node_conditional_prob: Simulate a Node Using Conditional Probabilities

Description

This function can be used to generate dichotomous or categorical variables dependent on one or more categorical variables where the probabilities of occurrence in each strata defined by those variables is known.

Usage

node_conditional_prob(data, parents, probs, default_probs=NULL,
                      default_val=NA, labels=NULL,
                      coerce2factor=FALSE, check_inputs=TRUE)

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.
probs: A named list where each element corresponds to one stratum defined by parents. If only one name is given in parents, this means that there should be one element for possible value of the variable given in parents. If the node has multiple parents, there needs to be one element for possible combinations of parents (see examples). The values of those elements should either be a single number, corresponding to the probability of occurrence of a single event/value in case of a dichotomous variable, or a vector of probabilities that sum to 1, corresponding to class probabilities. In either case, the length of all elements should be the same. If possible strata of parents (or their possible combinations in case of multiple parents) are omitted, the result will be set to default_val for these omitted strata. See argument default_val and argument default_probs for an alternative.
default_probs: If not all possible strata of parents are included in probs, the user may set default probabilities for all omitted strata. For example, if there are three strata (A, B and C) defined by parents and probs only contains defined probabilities for strata A, the probabilities for strata B and C can be set simultaneously by using this argument. Should be a single value between 0 and 1 for Bernoulli trials and a numeric vector with sum 1 for multinomial trials. If NULL (default) the value of the produced output for missing strata will be set to default_val (see below).
default_val: Value of the produced variable in strata that are not included in the probs argument. If default_probs is not NULL, that arguments functionality will be used instead.
labels: A vector of labels for the generated output. If NULL (default) and the output is dichotomous, a logical variable will be returned. If NULL and the output is categorical, it simply uses integers starting from 1 as class labels.
coerce2factor: A single logical value specifying whether to return the drawn events as a factor or not.
check_inputs: A single logical value specifying whether input checks should be performed or not. Set to FALSE to save some computation time in simulations.

Author

Robin Denz

Details

Utilizing the user-defined discrete probability distribution in each stratum of parents (supplied using the probs argument), this function simply calls either the rbernoulli or the rcategorical function.

Formal Description:

Formally, the data generation process can be described as a series of conditional equations. For example, suppose that there is just one parent node sex with the levels male and female with the goal of creating a binary outcome that has a probability of occurrence of 0.5 for males and 0.7 for females. The conditional equation is then:

$$Y \sim Bernoulli(p),$$

where:

$$p = \begin{cases} 0.5, & \text{if } \texttt{sex="male"} \\ 0.7, & \text{if } \texttt{sex="female"} \\ \end{cases},$$

and $Bernoulli(p)$ is the Bernoulli distribution with success probability $p$. If the outcome has more than two categories, the Bernoulli distribution would be replaced by $Multinomial(p)$ with $p$ being replaced by a matrix of class probabilities. If there are more than two variables, the conditional distribution would be stratified by the intersection of all subgroups defined by the variables.

An even more flexible node type, allowing arbitrary node definitions for different subsets of the previously generated data is included in node_mixture.

Examples

Run this code

library(simDAG)

set.seed(42)

#### two classes, one parent node ####

# define conditional probs
probs <- list(male=0.5, female=0.8)

# define DAG
dag <- empty_dag() +
  node("sex", type="rcategorical", labels=c("male", "female"),
       output="factor", probs=c(0.5, 0.5)) +
  node("chemo", type="rbernoulli", p=0.5) +
  node("A", type="conditional_prob", parents="sex", probs=probs)

# generate data
data <- sim_from_dag(dag=dag, n_sim=1000)


#### three classes, one parent node ####

# define conditional probs
probs <- list(male=c(0.5, 0.2, 0.3), female=c(0.8, 0.1, 0.1))

# define DAG
dag <- empty_dag() +
  node("sex", type="rcategorical", labels=c("male", "female"),
       output="factor", probs=c(0.5, 0.5)) +
  node("chemo", type="rbernoulli", p=0.5) +
  node("A", type="conditional_prob", parents="sex", probs=probs)

# generate data
data <- sim_from_dag(dag=dag, n_sim=1000)


#### two classes, two parent nodes ####

# define conditional probs
probs <- list(male.FALSE=0.5,
              male.TRUE=0.8,
              female.FALSE=0.1,
              female.TRUE=0.3)

# define DAG
dag <- empty_dag() +
  node("sex", type="rcategorical", labels=c("male", "female"),
       output="factor", probs=c(0.5, 0.5)) +
  node("chemo", type="rbernoulli", p=0.5) +
  node("A", type="conditional_prob", parents=c("sex", "chemo"), probs=probs)

# generate data
data <- sim_from_dag(dag=dag, n_sim=1000)


#### three classes, two parent nodes ####

# define conditional probs
probs <- list(male.FALSE=c(0.5, 0.1, 0.4),
              male.TRUE=c(0.8, 0.1, 0.1),
              female.FALSE=c(0.1, 0.7, 0.2),
              female.TRUE=c(0.3, 0.4, 0.3))

# define dag
dag <- empty_dag() +
  node("sex", type="rcategorical", labels=c("male", "female"),
       output="factor", probs=c(0.5, 0.5)) +
  node("chemo", type="rbernoulli", p=0.5) +
  node("A", type="conditional_prob", parents=c("sex", "chemo"), probs=probs)

# generate data
data <- sim_from_dag(dag=dag, n_sim=1000)

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