Generation of Synthetic Data Utilizing Data Augmentation

This function generates synthetic data utilizing data augmentation (Jiang et al., 2022; Grund et al., 2022). Continuous and ordinal variables can be handled. The order of the synthesized variables can be defined using the argument syn_vars.

syn_da(dat, syn_vars=NULL, fix_vars=NULL, ord_vars=NULL, da_noise=0.5,
   formula_syn=NULL, use_pls=TRUE, ncomp=20, exact_regression=TRUE,
   exact_marginal=TRUE, imp_maxit=5)

Arguments

dat

Original dataset

syn_vars

Vector with variable names that should be synthesized

fix_vars

Vector with variable names that are held fixed in the synthesis

ord_vars

Vector with ordinal variables that are treated as factors when modeled as predictors in the regression model

da_noise

Proportion of variance (i.e., unreliability) that is added as noise in data augmentation. The argument can be numeric or a vector, depending on whether it is made variable-specific. Can also be a vector of the same dimension as syn_vars if different unreliabilities should be used. Variables that should not receive a noise variable should be specified with an 1 entry (see Example 2). If da_noise=1, no noisy versions of the original variables are specified.

formula_syn

Optional list of regression formulas for conditional models. Formulas can be a specified for a subset of synthesized variables. Non-specified formulas are automatically specified by linear models.

use_pls

Logical indicating whether partial least squares (PLS) should be used for dimension reduction

ncomp

Number of PLS factors

exact_regression

Logical indicating whether residuals are forced to be uncorrelated with predictors in the synthesis model

exact_marginal

Logical indicating whether marginal distributions of the variables should be preserved

imp_maxit

Number of iterations in the imputation if the original dataset contains missing values

Value

A list with entries

dat_syn

generated synthetic data

dat2

Data frame containing original and synthetic data

...

more entries

References

Grund, S., Luedtke, O., & Robitzsch, A. (2022). Using synthetic data to improve the reproducibility of statistical results in psychological research. Psychological Methods. Epub ahead of print. doi:10.1037/met0000526

Jiang, B., Raftery, A. E., Steele, R. J., & Wang, N. (2022). Balancing inferential integrity and disclosure risk via model targeted masking and multiple imputation. Journal of the American Statistical Association, 117(537), 52-66. doi:10.1080/01621459.2021.1909597

Examples

if (FALSE) {
#############################################################################
# EXAMPLE 1: Generate synthetic data with item responses and covariates
#############################################################################

data(data.ma09, package="miceadds")
dat <- data.ma09

# fixed variables in synthesis
fix_vars <- c("PV1MATH", "SEX","AGE")
# ordinal variables in synthesis
ord_vars <- c("FISCED", "MISCED", items)
# variables that should be synthesized
syn_vars <- c("HISEI", "FISCED", "MISCED", items)

#-- synthesize data
mod <- miceadds::syn_da( dat=dat, syn_vars=syn_vars, fix_vars=fix_vars,
            ord_vars=ord_vars, da_noise=0.5, imp_maxit=2, use_pls=TRUE, ncomp=20,
            exact_regression=TRUE, exact_marginal=TRUE)
#- extract synthetic dataset
mod$dat_syn

#############################################################################
# EXAMPLE 2: Not all variables are augmented, formula specifications
#############################################################################

data(data.ma09, package="miceadds")
dat <- data.ma09

# fixed variables in synthesis
fix_vars <- c("PV1MATH", "SEX")
# ordinal variables in synthesis
ord_vars <- c("FISCED", "MISCED")
# variables that should be synthesized
syn_vars <- c("AGE","HISEI", "FISCED", "MISCED")
# no noise variable for FISCED and MISCED should be specified
da_noise <- c(AGE=0.1, HISEI=0.1, FISCED=0, MISCED=0)
# define conditional models for some variables
formula_syn <- list(
        AGE=AGE ~ 1 + PV1MATH + SEX + I(PV1MATH^2) + AGE_DA + HISEI_DA,
        HISEI=HISEI ~ 1 + PV1MATH + SEX + AGE + I(PV1MATH^2) + I(AGE^2) +
                   I(AGE*PV1MATH) + AGE_DA + HISEI_DA
                     )


#-- synthesize data
mod <- miceadds::syn_da( dat=dat, syn_vars=syn_vars, fix_vars=fix_vars,
            ord_vars=ord_vars, da_noise=da_noise,
            formula_syn=formula_syn, imp_maxit=2, use_pls=TRUE, ncomp=20,
            exact_regression=TRUE, exact_marginal=TRUE)
str(mod)
}