node_poisson {simDAG}

Simulate a Node Using Poisson Regression

Description

Data from the parents is used to generate the node using poisson regression by predicting the covariate specific lambda and sampling from a poisson distribution accordingly.

Usage

node_poisson(data, parents, formula=NULL, betas, intercept)

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.

Details

Essentially, this function simply calculates the linear predictor defined by the betas-coefficients, the intercept and the values of the parents. The exponential function is then applied to this predictor and the result is passed to the rpois function. The result is a draw from a subject-specific poisson distribution, resembling the user-defined poisson regression model.

Formal Description:

Formally, the data generation can be described as:

Y \sim Poisson(\lambda),

where Poisson() means that the variable is Poisson distributed with:

P_\lambda(k) = \frac{\lambda^k e^{-\lambda}}{k!}.

Here, k is the count and e is eulers number. The parameter \lambda is determined as:

\lambda = \exp(\texttt{intercept} + \texttt{parents}_1 \cdot \texttt{betas}_1 + ... + \texttt{parents}_n \cdot \texttt{betas}_n),

where n is the number of parents (length(parents)).

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

Y \sim Poisson(\exp(-15 + A \cdot 0.2 + B \cdot 1.3)).

Value

Returns a numeric vector of length nrow(data).

Author(s)

Robin Denz

See Also

empty_dag, node, node_td, sim_from_dag, sim_discrete_time

Examples

library(simDAG)

set.seed(345345)

dag <- empty_dag() +
  node("age", type="rnorm", mean=50, sd=4) +
  node("sex", type="rbernoulli", p=0.5) +
  node("smoking", type="poisson", parents=c("sex", "age"),
       betas=c(1.1, 0.4), intercept=-2)

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