Generate Data from a Beta Regression Model

Data from the parents is used to generate the node using beta regression by applying the betas to the design matrix, transforming the resulting linear predictor to a conditional mean, and sampling from the rbeta function.

Usage

node_beta(data, parents, formula=NULL, betas,
          intercept, precision, link="logit")

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. Random effects and random slopes are currently not supported here.
betas: A numeric vector with length equal to the number of columns in the design matrix, 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.
precision: A single finite, positive number specifying the precision parameter \(\phi\) of the beta distribution. The precision is the sum of the two shape parameters and determines the conditional variance of the generated values relative to their conditional mean.
link: The link function used to transform the linear predictor to the conditional mean. The default is "logit". Other allowed values are "probit", "cloglog", "loglog", and "cauchit".

Details

This function uses the linear predictor defined by the betas and the input design matrix to obtain an observation-specific conditional mean. It does so by calculating the linear predictor using the data, betas, and intercept, applying the inverse of the specified link function, and passing the resulting conditional mean to the rbeta function of the stats package.

For an observation with conditional mean \(\mu_i\) and precision parameter \(\phi\), the generated outcome follows a beta distribution with shape parameters \(\mu_i\phi\) and \((1-\mu_i)\phi\). Consequently, the conditional mean is \(E(Y_i\mid X_i)=\mu_i\) and the conditional variance is \(\mathrm{Var}(Y_i\mid X_i)=\mu_i(1-\mu_i)/(\phi+1)\).

Every non-missing conditional mean must be finite and strictly between zero and one. This node type currently does not support inclusion of random effects or random slopes in the formula. The precision parameter is fixed across observations.

Author

Robin Denz

Value

Returns a numeric vector of length nrow(data).

Examples

library(simDAG)

set.seed(124554)

dag <- empty_dag() +
  node("age", type="rnorm", mean=50, sd=4) +
  node("sex", type="rbernoulli", p=0.5) +
  node("proportion", type="beta", precision=10,
       formula= ~ -1 + age*0.01 + sexTRUE*0.2)

sim_dat <- sim_from_dag(dag=dag, n_sim=100, sort_dag=FALSE)
head(sim_dat)
#>         age    sex proportion
#>       <num> <lgcl>      <num>
#> 1: 52.81824  FALSE  0.1708070
#> 2: 50.86212  FALSE  0.3775658
#> 3: 52.92595   TRUE  0.5807400
#> 4: 51.01464  FALSE  0.4498672
#> 5: 43.14107  FALSE  0.4546994
#> 6: 54.15130   TRUE  0.4961721