Temporal Bayesian Information Criterion (Score criterion)

A Reference Class for Gaussian Observational Data Scoring with Tiered Background Knowledge. This class represents a score for causal discovery using tiered background knowledge from observational Gaussian data; it is used in the causal discovery function tges().

Arguments

data: A numeric matrix with \(n\) rows and \(p\) columns. Each row corresponds to one observational realization.
order: A vector specifying the order each variable. Can be either a vector of integers or an vector of prefixes. If integers, such that the ith entry will detail the order of the ith variable in the dataset. Must start at 1 an increase with increments of 1. If prefixes, must be in order.
lambda: Penalization constant (see details).
intercept: Logical; indicates whether an intercept is allowed in the linear structural equations (i.e., whether a nonzero mean is allowed).

Details

The class implements a score which scores all edges contradicting the ordering (edge going from a later tier to an earlier) to minus \(\infty\). If the edges does not contradict, the score is equal to that of the standard BIC. The class implements an \(\ell_0\)-penalized Gaussian maximum likelihood estimator. The penalization is a constant (specified by the argument lambda in the constructor) times the number of parameters of the DAG model. By default, the constant \(\lambda\) is chosen as \(\log(n)/2\), which corresponds to the BIC score.

Extends

Class GaussL0penObsScore from pcalg, directly.

All reference classes extend and inherit methods from envRefClass.

Constructor


new(
 "TemporalBIC",
 data = matrix(1, 1, 1),
 order =  rep(1,ncol(data)),
 lambda = 0.5 * log(nrow(data)),
 intercept = TRUE,
 ...
)

Author

Tobias Ellegaard Larsen

Examples

# Simulate Gaussian data
set.seed(1405)
n <- 500
child_x <- rnorm(n)
child_y <- 0.5 * child_x + rnorm(n)
child_z <- 2 * child_x + child_y + rnorm(n)

adult_x <- child_x + rnorm(n)
adult_z <- child_z + rnorm(n)
adult_w <- 2 * adult_z + rnorm(n)
adult_y <- 2 * child_x + adult_w + rnorm(n)

simdata <- data.frame(
  child_x,
  child_y,
  child_z,
  adult_x,
  adult_z,
  adult_w,
  adult_y
)

# Define order in prefix way
kn <- knowledge(
  simdata,
  tier(
    child ~ tidyselect::starts_with("child"),
    adult ~ tidyselect::starts_with("adult")
  )
)

# Define TBIC score
t_score <- new("TemporalBIC", knowledge = kn, data = simdata)
# Run tges
tges_pre <- tges_run(t_score)

# Plot MPDAG
# plot(tges_pre)