SimCorMultRes: Simulates Correlated Multinomial Responses

Installation

You can install the release version of SimCorMultRes:

install.packages("SimCorMultRes")

The source code for the release version of SimCorMultRes is available on CRAN at:

• https://CRAN.R-project.org/package=SimCorMultRes

Or you can install the development version of SimCorMultRes:

# install.packages('devtools')
devtools::install_github("AnestisTouloumis/SimCorMultRes")

The source code for the development version of SimCorMultRes is available on github at:

• https://github.com/AnestisTouloumis/SimCorMultRes

To use SimCorMultRes, you should load the package as follows:

library("SimCorMultRes")

Usage and functions

This package provides five core functions to simulate correlated binary (rbin), nominal (rmult.bcl) and ordinal (rmult.acl, rmult.clm and rmult.crm) responses, which are drawn as realizations of a latent regression model for continuous random vectors as proposed by Touloumis (2016):

• rbin to simulate correlated binary responses under a marginal model with logit, probit, cloglog and cauchit link function,
• rmult.bcl to simulate correlated nominal multinomial responses under a marginal baseline-category logit model,
• rmult.acl to simulate correlated ordinal responses under a marginal adjacent-category logit model,
• rmult.clm to simulate correlated ordinal responses under a marginal cumulative link model,
• rmult.crm to simulate correlated ordinal responses under a marginal continuation-ratio link model.

All five functions, assume that you provide either the correlation matrix of the multivariate normal distribution in NORTA (via cor.matrix) or the values of the latent responses (via the rlatent). Based on a simulation study (see Section 3.5 of the vignette and dataset simulation), it is indicated that the correlation matrix of the multivariate normal distribution used in the NORTA method (via cor.matrix) can be considered a reliable approximation of the actual correlation matrix of the latent responses generated by the NORTA method. This appears to be the case irrespective of the marginal distributions of the latent responses for all the threshold approaches implemented in SimCorMultRes.

There are also two utility functions:

• rnorta for simulating continuous or discrete random vectors with prescribed marginal distributions using the NORTA method,
• rsmvnorm for simulating continuous random vectors from a multivariate normal distribution.

Example

The following R code illustrates how to use the core function rbin:

## See Example 3.5 in the Vignette.
set.seed(123)
## define number of random vectors
sample_size <- 100
## define size of each random vector
cluster_size <- 4
## define intercept of the binary probit regression model
beta_intercepts <- 0
## define coefficients of the explanatory variables
beta_coefficients <- 0.2
## provide explanatory variables
x <- rep(rnorm(sample_size), each = cluster_size)
## define correlation matrix for the multivariate normal distribution in NORTA
latent_correlation_matrix <- toeplitz(c(1, 0.9, 0.9, 0.9))
## use rbin function to create the desired dataset
simulated_binary_responses <- rbin(clsize = cluster_size, intercepts = beta_intercepts,
    betas = beta_coefficients, xformula = ~x, cor.matrix = latent_correlation_matrix,
    link = "probit")
library("gee")
binary_gee_model <- gee(y ~ x, family = binomial("probit"), id = id, data = simulated_binary_responses$simdata)
#> Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
#> running glm to get initial regression estimate
#> (Intercept)           x 
#>   0.1315121   0.2826005
summary(binary_gee_model)$coefficients
#>              Estimate Naive S.E.  Naive z Robust S.E. Robust z
#> (Intercept) 0.1315121 0.06399465 2.055048   0.1106696 1.188331
#> x           0.2826006 0.07191931 3.929412   0.1270285 2.224703

Additional examples can be found in Touloumis (2016) and in the vignette of SimCorMultRes. To access these two documents, run the following command:

browseVignettes("SimCorMultRes")

How to cite

To cite 'SimCorMultRes' in publications, please use:

  Touloumis A (2016). "Simulating Correlated Binary and Multinomial
  Responses under Marginal Model Specification: The SimCorMultRes
  Package." _The R Journal_, *8*(2), 79-91. R package version 1.9.0,
  <https://journal.r-project.org/archive/2016/RJ-2016-034/index.html>.

A BibTeX entry for LaTeX users is

  @Article{,
    title = {Simulating Correlated Binary and Multinomial Responses under
         Marginal Model Specification: The SimCorMultRes Package},
    author = {Anestis Touloumis},
    year = {2016},
    journal = {The R Journal},
    volume = {8},
    number = {2},
    note = {R package version 1.9.0},
    pages = {79-91},
    url = {https://journal.r-project.org/archive/2016/RJ-2016-034/index.html},
  }

References

Touloumis, A. (2016) Simulating Correlated Binary and Multinomial Responses under Marginal Model Specification: The SimCorMultRes Package. The R Journal, 8, 79–91.