Simulate a Node Using Poisson Regression

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:

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

Author

Robin Denz

Value

Returns a numeric vector of length nrow(data).

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",
       formula= ~ -2 + sexTRUE*1.1 + age*0.4)

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