causalDisco (version 0.9.5)

TemporalBIC-class: Temporal Bayesian Information Criterion (Score criterion)

Description

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).

Extends

Class pcalg::GaussL0penObsScore 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

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 the edges does not contradict, the score is equal to that of pcalg::GaussL0penObsScore: 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.

See Also

tges

Examples

#Simulate Gaussian data
set.seed(123)
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
prefix_order <- c("child", "adult")

# Define TBIC score
t_score <- new("TemporalBIC", order = prefix_order
               , data = simdata)
# Run tges
tges_pre <- tges(t_score)

# Plot MPDAG
plot(tges_pre)

# Define order in integer way
integer_order <- c(1,1,1,2,2,2,2)

# Define TBIC score
t_score <- new("TemporalBIC", order = integer_order
               , data = simdata)
# Run tges
tges_int <- tges(t_score)

# Plot MPDAG
plot(tges_int)