simDAG (version 0.2.2)

node_gaussian: Simulate a Node Using Linear Regression

Description

Data from the parents is used to generate the node using linear regression by predicting the covariate specific mean and sampling from a normal distribution with that mean and a specified standard deviation.

Usage

node_gaussian(data, parents, formula=NULL, betas, intercept, error)

Value

Returns a numeric vector of length nrow(data).

Arguments

data

A data.table (or something that can be coerced to a data.table) containing all columns specified by parents.

parents

A character vector specifying the names of the parents that this particular child node has. If non-linear combinations or interaction effects should be included, the user may specify the formula argument instead.

formula

An optional formula object to describe how the node should be generated or NULL (default). If supplied it should start with ~, having nothing else on the left hand side. The right hand side may contain any valid formula syntax, such as A + B or A + B + I(A^2), allowing non-linear effects. If this argument is defined, there is no need to define the parents argument. For example, using parents=c("A", "B") is equal to using formula= ~ A + B.

betas

A numeric vector with length equal to parents, specifying the causal beta coefficients used to generate the node.

intercept

A single number specifying the intercept that should be used when generating the node.

error

A single number specifying the sigma error that should be used when generating the node.

Author

Robin Denz

Details

Using the general linear regression equation, the observation-specific value that would be expected given the model is generated for every observation in the dataset generated thus far. We could stop here, but this would create a perfect fit for the node, which is unrealistic. Instead, we add an error term by taking one sample of a normal distribution for each observation with mean zero and standard deviation error. This error term is then added to the predicted mean.

Formal Description:

Formally, the data generation can be described as:

$$Y \sim \texttt{intercept} + \texttt{parents}_1 \cdot \texttt{betas}_1 + ... + \texttt{parents}_n \cdot \texttt{betas}_n+ N(0, \texttt{error}),$$

where \(N(0, \texttt{error})\) denotes the normal distribution with mean 0 and a standard deviation of error and \(n\) is the number of parents (length(parents)).

For example, given intercept=-15, parents=c("A", "B"), betas=c(0.2, 1.3) and error=2 the data generation process is defined as:

$$Y \sim -15 + A \cdot 0.2 + B \cdot 1.3 + N(0, 2).$$

See Also

empty_dag, node, node_td, sim_from_dag, sim_discrete_time

Examples

library(simDAG)

set.seed(12455432)

# define a DAG
dag <- empty_dag() +
  node("age", type="rnorm", mean=50, sd=4) +
  node("sex", type="rbernoulli", p=0.5) +
  node("bmi", type="gaussian", parents=c("sex", "age"),
       betas=c(1.1, 0.4), intercept=12, error=2)

# define the same DAG, but with a pretty formula for the child node
dag <- empty_dag() +
  node("age", type="rnorm", mean=50, sd=4) +
  node("sex", type="rbernoulli", p=0.5) +
  node("bmi", type="gaussian", error=2,
       formula= ~ 12 + sexTRUE*1.1 + age*0.4)

sim_dat <- sim_from_dag(dag=dag, n_sim=100)