Generate Synthetic Data from a Linear Gaussian DAG

Generates synthetic data from a directed acyclic graph (DAG) specified as a caugi graph object. Each node is modeled as a linear combination of its parents plus additive Gaussian noise. Coefficients are randomly signed with a minimum absolute value, and noise standard deviations are sampled log-uniformly from a specified range. Custom node equations can override automatic linear generation.

Usage

generate_dag_data(
  cg,
  n,
  ...,
  standardize = TRUE,
  coef_range = c(0.1, 0.9),
  error_sd = c(0.3, 2),
  seed = NULL
)

Arguments

cg

A caugi graph object representing a DAG.

n

Integer. Number of observations to simulate.

...

Optional named node equations to override automatic linear generation. Each should be an expression referencing all parent nodes.

standardize

Logical. If TRUE, each column of the output is standardized to mean 0 and standard deviation 1.

coef_range

Numeric vector of length 2 specifying the minimum and maximum absolute value of edge coefficients. For each edge, an absolute value is sampled uniformly from this range and then assigned a positive or negative sign with equal probability. Must satisfy coef_range[1] > 0 and coef_range[2] >= coef_range[1].

error_sd

Numeric vector of length 2 specifying the minimum and maximum standard deviation of the additive Gaussian noise at each node. For each node, a standard deviation is sampled from a log-uniform distribution over this range. Must satisfy error_sd[1] > 0 and error_sd[2] >= error_sd[1].

seed

Optional integer. Sets the random seed for reproducibility.

Value

A tibble of simulated data with one column per node in the DAG, ordered according to the graph's node order. Standardization is applied if standardize = TRUE.

The returned tibble has an attribute generating_model, which is a list containing:

• sd: Named numeric vector of node-specific noise standard deviations.

• coef: Named list of numeric vectors, where each element corresponds to a child node. For a child node, the vector stores the coefficients of its parent nodes in the linear structural equation. That is: generating_model$coef[[child]][parent] gives the coefficient of parent in the equation for child.

Examples

cg <- caugi::caugi(A %-->% B, B %-->% C, A %-->% C, class = "DAG")

# Simulate 1000 observations
sim_data <- generate_dag_data(
  cg,
  n = 1000,
  coef_range = c(0.2, 0.8),
  error_sd = c(0.5, 1.5)
)

head(sim_data)
#> # A tibble: 6 × 3
#>        A      B       C
#>    <dbl>  <dbl>   <dbl>
#> 1  1.02  -1.67   0.775 
#> 2 -0.313  1.50   2.18  
#> 3 -0.532  0.182 -0.915 
#> 4  0.679 -1.12  -0.0110
#> 5  0.541  0.594  1.24  
#> 6  1.04  -1.08   0.271 
attr(sim_data, "generating_model")
#> $dgp
#> $dgp$A
#> rnorm(n, sd = 1.027)
#> 
#> $dgp$B
#> A * -0.563 + rnorm(n, sd = 0.623)
#> 
#> $dgp$C
#> A * 0.623 + B * 0.398 + rnorm(n, sd = 0.865)
#> 
#> 

# Simulate with custom equation for node C
sim_data_custom <- generate_dag_data(
  cg,
  n = 1000,
  C = A^2 + B + rnorm(n, sd = 0.7),
  seed = 1405
)
head(sim_data_custom)
#> # A tibble: 6 × 3
#>         A      B      C
#>     <dbl>  <dbl>  <dbl>
#> 1  0.301   0.148 -0.114
#> 2 -1.13    2.02   1.71 
#> 3  0.727  -0.719 -0.696
#> 4 -0.179   0.781  0.276
#> 5  0.0492  0.840  0.449
#> 6  0.179   0.232 -0.641
attr(sim_data_custom, "generating_model")
#> $dgp
#> $dgp$A
#> rnorm(n, sd = 0.95)
#> 
#> $dgp$B
#> A * -0.856 + rnorm(n, sd = 1.266)
#> 
#> $dgp$C
#> A^2 + B + rnorm(n, sd = 0.7)
#> 
#>