Simulated dataset following the mglrm for two groups.

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A data frame with 4000 respondents allocated equally to two groups via indicator
variable S. They face a test of 20 items Y of which the first 18 are binary and the last two
are ordinal with 4 categories. Three covariates X are generated from a multivariate normal
distribution, where the variables each have a mean of 0, unit variance and pairwise
correlations equal to 0.5. X1 is transformed into a binary variable with a split value of 0.
The corresponding parameters of the population model including an intercept are set to
*γ_1=(-0.5,0.2,0.2,-0.5)'*, *γ_2=(1,0.4,-0.2,-0.7)'*,
*σ^2_1=0.5^2* and *σ^2_2=0.6^2*. 5 percent of the observations in Y18,
Y20, X1 and X2 are deleted completely at random.

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