Oftentimes, it is not possible to share original research data
publicly, for example, due to privacy constraints. As explained in the
worcs paper, in such cases, it is advantageous to share a
synthetic dataset instead, so that the code can still be vetted,
debugged, and adapted by others. By default, the function
closed_data() generates a synthetic dataset using the
function synthetic(); a rudimentary random forest-based
algorithm. However, sometimes this default option falls short. In such
cases, it is possible to fully customize synthetic dataset generation.
This vignette discusses some of the options.
Structural equation models may have problems converging when estimated on synthetic datasets. To avoid this problem, synthetic data can be generated directly from the SEM model. Generating data from an SEM model will often result in a synthetic dataset that will closely reproduce the model parameters estimated on the original dataset.
For this example, we will use the PoliticalDemocracy
data included with the lavaan package. Imagine that we
collected these data, and are not allowed to share them. In an existing
worcs project, we could then store them using the
command:
Now, we estimate our SEM-model, based on the example in the
lavaan documentation:
load_data()
model <- '
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + a*y2 + b*y3 + c*y4
dem65 =~ y5 + a*y6 + b*y7 + c*y8
# regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60
# residual correlations
y1 ~~ y5
y2 ~~ y4 + y6
y3 ~~ y7
y4 ~~ y8
y6 ~~ y8'
fit <- lavaan::sem(model, data = dat)
tidySEM::table_results(fit)#> label est_sig se pval confint
#> 1 ind60.BY.x1 1.00 0.00 <NA> [1.00, 1.00]
#> 2 ind60.BY.x2 2.18*** 0.14 0.00 [1.91, 2.45]
#> 3 ind60.BY.x3 1.82*** 0.15 0.00 [1.52, 2.12]
#> 4 dem60.BY.y1 1.00 0.00 <NA> [1.00, 1.00]
#> 5 dem60.BY.y2 1.19*** 0.14 0.00 [0.92, 1.46]
#> 6 dem60.BY.y3 1.17*** 0.12 0.00 [0.94, 1.41]
#> 7 dem60.BY.y4 1.25*** 0.12 0.00 [1.02, 1.48]
#> 8 dem65.BY.y5 1.00 0.00 <NA> [1.00, 1.00]
#> 9 dem65.BY.y6 1.19*** 0.14 0.00 [0.92, 1.46]
#> 10 dem65.BY.y7 1.17*** 0.12 0.00 [0.94, 1.41]
#> 11 dem65.BY.y8 1.25*** 0.12 0.00 [1.02, 1.48]
#> 12 dem60.ON.ind60 1.47*** 0.39 0.00 [0.70, 2.24]
#> 13 dem65.ON.ind60 0.60** 0.23 0.01 [0.16, 1.04]
#> 14 dem65.ON.dem60 0.87*** 0.07 0.00 [0.72, 1.01]
#> 15 y1.WITH.y5 0.58 0.36 0.10 [-0.11, 1.28]
#> 16 y2.WITH.y4 1.44* 0.69 0.04 [0.09, 2.79]
#> 17 y2.WITH.y6 2.18** 0.74 0.00 [0.74, 3.63]
#> 18 y3.WITH.y7 0.71 0.61 0.24 [-0.49, 1.91]
#> 19 y4.WITH.y8 0.36 0.44 0.41 [-0.51, 1.23]
#> 20 y6.WITH.y8 1.37* 0.58 0.02 [0.24, 2.50]
#> 21 Variances.x1 0.08*** 0.02 0.00 [0.04, 0.12]
#> 22 Variances.x2 0.12 0.07 0.08 [-0.02, 0.26]
#> 23 Variances.x3 0.47*** 0.09 0.00 [0.29, 0.64]
#> 24 Variances.y1 1.85*** 0.43 0.00 [1.01, 2.70]
#> 25 Variances.y2 7.58*** 1.37 0.00 [4.90, 10.26]
#> 26 Variances.y3 4.96*** 0.96 0.00 [3.08, 6.83]
#> 27 Variances.y4 3.22*** 0.72 0.00 [1.81, 4.64]
#> 28 Variances.y5 2.31*** 0.48 0.00 [1.37, 3.25]
#> 29 Variances.y6 4.97*** 0.92 0.00 [3.16, 6.77]
#> 30 Variances.y7 3.56*** 0.71 0.00 [2.17, 4.95]
#> 31 Variances.y8 3.31*** 0.70 0.00 [1.93, 4.69]
#> 32 Variances.ind60 0.45*** 0.09 0.00 [0.28, 0.62]
#> 33 Variances.dem60 3.88*** 0.87 0.00 [2.18, 5.57]
#> 34 Variances.dem65 0.16 0.23 0.47 [-0.28, 0.61]This should work fine. But what if someone tries to reproduce our analysis? They would not have access to the original data, only the synthetic dataset. To simulate their experience reproducing the analysis, we can load the synthetic dataset and try to run our model:
dat2 <- read.csv("synthetic_dat.csv", stringsAsFactors = FALSE)
fit2 <- lavaan::sem(model, data = dat2)#> Warning: lavaan->lav_object_post_check():
#> some estimated lv variances are negative
#> Warning: lavaan->lav_object_post_check():
#> the covariance matrix of the residuals of the observed variables (theta)
#> is not positive definite ; use lavInspect(fit, "theta") to investigate.This should result in several warnings, about negative latent
variable variances (an impossibility) and a warning that the observed
covariance matrix of the residuals is not positive definite. In other
words: the model cannot be fit to the synthetic data, because the
structure in the data is not adequately reproduced by the default
algorithm of synthetic().
A dataset generated from the model will be much better able to reproduce that model. So, let’s use this SEM model to generate a synthetic dataset:
Note that the function simulateData() accepts a
parameter table as its argument, which must first be extracted from the
fitted model object using partable().
To add this custom synthetic dataset to our original dataset, use the
function below. Note that original_name should reference
the file name of the data the synthetic dataset should be
associated with, not the name of the R-object. We started with an
R-object called dat, which we saved to a file called
dat.csv using the function closed_data().
If we now remove the original data, and call load_data()
again, we can verify that the synthetic dataset is loaded, and we can
see that it’s possible to reproduce the analysis - if not the exact
results - with it:
file.remove("dat.csv")
load_data()
fit2 <- lavaan::sem(model, data = dat)
tidySEM::table_results(fit2)#> [1] TRUE
#> label est_sig se pval confint
#> 1 ind60.BY.x1 1.00 0.00 <NA> [1.00, 1.00]
#> 2 ind60.BY.x2 2.15*** 0.05 0.00 [2.05, 2.25]
#> 3 ind60.BY.x3 1.78*** 0.06 0.00 [1.67, 1.90]
#> 4 dem60.BY.y1 1.00 0.00 <NA> [1.00, 1.00]
#> 5 dem60.BY.y2 1.15*** 0.05 0.00 [1.06, 1.25]
#> 6 dem60.BY.y3 1.13*** 0.04 0.00 [1.04, 1.21]
#> 7 dem60.BY.y4 1.13*** 0.04 0.00 [1.05, 1.21]
#> 8 dem65.BY.y5 1.00 0.00 <NA> [1.00, 1.00]
#> 9 dem65.BY.y6 1.15*** 0.05 0.00 [1.06, 1.25]
#> 10 dem65.BY.y7 1.13*** 0.04 0.00 [1.04, 1.21]
#> 11 dem65.BY.y8 1.13*** 0.04 0.00 [1.05, 1.21]
#> 12 dem60.ON.ind60 1.51*** 0.16 0.00 [1.20, 1.82]
#> 13 dem65.ON.ind60 0.75*** 0.09 0.00 [0.57, 0.93]
#> 14 dem65.ON.dem60 0.86*** 0.03 0.00 [0.80, 0.91]
#> 15 y1.WITH.y5 0.52*** 0.14 0.00 [0.25, 0.79]
#> 16 y2.WITH.y4 1.79*** 0.26 0.00 [1.27, 2.30]
#> 17 y2.WITH.y6 1.74*** 0.24 0.00 [1.26, 2.22]
#> 18 y3.WITH.y7 0.80** 0.24 0.00 [0.32, 1.28]
#> 19 y4.WITH.y8 0.53*** 0.16 0.00 [0.21, 0.84]
#> 20 y6.WITH.y8 1.46*** 0.21 0.00 [1.04, 1.88]
#> 21 Variances.x1 0.07*** 0.01 0.00 [0.06, 0.08]
#> 22 Variances.x2 0.10*** 0.02 0.00 [0.06, 0.15]
#> 23 Variances.x3 0.48*** 0.03 0.00 [0.41, 0.55]
#> 24 Variances.y1 1.83*** 0.18 0.00 [1.48, 2.17]
#> 25 Variances.y2 6.85*** 0.48 0.00 [5.90, 7.80]
#> 26 Variances.y3 5.22*** 0.39 0.00 [4.46, 5.98]
#> 27 Variances.y4 3.33*** 0.27 0.00 [2.80, 3.87]
#> 28 Variances.y5 1.98*** 0.17 0.00 [1.64, 2.32]
#> 29 Variances.y6 4.32*** 0.32 0.00 [3.70, 4.94]
#> 30 Variances.y7 3.62*** 0.28 0.00 [3.07, 4.17]
#> 31 Variances.y8 3.38*** 0.27 0.00 [2.86, 3.90]
#> 32 Variances.ind60 0.43*** 0.03 0.00 [0.37, 0.49]
#> 33 Variances.dem60 4.10*** 0.35 0.00 [3.41, 4.79]
#> 34 Variances.dem65 0.25** 0.10 0.01 [0.06, 0.44]