Fully Latent Principal Stratification (FLPS)

Fully Latent Principal Stratification (FLPS) is an extension of principal stratification.

Install

Install the latest release from CRAN:

devtools::install_github("sooyongl/flps")

The documentation is available at here.

If compiling errors occur, see here.

Basic working example

Running with the package

• Generate a simulated rectangular data.
• This data will be converted to a list of data for rstan package.
• For latent variable models, Rasch, 2PL, GRM, and SEM (one-factor CFA) are available.

set.seed(10000)
inp_data <- flps::makeInpData(
  N       = 200,  # sample size
  R2Y     = 0.2,  # r^2 of outcome
  R2eta   = 0.5,  # r^2 of eta by one covariates
  omega   = 0.2,  # the effect of eta
  tau0    = 0.23, # direct effect
  tau1    = -0.16,# interaction effect between Z and eta
  betaL   = 0.2,
  betaY   = 0.4,
  lambda  = 0.8,  # the proportion of administered items
  nitem    = 10,   # the total number of items
  nfac    = 1,    # the number of latent factors
  lvmodel = 'rasch' # tag for latent variable model; case-sensitive (use lower-case letters)
)

makeInpData() creates input data for running FLPS.

• inp_data: a data frame containing all the data for FLPS. It is used in runFLPS function.

# Input data matrix
data.table::data.table(inp_data)

##                Y Z          X1        eta1 v1 v2 v3 v4 v5 v6 v7 v8 v9 v10
##   1: -0.72862564 1 -0.20087849  0.49705730  0  1  0  0  1  0  1  0  1   1
##   2:  0.43624761 1 -0.81367558  0.09644683  1  1  1  1  1  1  0  0  0   1
##   3:  0.71005101 1 -0.09306958 -0.30660832  1  1  1  0  0  1  1  1  0   1
##   4:  0.01947398 1 -0.08743884 -0.37419814  0  1  1  0  0  0  1  0  0   0
##   5: -1.00950577 1 -2.16774891 -1.81547040  0  1  0  0  0  0  0  0  0   0
##  ---                                                                     
## 196: -0.47559245 0  0.23763106 -0.27108910 NA NA NA NA NA NA NA NA NA  NA
## 197:  0.46877629 0 -0.03646065  1.12609970 NA NA NA NA NA NA NA NA NA  NA
## 198:  0.78717334 0  0.06867924  0.07008599 NA NA NA NA NA NA NA NA NA  NA
## 199:  0.56380180 0  0.56467755  0.34826071 NA NA NA NA NA NA NA NA NA  NA
## 200:  0.36809486 0  0.82158503 -0.35012492 NA NA NA NA NA NA NA NA NA  NA

• Fit your FLPS model

Now, provide information about your model. runFLPS internally coverts inp_data into the data format for rstan given the information, and runs FLPS.

To avoid having to compile the Stan code every time you run it, you can pre-compile the code using the modelBuilder() function along with the relevant measurement model. This function will compile the Stan code and store the resulting stanmodel object in the flps package directory (If error, update the latest Rcpp package; After running modelBuilder(), it is recommended to refresh R session). The next time you run runFLPS(), the code will skip the compilation step, making your analysis faster and more efficient. Otherwise, it will take a while for runFLPS() to compile the Stan code.

modelBuilder(type = "rasch")

Also, if you have any errors, try the latest rstan and StanHeaders packages.

remove.packages(c("rstan", "StanHeaders"))
install.packages("rstan", repos = c("https://mc-stan.org/r-packages/", getOption("repos")))

res <- runFLPS(
  inp_data = inp_data,
  outcome = "Y",
  group = "Z",
  covariate = c("X1"),
  lv_type = "rasch",
  lv_model = "F =~ v1 + v2 + v3 + v4 + v5 + v6 + v7 + v8 + v9 + v10",
  stan_options = list(iter = 1000, warmup = 500, cores = 1, chains = 2)
)

## 
## SAMPLING FOR MODEL 'FLPS' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 0.000804 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 8.04 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1: 
## Chain 1: 
## Chain 1: Iteration:   1 / 1000 [  0%]  (Warmup)
## Chain 1: Iteration: 100 / 1000 [ 10%]  (Warmup)
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## Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling)
## Chain 1: 
## Chain 1:  Elapsed Time: 15.46 seconds (Warm-up)
## Chain 1:                10.842 seconds (Sampling)
## Chain 1:                26.302 seconds (Total)
## Chain 1:

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#bulk-ess

## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-ess

The summary of results can be shown by summary().

summary(res, type = "causal")

##               mean     se_mean        sd        2.5%        25%        50%
## tau0     0.2292788 0.005370111 0.1353325 -0.04784608  0.1410179  0.2345303
## tau1[1] -0.2288520 0.101820994 0.4674258 -0.92391714 -0.5972068 -0.3055769
##                75%     97.5%     n_eff      Rhat
## tau0    0.32088555 0.4838128 635.09305 0.9983786
## tau1[1] 0.07374961 0.7885876  21.07418 1.0158583

The flps_plot() shows the plot related to FLPS models

flps_plot(res, type = "causal")

flps_plot(res, type = "latent")