In ErickChacon/datasim: Data Simulation Based on Models Formulas

knitr::opts_chunk$set(echo = TRUE, fig.align = "center")
knitr::opts_chunk$set(fig.width = 6, fig.height = 4)
knitr::opts_chunk$set(comment = "#>")
options(width = 100)

Introduction

In this vignette, we show how to simulate datasets to fit generalized linear models. We will start with a logistic linear model and then we will extend to common models used in the GLM framework.

Required packages

library(datasim)

Logistic Models

To simulate datasets for GLM, we need to identify the generator that can be used to simulate the response variable and its parameters. In the case of a logistic model, the generator is the rbinom function with parameters size and prob. We need to define a list of formulas specifying the type of effect that are included in the linear predictor of each parameter. For example, this list can be defined as follows.

f <- list(
  prob ~ I(1 * x1) + fa(sex, beta = c(0, -1), levels = c("male", "female")),
  size ~ I(1)
  )

In this formula, a linear effect on x1 and a factor effect on sex are included on the linear predictor of the prob parameter, while the size is equal to 1 to obtain a Bernoulli density.

The data for our model can be simulated with the function sim_model, which requires the inverse link function for each parameter through the argument link_inv, the generator and the sample size n. In the case of a logistic model model, the inverse link function for prob is the logistic function and identity function for size.

data_model <- sim_model(formula = f,
                        link_inv = list(psych::logistic, identity),
                        generator = rbinom,
                        n = 100, seed = 1)

The first 10 rows of the generated dataset looks as follows:

knitr::kable(head(data_model, 10))

it contains an unique id for each individual, all the predictors included in the formula (i.e. x1 and sex), the parameters (prob and size), and the simulated response variable.

Once the data is simulated, we can use it to compare models, effects, etc. For example, we can fit a logistic model to our simulated data with:

logis <- glm(response ~ x1 + sex, binomial, data_model)
logis_sum <- confint(logis)

The confidence intervals can be compared with the real parameters.

knitr::kable(logis_sum)

ErickChacon/datasim documentation built on March 25, 2020, 7:53 p.m.