Help for package DPI

Title:

The Directed Prediction Index for Quasi-Causal Inference with Cross-Sectional Data

Version:

2025.9

Date:

2025-09-20

Maintainer:

Han Wu Shuang Bao <baohws@foxmail.com>

Description:

The Directed Prediction Index ('DPI') is a quasi-causal inference method for cross-sectional data designed to quantify the relative endogeneity (relative dependence) of outcome (Y) versus predictor (X) variables in 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 possible confounders, it suggests a plausible (admissible) direction of influence 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, cowplot, qgraph, bnlearn, MASS

Suggests:

bruceR, aplot

RoxygenNote:

7.3.3

NeedsCompilation:

Packaged:

2025-09-20 15:05:57 UTC; Bruce

Author:

Han Wu Shuang Bao

[aut, cre]

Repository:

CRAN

Date/Publication:

2025-09-20 15:20:02 UTC

DPI: The Directed Prediction Index for Quasi-Causal Inference with Cross-Sectional Data

Description

Author(s)

Maintainer: Han Wu Shuang Bao baohws@foxmail.com (ORCID)

The Directed Prediction Index (DPI).

Description

The Directed Prediction Index (DPI) is a quasi-causal inference method for cross-sectional data designed to quantify the relative endogeneity (relative dependence) of outcome (Y) vs. predictor (X) variables in 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 possible confounders, it suggests a plausible (admissible) direction of influence 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,
  alpha = 0.05,
  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.

alpha

Significance level for computing the Strength score (0~1) based on p value of partial correlation between X and Y. Defaults to 0.05.

Direction = R2.Y - R2.X
Strength = 1 - tanh(p.beta.xy/alpha/2)

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
- ⁠= Direction * Strength⁠
- ⁠= (R2.Y - R2.X) * (1 - tanh(p.beta.xy/alpha/2))⁠
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
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
p.beta.xy
- p value for coefficient of X predicting Y (always equal to p 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

Examples

# input a fitted model
model = lm(Ozone ~ ., data=airquality)
DPI(model, y="Ozone", x="Solar.R", seed=1)  # DPI > 0
DPI(model, y="Ozone", x="Wind", seed=1)     # DPI > 0
DPI(model, y="Wind", x="Solar.R", seed=1)   # unrelated

# input raw data, test with more random covs
DPI(data=airquality, y="Ozone", x="Solar.R", k.cov=10, seed=1)
DPI(data=airquality, y="Ozone", x="Wind", k.cov=10, seed=1)
DPI(data=airquality, y="Wind", 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,
  alpha = 0.05,
  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.

alpha

Significance level for computing the Strength score (0~1) based on p value of partial correlation between X and Y. Defaults to 0.05.

Direction = R2.Y - R2.X
Strength = 1 - tanh(p.beta.xy/alpha/2)

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

[S3 methods] for `DPI()` and `DPI_curve()`.

Description

summary(dpi): Summarize DPI results. Return a list (class summary.dpi) of summarized results and raw DPI data.frame.
print(summary.dpi): Print DPI summary.
plot(dpi): Plot DPI results. Return a ggplot object.
print(dpi): Print DPI summary and plot.
plot(dpi.curve): Plot DPI curve analysis results. Return a ggplot object.

Usage

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

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

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

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

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

Arguments

object

Object (class dpi) returned from DPI().

...

Other arguments (currently not used).

x

Object (class dpi or dpi.curve) returned from DPI() or DPI_curve().

digits

Number of decimal places. Defaults to 3.

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.

[S3 methods] for `cor_network()` and `dag_network()`.

Description

print(cor.net): Plot (partial) correlation network results.
print(dag.net): Plot Bayesian network (DAG) results.

Usage

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

## S3 method for class 'dag.net'
print(
  x,
  file = NULL,
  width = 6,
  height = 4,
  dpi = 500,
  algorithm = names(x),
  ...
)

Arguments

x

Object (class cor.net or dag.net) returned from cor_network() or dag_network().

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).

algorithm

[For dag.net] Algorithm(s) to display. Defaults to plot the final integrated DAG from BN results for each algorithm in x.

Value

Invisibly return a grob object ("Grid Graphical Object", or a list of them) that can be further reused in ggplot2::ggsave() and cowplot::plot_grid().

Correlation and partial correlation networks.

Description

Correlation and partial correlation networks (also called Gaussian graphical models, GGMs).

Usage

cor_network(
  data,
  index = c("cor", "pcor"),
  show.value = TRUE,
  show.insig = FALSE,
  show.cutoff = FALSE,
  faded = FALSE,
  node.text.size = 1.2,
  node.group = NULL,
  node.color = NULL,
  edge.color.pos = "#0571B0",
  edge.color.neg = "#CA0020",
  edge.color.non = "#EEEEEEEE",
  edge.label.mrg = 0.01,
  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 alpha (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.

node.text.size

Scalar on the font size of node (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 values. Defaults to "#0571B0" (blue in ColorBrewer's RdBu palette).

edge.color.neg

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

edge.color.non

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

edge.label.mrg

Margin of the background box around the edge label. Defaults to 0.01.

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.

...

Arguments passed on to qgraph().

Value

Return a list (class cor.net) of (partial) correlation results and qgraph object with its grob (Grid Graphical Object).

Examples

# correlation network
cor_network(airquality)
cor_network(airquality, show.insig=TRUE)

# partial correlation network
cor_network(airquality, "pcor")
cor_network(airquality, "pcor", show.insig=TRUE)

Directed acyclic graphs (DAGs) via Bayesian networks (BNs).

Description

Directed acyclic graphs (DAGs) via Bayesian networks (BNs). It uses bnlearn::boot.strength() to estimate the strength of each edge as its empirical frequency over a set of networks learned from bootstrap samples. It computes (1) the probability of each edge (modulo its direction) and (2) the probabilities of each edge's directions conditional on the edge being present in the graph (in either direction). Stability thresholds are usually set as 0.85 for strength (i.e., an edge appearing in more than 85% of BNs bootstrap samples) and 0.50 for direction (i.e., a direction appearing in more than 50% of BNs bootstrap samples) (Briganti et al., 2023). Finally, for each chosen algorithm, it returns the stable Bayesian network as the final DAG.

Usage

dag_network(
  data,
  algorithm = c("pc.stable", "hc", "rsmax2"),
  algorithm.args = list(),
  n.boot = 1000,
  seed = NULL,
  strength = 0.85,
  direction = 0.5,
  node.text.size = 1.2,
  edge.width.max = 1.5,
  edge.label.mrg = 0.01,
  file = NULL,
  width = 6,
  height = 4,
  dpi = 500,
  verbose = TRUE,
  ...
)

Arguments

data

Data.

algorithm

Structure learning algorithms for building Bayesian networks (BNs). Should be function name(s) from the bnlearn package. Better to perform BNs with all three classes of algorithms to check the robustness of results (Briganti et al., 2023).

Defaults to the most common algorithms: "pc.stable" (PC), "hc" (HC), and "rsmax2" (RS), for the three classes, respectively.

(1) Constraint-based Algorithms
- PC: "pc.stable" (the first practical constraint-based causal structure learning algorithm by Peter & Clark)
- Others: "gs", "iamb", "fast.iamb", "inter.iamb", "iamb.fdr"
(2) Score-based Algorithms
- Hill-Climbing: "hc" (the hill-climbing greedy search algorithm, exploring DAGs by single-edge additions, removals, and reversals, with random restarts to avoid local optima)
- Others: "tabu"
(3) Hybrid Algorithms (combination of constraint-based and score-based algorithms)
- Restricted Maximization: "rsmax2" (the general 2-phase restricted maximization algorithm, first restricting the search space and then finding the optimal [maximizing the score of] network structure in the restricted space)
- Others: "mmhc", "h2pc"

algorithm.args

An optional list of extra arguments passed to the algorithm.

n.boot

Number of bootstrap samples (for learning a more "stable" network structure). Defaults to 1000.

seed

Random seed for replicable results. Defaults to NULL.

strength

Stability threshold of edge strength: the minimum proportion (probability) of BNs (among the n.boot bootstrap samples) in which each edge appears.

Defaults to 0.85 (85%).
Two reverse directions share the same edge strength.
Empirical frequency (?~100%) will be mapped onto edge width/thickness in the final integrated DAG, with wider (thicker) edges showing stronger links, though they usually look similar since the default range has been limited to 0.85~1.

direction

Stability threshold of edge direction: the minimum proportion (probability) of BNs (among the n.boot bootstrap samples) in which a direction of each edge appears.

Defaults to 0.50 (50%).
The proportions of two reverse directions add up to 100%.
Empirical frequency (?~100%) will be mapped onto edge greyscale/transparency in the final integrated DAG, with its value shown as edge text label.

node.text.size

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

edge.width.max

Maximum value of edge strength to scale all edge widths. Defaults to 1.5 for better display of arrow.

edge.label.mrg

Margin of the background box around the edge label. Defaults to 0.01.

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.

verbose

Print information about BN algorithm and number of bootstrap samples when running the analysis. Defaults to TRUE.

...

Arguments passed on to qgraph().

Value

Return a list (class dag.net) of Bayesian network results and qgraph object with its grob (Grid Graphical Object).

References

Briganti, G., Scutari, M., & McNally, R. J. (2023). A tutorial on Bayesian networks for psychopathology researchers. Psychological Methods, 28(4), 947–961. doi:10.1037/met0000479

Burger, J., Isvoranu, A.-M., Lunansky, G., Haslbeck, J. M. B., Epskamp, S., Hoekstra, R. H. A., Fried, E. I., Borsboom, D., & Blanken, T. F. (2023). Reporting standards for psychological network analyses in cross-sectional data. Psychological Methods, 28(4), 806–824. doi:10.1037/met0000471

Scutari, M., & Denis, J.-B. (2021). Bayesian networks: With examples in R (2nd ed.). Chapman and Hall/CRC. doi:10.1201/9780429347436

https://www.bnlearn.com/

Examples

bn = dag_network(airquality, seed=1)
bn
# bn$pc.stable
# bn$hc
# bn$rsmax2

## All DAG objects can be directly plotted
## or saved with print(..., file="xxx.png")
# bn$pc.stable$DAG.edge
# bn$pc.stable$DAG.strength
# bn$pc.stable$DAG.direction
# bn$pc.stable$DAG
# ...

## Not run: 

print(bn, file="airquality.png")
# will save three plots with auto-modified file names:
- "airquality_DAG.NET_BNs.01_pc.stable.png"
- "airquality_DAG.NET_BNs.02_hc.png"
- "airquality_DAG.NET_BNs.03_rsmax2.png"

# arrange multiple plots using aplot::plot_list()
# install.packages("aplot")
c1 = cor_network(airquality, "cor")
c2 = cor_network(airquality, "pcor")
bn = dag_network(airquality, seed=1)
p = aplot::plot_list(
  c1$plot,
  c2$plot,
  bn$pc.stable$DAG$plot,
  bn$hc$DAG$plot,
  bn$rsmax2$DAG$plot,
  design="111222
          334455",
  tag_levels="A"
)  # return a patchwork object
ggsave(p, filename="p.png", width=12, height=8, dpi=500)
ggsave(p, filename="p.pdf", width=12, height=8)

## End(Not run)

Produce a symmetric correlation matrix from values.

Description

Produce a symmetric correlation matrix from values.

Usage

matrix_cor(...)

Arguments

...

Correlation values to transform into the symmetric correlation matrix (by row).

Value

Return a symmetric correlation matrix.

Examples

matrix_cor(
  1.0, 0.7, 0.3,
  0.7, 1.0, 0.5,
  0.3, 0.5, 1.0
)

Simulate data from a multivariate normal distribution.

Description

Simulate data from a multivariate normal distribution.

Usage

sim_data(n, k, cor = NULL, exact = TRUE, seed = NULL)

Arguments

n

Number of observations (cases).

k

Number of variables. Will be ignored if cor specifies a correlation matrix.

cor

A correlation value or correlation matrix of the variables. Defaults to NULL that generates completely random data regardless of their empirical correlations.

exact

Ensure the sample correlation matrix to be exact as specified in cor. This argument is passed on to empirical in mvrnorm(). Defaults to TRUE.

seed

Random seed for replicable results. Defaults to NULL.

Value

Return a data.frame of simulated data.

Examples

d1 = sim_data(n=100, k=5, seed=1)
cor_network(d1)

d2 = sim_data(n=100, k=5, cor=0.2, seed=1)
cor_network(d2)

cor.mat = matrix_cor(
  1.0, 0.7, 0.3,
  0.7, 1.0, 0.5,
  0.3, 0.5, 1.0
)
d3 = sim_data(n=100, cor=cor.mat, seed=1)
cor_network(d3)

Simulate experiment-like data with independent binary Xs.

Description

Simulate experiment-like data with independent binary Xs.

Usage

sim_data_exp(
  n,
  r.xy,
  approx = TRUE,
  tol = 0.01,
  max.iter = 30,
  verbose = FALSE,
  seed = NULL
)

Arguments

n

Number of observations (cases).

r.xy

A vector of expected correlations of each X (binary independent variable: 0 or 1) with Y.

approx

Make the sample correlation matrix approximate more to values as specified in r.xy, using the method of orthogonal decomposition of residuals (i.e., making residuals more independent of Xs). Defaults to TRUE.

tol

Tolerance of absolute difference between specified and empirical correlations. Defaults to 0.01.

max.iter

Maximum iterations for approximation. More iterations produce more approximate correlations, but the absolute differences will be convergent after about 30 iterations. Defaults to 30.

verbose

Print information about iterations that satisfy tolerance. Defaults to FALSE.

seed

Random seed for replicable results. Defaults to NULL.

Value

Return a data.frame of simulated data.

Examples

data = sim_data_exp(n=1000, r.xy=c(0.5, 0.3), seed=1)
cor(data)  # tol = 0.01

data = sim_data_exp(n=1000, r.xy=c(0.5, 0.3), seed=1,
                    verbose=TRUE)
cor(data)  # print iteration information

data = sim_data_exp(n=1000, r.xy=c(0.5, 0.3), seed=1,
                    verbose=TRUE, tol=0.001)
cor(data)  # more approximate, though not exact

data = sim_data_exp(n=1000, r.xy=c(0.5, 0.3), seed=1,
                    approx=FALSE)
cor(data)  # far less exact

DPI: The Directed Prediction Index for Quasi-Causal Inference with Cross-Sectional Data

Description

Author(s)

See Also

The Directed Prediction Index (DPI).

Description

Usage

Arguments

Value

See Also

Examples

The DPI curve analysis.

Description

Usage

Arguments

Value

See Also

Examples

[S3 methods] for DPI() and DPI_curve().

Description

Usage

Arguments

[S3 methods] for cor_network() and dag_network().

Description

Usage

Arguments

Value

Correlation and partial correlation networks.

Description

Usage

Arguments

Value

See Also

Examples

Directed acyclic graphs (DAGs) via Bayesian networks (BNs).

Description

Usage

Arguments

Value

References

See Also

Examples

Produce a symmetric correlation matrix from values.

Description

Usage

Arguments

Value

Examples

Simulate data from a multivariate normal distribution.

Description

Usage

Arguments

Value

See Also

Examples

Simulate experiment-like data with independent binary Xs.

Description

Usage

Arguments

Value

See Also

Examples

[S3 methods] for `DPI()` and `DPI_curve()`.

[S3 methods] for `cor_network()` and `dag_network()`.