (lm).

y

Dependent (outcome) variable.

x

Independent (predictor) variable.

data

[Optional] Defaults to NULL. If data is specified, then model will be ignored and a linear model lm({y} ~ {x} + .) will be fitted inside. This is helpful for exploring all variables in a dataset.

k.cov

Number of random covariates (simulating potential omitted variables) added to each simulation sample.

Defaults to 1. Please also test different k.cov values as robustness checks (see DPI_curve).
If k.cov > 0, the raw data (without bootstrapping) are used, with k.cov random variables appended, for simulation.
If k.cov = 0 (not suggested), bootstrap samples (resampling with replacement) are used for simulation.

n.sim

Number of simulation samples. Defaults to 1000.

seed

Random seed for replicable results. Defaults to NULL.

progress

Show progress bar. Defaults to FALSE (if n.sim < 5000).

file

File name of saved plot (".png" or ".pdf").

width, height

Width and height (in inches) of saved plot. Defaults to 6 and 4.

dpi

Dots per inch (figure resolution). Defaults to 500.

Value

Return a data.frame of simulation results:

DPI
- t.beta.xy^2 * (R2.Y - R2.X)
t.beta.xy
- t value for coefficient of X predicting Y (always equal to t value for coefficient of Y predicting X) when controlling for all other covariates
df.beta.xy
- residual degree of freedom (df) of t.beta.xy
r.partial.xy
- partial correlation (always with the same t value as t.beta.xy) between X and Y when controlling for all other covariates
delta.R2
- R2.Y - R2.X
R2.Y
- R^2 of regression model predicting Y using X and all other covariates
R2.X
- R^2 of regression model predicting X using Y and all other covariates

Examples

model = lm(Ozone ~ ., data=airquality)
DPI(model, y="Ozone", x="Solar.R", seed=1)
DPI(data=airquality, y="Ozone", x="Solar.R", k.cov=10, seed=1)

The DPI curve analysis.

Description

The DPI curve analysis.

Usage

DPI_curve(
  model,
  y,
  x,
  data = NULL,
  k.covs = 1:10,
  n.sim = 1000,
  seed = NULL,
  file = NULL,
  width = 6,
  height = 4,
  dpi = 500
)

Arguments

model

Model object (lm).

y

Dependent (outcome) variable.

x

Independent (predictor) variable.

data

k.covs

An integer vector of number of random covariates (simulating potential omitted variables) added to each simulation sample. Defaults to 1:10 (producing DPI results for k.cov=1~10). For details, see DPI.

n.sim

Number of simulation samples. Defaults to 1000.

seed

Random seed for replicable results. Defaults to NULL.

file

File name of saved plot (".png" or ".pdf").

width, height

Width and height (in inches) of saved plot. Defaults to 6 and 4.

dpi

Dots per inch (figure resolution). Defaults to 500.

Value

Return a data.frame of DPI curve results.

Examples

model = lm(Ozone ~ ., data=airquality)
DPIs = DPI_curve(model, y="Ozone", x="Solar.R", seed=1)
plot(DPIs)  # ggplot object

Correlation network plot.

Description

Correlation network plot.

Usage

cor_network(
  data,
  index = c("cor", "pcor"),
  show.value = TRUE,
  show.insig = FALSE,
  show.cutoff = FALSE,
  faded = FALSE,
  text.size = 1.2,
  node.group = NULL,
  node.color = NULL,
  edge.color.pos = "#0571B0",
  edge.color.neg = "#CA0020",
  edge.color.insig = "#EEEEEEEE",
  title = NULL,
  file = NULL,
  width = 6,
  height = 4,
  dpi = 500,
  ...
)

Arguments

data

Data.

index

Type of graph: "cor" (raw correlation network) or "pcor" (partial correlation network). Defaults to "cor".

show.value

Show correlation coefficients and their significance on edges. Defaults to TRUE.

show.insig

Show edges with insignificant correlations (p > 0.05). Defaults to FALSE. To change significance level, please set the alpha parameter (defaults to alpha=0.05).

show.cutoff

Show cut-off values of correlations. Defaults to FALSE.

faded

Transparency of edges according to the effect size of correlation. Defaults to FALSE.

text.size

Scalar on the font size of variable labels. Defaults to 1.2.

node.group

A list that indicates which nodes belong together, with each element of list as a vector of integers identifying the column numbers of variables that belong together.

node.color

A vector with a color for each element in node.group, or a color for each node.

edge.color.pos

Color for (significant) positive correlations. Defaults to "#0571B0" (blue in ColorBrewer's RdBu palette).

edge.color.neg

Color for (significant) negative correlations. Defaults to "#CA0020" (red in ColorBrewer's RdBu palette).

edge.color.insig

Color for insignificant correlations. Defaults to "#EEEEEEEE" (transparent grey).

title

Plot title.

file

File name of saved plot (".png" or ".pdf").

width, height

Width and height (in inches) of saved plot. Defaults to 6 and 4.

dpi

Dots per inch (figure resolution). Defaults to 500.

...

Other parameters passed to qgraph.

Value

Invisibly return a qgraph object.

Examples

cor_network(airquality)
cor_network(airquality, show.insig=TRUE)

Generate random data.

Description

Generate random data.

Usage

data_random(k, n, seed = NULL)

Arguments

k

Number of variables.

n

Number of observations (cases).

seed

Random seed for replicable results. Defaults to NULL.

Value

Return a data.frame of random data.

Examples

d = data_random(k=5, n=100, seed=1)
cor_network(d)

[S3 method] Plot DPI results.

Description

[S3 method] Plot DPI results.

Usage

## S3 method for class 'dpi'
plot(x, file = NULL, width = 6, height = 4, dpi = 500, ...)

Arguments

x

A data.frame (of new class dpi) returned from DPI.

file

File name of saved plot (".png" or ".pdf").

width, height

Width and height (in inches) of saved plot. Defaults to 6 and 4.

dpi

Dots per inch (figure resolution). Defaults to 500.

...

Other arguments (currently not used).

Value

Return a ggplot object.

[S3 method] Plot DPI curve analysis results.

Description

[S3 method] Plot DPI curve analysis results.

Usage

## S3 method for class 'dpi.curve'
plot(x, file = NULL, width = 6, height = 4, dpi = 500, ...)

Arguments

x

A data.frame (of new class dpi.curve) returned from DPI_curve.

file

File name of saved plot (".png" or ".pdf").

width, height

Width and height (in inches) of saved plot. Defaults to 6 and 4.

dpi

Dots per inch (figure resolution). Defaults to 500.

...

Other arguments (currently not used).

Value

Return a ggplot object.

[S3 method] Print DPI summary and plot.

Description

[S3 method] Print DPI summary and plot.

Usage

## S3 method for class 'dpi'
print(x, digits = 3, ...)

Arguments

x

A data.frame (of new class dpi) returned from DPI.

digits

Number of decimal places. Defaults to 3.

...

Other arguments (currently not used).

Value

No return value.

[S3 method] Print DPI summary.

Description

[S3 method] Print DPI summary.

Usage

## S3 method for class 'summary.dpi'
print(x, digits = 3, ...)

Arguments

x

A data.frame (of new class dpi) returned from DPI.

digits

Number of decimal places. Defaults to 3.

...

Other arguments (currently not used).

Value

No return value.

[S3 method] Summarize DPI results.

Description

[S3 method] Summarize DPI results.

Usage

## S3 method for class 'dpi'
summary(object, ...)

Arguments

object

A data.frame (of new class dpi) returned from DPI.

...

Other arguments (currently not used).

Value

Return a list with new class summary.dpi of summarized results and raw DPI data.frame.