Ex. 2 - Understanding the elements in output"

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")

questionnaire_gen(n_obs, cat_prop = NULL, n_vars = NULL, n_X = NULL, n_W = NULL,
                  cor_matrix = NULL, cov_matrix = NULL,
                  c_mean = NULL, c_sd = NULL,
                  theta = FALSE, family = NULL,
                  full_output = FALSE, verbose = TRUE)

By default, the function returns a data.frame object where the first column ("subject") is a $1, \ldots, n$ ordered list of the $n$ observations and the other columns correspond to the questionnaire answers. If theta = TRUE, the first column after "subject" will be the latent variable theta; in any case, the continuous variables always come before the categorical ones.

If the logical argument full_output is TRUE, output will be a list containing the questionnaire data as well as several objects that might be of interest for further analysis of the data, listed below:

• bg: a data frame containing the background questionnaire answers (i.e., the same object output if full_output = FALSE).
• c_mean: is a vector of population means for each continuous variable ($Y$ and $X$).
• c_sd: is a vector of population standard deviations for each continuous variable ($Y$ and $X$).
• cat_prop: list of cumulative proportions for each item. If theta = TRUE, the first element of cat_prop must be a scalar 1, which corresponds to theta.
• cat_prop_W_p: a list containing the probabilities for each category of the categorical variables (cat_prop_W contains the cumulative probabilities).
• cor_matrix: latent correlation matrix. The first row/column corresponds to the latent trait ($Y$). The other rows/columns correspond to the continuous ($X$ or $Z$) or the discrete ($W$) background variables, in the same order as cat_prop.
• cov_matrix: latent covariance matrix, formatted as cor_matrix.
• family: distribution of the background variables. Can be NULL (default) or 'gaussian'.
• n_obs: number of observations to generate.
• n_tot: named vector containing the number of total variables, the number of continuous background variables (i.e., the total number of background variables except theta) and the number of categorical variables.
• n_W: vector containing the number of categorical variables.
• n_X: vector containing the number of continuous variables (except theta).
• sd_YXW: vector with the standard deviations of all the variables
• sd_YXZ: vector containing the standard deviations of theta, the background continuous variables ($X$) and the Normally-distributed variables $Z$ which will generate the background categorical variables ($W$).
• theta: if TRUE, the first continuous variable will be labeled "theta". Otherwise, it will be labeled q1.
• var_W: list containing the variances of the categorical variables.
• var_YX: list containing the variances of the continuous variables (including theta)
• linear_regression: This list is printed only if theta = TRUE, family = "gaussian" and full_output = TRUE. It contains one vector named betas and one tabled named cov_YXW. The former displays the true linear regression coefficients of theta on the background questionnaire answers; the latter contains the covariance matrix between all these variables.

---

We generate one continuous and two ordinal covariates. We specify the covariance matrix between the numeric and ordinal variables. The data is generated from a multivariate normal distribution. And we set the logical argument full_output = TRUE.

set.seed(1234)
(props <- list(1, c(.25, 1), c(.2, .8, 1)))
(yw_cov <- matrix(c(1, .5, .5, .5, 1, .8, .5, .8, 1), nrow = 3))
bg <- questionnaire_gen(n_obs = 10, cat_prop = props, cov_matrix = yw_cov, theta = TRUE,
                  family = "gaussian", full_output = TRUE)
names(bg)

The output is a list containing the following elements: r names(bg).

?questionnaire_gen

set.seed(1234)
(props <- list(1, c(.25, 1), c(.2, .8, 1)))
(yw_cov <- matrix(c(1, .5, .5, .5, 1, .8, .5, .8, 1), nrow = 3))

questionnaire_gen(n_obs = 10, cat_prop = props, cov_matrix = yw_cov, theta = TRUE,
                  family = "gaussian", full_output = TRUE)

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