Retrieving regression coefficients - tmatta/lsasim GitHub Wiki
library(lsasim)
packageVersion("lsasim")
[1] '2.0.0'
With the arguments theta = TRUE, full_Output = TRUE and
family = "gaussian", the output will automatically contain the β
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)
'data.frame': 1000 obs. of 6 variables:
$ subject: int 1 2 3 4 5 6 7 8 9 10 ...
$ theta : num -1.732 0.707 0.911 1.509 -0.5 ...
$ q1 : num -0.491 0.16 -0.39 -1.307 0.602 ...
$ q2 : num 0.5499 0.0669 0.087 -1.628 0.2559 ...
$ q3 : Factor w/ 2 levels "1","2": 2 2 2 1 2 2 1 1 2 1 ...
$ q4 : Factor w/ 3 levels "1","2","3": 1 2 3 2 1 2 1 1 1 3 ...
linear_regression is a list that contains two elements. The first
element, betas, summarizes the true regression coefficients β. The
second element, vcov_YXW, shows the R matrix.
bg$linear_regression
$betas
theta q1 q2 q3.2 q4.2 q4.3
-0.8174844 -0.5836818 -0.5402292 -0.1049199 0.8699444 1.7398887
$vcov_YXW
theta q1 q2 q3.2 q4.2 q4.3
theta 1.00000000 -0.17564245 -0.26487195 -0.07889541 0.00 0.12421718
q1 -0.17564245 1.00000000 -0.28027150 0.03541595 0.00 0.14963273
q2 -0.26487195 -0.28027150 1.00000000 0.25560791 0.00 0.07965237
q3.2 -0.07889541 0.03541595 0.25560791 0.25000000 0.00 0.06097692
q4.2 0.00000000 0.00000000 0.00000000 0.00000000 0.24 -0.12000000
q4.3 0.12421718 0.14963273 0.07965237 0.06097692 -0.12 0.21000000
beta_gen uses the output from questionnaire_gen to generate linear
regression coefficients.
beta_gen(bg)
theta x1 x2 w12 w22 w23
-0.8174844 -0.5836818 -0.5402292 -0.1049199 0.8699444 1.7398887
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 β, 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 β, 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)
cov_matrix MC 0.5% 99.5% cov_in_CI
theta -0.8174844 -0.7528447 -0.8380719 -0.64147366 1
q1 -0.5836818 -0.5627695 -0.6279581 -0.49666666 1
q2 -0.5402292 -0.4950472 -0.5571855 -0.44193911 1
q3.2 -0.1049199 -0.1876017 -0.3357658 -0.08231601 1
q4.2 0.8699444 0.8165117 0.7057719 0.92812704 1
q4.3 1.7398887 1.7389447 1.5867220 1.88949655 1
beta_gen(bg, MC = TRUE, MC_replications = 100, rename_to_q = TRUE)
cov_matrix MC 0.5% 99.5% cov_in_CI
theta -0.8174844 -0.7485083 -0.8550206 -0.63323259 1
q1 -0.5836818 -0.5650178 -0.6309527 -0.51627209 1
q2 -0.5402292 -0.4954573 -0.5544919 -0.43396311 1
q3.2 -0.1049199 -0.1793640 -0.3039317 -0.05262306 1
q4.2 0.8699444 0.8092411 0.6481412 0.95344844 1
q4.3 1.7398887 1.7205485 1.5569970 1.90153362 1