Simulate a Node Using (Mixed) Logistic Regression

Data from the parents is used to generate the node using logistic regression by predicting the covariate specific probability of 1 and sampling from a Bernoulli distribution accordingly. Allows inclusion of arbitrary random effects and slopes.

Usage

node_binomial(data, parents, formula=NULL, betas, intercept,
              return_prob=FALSE, output="logical", labels=NULL,
              var_corr=NULL)

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. May contain random effects and random slopes, in which case the simr package is used to generate the data. See details.
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.
return_prob: Either TRUE or FALSE (default). If TRUE, the calculated probability is returned instead of the results of bernoulli trials. This argument is ignored if random effects or random slopes are specified in the formula input.
output: A single character string, must be either "logical" (default), "numeric", "character" or "factor". If output="character" or output="factor", the labels (or levels in case of a factor) can be set using the labels argument.
labels: A character vector of length 2 or NULL (default). If NULL, the resulting vector is returned as is. If a character vector is supplied and output="character" or output="factor" is used, all TRUE values are replaced by the first entry of this vector and all FALSE values are replaced by the second argument of this vector. The output will then be a character variable or factor variable, depending on the output argument. This argument is ignored if output is set to "numeric" or "logical".
var_corr: Variances and covariances for random effects. Only used when formula contains mixed model syntax. If there are multiple random effects, their parameters should be supplied as a named list. More complex structures are also supported. This argument is directly passed to the makeLmer function of the simr package. Please consult the documentation of that package for more information on how mixed models should be specified. Some guidance can also be found in the "Issues" section of the official simr github page.

Details

Using the normal form a logistic regression model, the observation specific event probability is generated for every observation in the dataset. Using the rbernoulli function, this probability is then used to take one bernoulli sample for each observation in the dataset. If only the probability should be returned return_prob should be set to TRUE.

Formal Description:

Formally, the data generation can be described as:

$$Y \sim Bernoulli(logit(\texttt{intercept} + \texttt{parents}_1 \cdot \texttt{betas}_1 + ... + \texttt{parents}_n \cdot \texttt{betas}_n)),$$

where $Bernoulli(p)$ denotes one Bernoulli trial with success probability $p$, $n$ is the number of parents (length(parents)) and the $logit(x)$ function is defined as:

$$logit(x) = ln(\frac{x}{1-x}).$$

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

$$Y \sim Bernoulli(logit(-15 + A \cdot 0.2 + B \cdot 1.3)).$$

Output Format:

By default this function returns a logical vector containing only TRUE and FALSE entries, where TRUE corresponds to an event and FALSE to no event. This may be changed by using the output and labels arguments. The last three arguments of this function are ignored if return_prob is set to TRUE.

Random Effects and Random Slopes:

This function also allows users to include arbitrary amounts of random slopes and random effects using the formula argument. If this is done, the formula, and data arguments are passed to the variables of the same name in the makeGlmer function of the simr package. The fixef argument of that function will be passed the numeric vector c(intercept, betas) and the VarCorr argument receives the var_corr argument as input. If used as a node type in a DAG, all of this is taken care of behind the scenes. Users can simply use the regular enhanced formula interface of the node function to define these formula terms, as shown in detail in the formula vignette (vignette(topic="v_using_formulas", package="simDAG")). Please consult that vignette for examples. Also, please note that inclusion of random effects or random slopes usually results in significantly longer computation times.

Author

Robin Denz

Value

Returns a logical vector (or numeric vector if return_prob=TRUE) of length nrow(data).

Examples

library(simDAG)

set.seed(5425)

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

# define the same DAG, but using a pretty formula
dag <- empty_dag() +
  node("age", type="rnorm", mean=50, sd=4) +
  node("sex", type="rbernoulli", p=0.5) +
  node("smoking", type="binomial",
       formula= ~ -2 + age*1.1 + sexTRUE*0.4)

# simulate data from it
sim_dat <- sim_from_dag(dag=dag, n_sim=100)

# returning only the estimated probability instead
dag <- empty_dag() +
  node("age", type="rnorm", mean=50, sd=4) +
  node("sex", type="rbernoulli", p=0.5) +
  node("smoking", type="binomial", parents=c("age", "sex"),
       betas=c(1.1, 0.4), intercept=-2, return_prob=TRUE)

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

## an example using a random effect
if (requireNamespace("simr")) {

library(simr)

dag_mixed <- empty_dag() +
  node("School", type="rcategorical", probs=rep(0.1, 10),
       labels=LETTERS[1:10]) +
  node("Age", type="rnorm", mean=12, sd=2) +
  node("Grade", type="binomial", formula= ~ -10 + Age*1.2 + (1|School),
       var_corr=0.3)

sim_dat <- sim_from_dag(dag=dag_mixed, n_sim=100)
}
#> Loading required namespace: simr
#> Loading required package: lme4
#> Loading required package: Matrix
#> 
#> Attaching package: ‘simr’
#> The following object is masked from ‘package:lme4’:
#> 
#>     getData