Ex. 3 - Retrieving regression coefficients"

In lsasim: Functions to Facilitate the Simulation of Large Scale Assessment Data

library(knitr)
options(width = 90, tidy = TRUE, warning = FALSE, message = FALSE)
opts_chunk$set(comment = "", warning = FALSE, message = FALSE,
               echo = TRUE, tidy = TRUE)

library(lsasim)

packageVersion("lsasim")

---

With the arguments theta = TRUE, full_Output = TRUE and family = "gaussian", the output will automatically contain the $\beta$ vector and the $R$ matrix (i.e., beta_gen will be called automatically from within questionnaire_gen).

---

We generate one latent trait, two continuous, one binary, and one 3-category covariates. The data is generated from a multivariate normal distribution. The logical argument full_output is TRUE.

set.seed(1234)
bg <- questionnaire_gen(n_obs = 1000, n_X = 2, n_W = list(2, 3), theta = TRUE,
                        family = "gaussian", full_output = TRUE)

str(bg$bg)

linear_regression is a list that contains two elements. The first element, betas, summarizes the true regression coefficients $\beta$. The second element, vcov_YXW, shows the $R$ matrix.

bg$linear_regression

---

beta_gen uses the output from questionnaire_gen to generate linear regression coefficients.

beta_gen(bg)

If the logical argument MC is TRUE in beta_gen, Monte Carlo simulation is used to estimate regression coefficients. If the logical argument rename_to_q is TRUE, the background variables are all labeled as q to match the default behavior of questionnaire_gen.

The first column contains the true $\beta$, as estimated by the covariance matrix, which will always be the same for the same data. The column of MC reports the Monte Carlo simulation estimates for $\beta$, which is sample-dependent and will change each time the beta_gen function is called. The next two columns summarize the 99% confidence interval for these estimates. And the column of cov_in_CI return to logical argument whether the cov_matrix estimates are contained within their respective confidence intervals ("1" corresponds to "yes" and "0" to "no").

beta_gen(bg, MC = TRUE, MC_replications = 100, rename_to_q = TRUE)

beta_gen(bg, MC = TRUE, MC_replications = 100, rename_to_q = TRUE)

lsasim documentation built on Aug. 22, 2023, 5:09 p.m.