multilevelLCMI: Multilevel Latent Class models for the Multiple Imputation of...

In davidevdt/BMLCimpute: BMLCimpute: Bayesian Multilevel Latent Class Models for the Multiple Imputation of Nested Categorical Data

Description

Perform single- and multi-level multiple imputation of categorical data through single/multi level Bayesian Latent Class models.

Usage

multilevelLCMI(convData, L, K, it1, it2, it3, it.print, v, I = 5, pri2 = 1, 
   pri1 = 1, priresp = 1, priresp2 = 1, random = TRUE, estimates = TRUE,
   count = FALSE, plot.loglik = FALSE, prec = 3, scale = 1)

## Default S3 method:
multilevelLCMI(convData, L, K, it1, it2, it3, it.print, v, I = 5, pri2 = 1,
     pri1 = 1, priresp = 1, priresp2 = 1, random = TRUE, estimates = TRUE,
     count = FALSE, plot.loglik = FALSE, prec = 3, scale = 1)

## S3 method for class 'multilevelLCMI'
print(x, ... )

Arguments

convData	Dataset produced as output by the convData function.
L	Number of higher-level mixture components. When L=1, single-level Latent Class multiple imputation is performed.
K	Number of Latent Classes at the lower-level.
it1	Number of Gibbs sampler iterations for the burn-in (must be larger than 0).
it2	Number of Gibbs sampler iterations for the imputations.
it3	Every it3 iterations, the sampler stores new parameter estimates for the calculation of psoterior estimates. Meaningful only when estimates=TRUE.
it.print	Every it.print iterations, the state of the Gibbs sampler is screen-printed.
v	The Gibbs sampler will produce the first set of imputations at the iteration number (it1+V), where V~Unif(1,v). Subsequent imputations are automatically spaced from each others across the remaining iterations, so that the last imputation (imputation I) occurs at the iteration number (it1+it2).
I	Number of imputations to be performed.
pri2	Hyperparameter value for the higher-level mixture probabilities. Default to 1.
pri1	Hyperparameter value for the lower-level mixture probabilities. Default to 1.
priresp	Hyperparameter value for the lower-level conditional response probabilities. Default to 1.
priresp2	Hyperparameter value for the higher-level conditional response probabilities. Default to 1.
random	Logical. Should the model parameters be initialized at random values? If TRUE, parameters are initialized through draws from uniform Dirichlet distributions. If FALSE, parameters are initialized to be equal to 1/D, with D the number of categories in the (observed/latent) variable of interest.
estimates	Logical. If TRUE, the function returns the posterior means of the model parameters. Default to TRUE.
count	Logical. Should the output include the posterior distribution of L and K? (only K if L=1)
plot.loglik	Logical. Should the output include a traceplot of the log-likelihood ratios obtained through the Gibbs sampler iterations? Helpful for assessing convergence.
prec	When estimates=TRUE, prec defines the number of digits with which the estimates are returned.
scale	Re-scale the log-likelihood value by a factor equal to scale; this parameter is useful to avoid underflow in the calculation of the log-likelihood (which can occur in large datasets) and consequently to prevent error messages for the visualization of the log-likelihood traceplot. This parameter is meaningful only when plot.loglik is set to TRUE. Default value equal to 1.0.
x	A multilevelLCMI object (print method).
...	Not used.

Details

Function for performing Multiple Imputation with the Bayesian Multilevel Latent Class Model. The model takes the list produced by the 'convData' function as input, in which the dataset converted and prepared for the imputations is present, along with other parameters specified by the user (e.g., number of latent classes and specification of the prior distribution hyperparameters). The function can also offer (when the corresponding boolean parameter is activated) a graphical representation of the posterior distribution of the number of occupied classes during the Gibbs sampler iterations. In this way, multilevelLCMI' can also perform model selection in a pre-imputation stage. For model selection, set count=TRUE. Symmetric Dirichlet priors are used.

Value

A multilevelLCMI object, a list containing:

imp	Set of imputations for the level-1 variables and units.
imp2	Set of imputations for the level-2 variables and units.
piL	posterior means of the level-2 class probabilities. Calculated only if estimates = TRUE.
piLses	Posterior standard deviations of the level-2 class probabilities. Calculated only if estimates = TRUE.
piK	Posterior means of the level-1 class probabilities. Calculated only if estimates = TRUE.
piKses	Posterior standard deviations of the level-2 class probabilities. Calculated only if estimates = TRUE.
picondlev1	Posterior means of the level-1 conditional probabilities. Calculated only if estimates = TRUE.
picondlev1ses	Posterior standard deviations of the level-1 conditional probabilities. Calculated only if estimates = TRUE.
picondlev2	Posterior means of the level-2 conditional probabilities. Calculated only if estimates = TRUE.
picondlev1ses	Posterior standard deviations of the level-2 conditional probabilities. Calculated only if estimates = TRUE.
DIC	DIC index for the BMLC model. Calculated only if estimates = TRUE.
freqL	Posterior distribution of the number of latent classes at level-2. Calculated only if count is set to TRUE.
freqK	Posterior distribution of the number of latent classes at level-1. Calculated only if count is set to TRUE.
time	Running time of the Gibbs sampler iterations.

Author(s)

D. Vidotto <[e-mail]>

References

• [1] Vidotto D., Vermunt J.K., Van Deun K. (2018). 'Bayesian Multilevel Latent Class Models for the Multiple Imputation of Nested Categorical Data'. Journal of Educational and Beahvioral Statistics 43(5), 511-539.

Examples

## Not run: 

library(BMLCimpute)

# Load data 
data(simul_incomplete)

# Preprocess the Data
cd <- convData(simul_incomplete, GID = 1, UID = 2, var2 = 8:12)

# Model Selection
set.seed(1)
mmLC <- multilevelLCMI( convData = cd, L = 10, K = 10, it1 = 1000, it2 = 3000, it3 = 100,
    it.print = 250, v = 10, I = 0, pri2 = 1 / 10, pri1 = 1 / 15, priresp =  0.01,
    priresp2 = 0.01, random = TRUE, estimates = FALSE, count = TRUE, plot.loglik = FALSE,
    prec = 3, scale = 1.0)

# Select posterior maxima of the number of classes for the imputations 
# (Other alternatives are possible, such as posterior modes or posterior quantiles)
L = max(which(mmLC[[12]] != 0))
K = max(apply(mmLC[[13]], 1, function(x) max(which( x != 0))), na.rm = TRUE)

# Perform 5 imutations on the dataset 
mmLC <- multilevelLCMI( convData = cd, L = L, K = K, it1 = 2000, it2 = 4000, it3 = 100, 
     it.print = 250, v = 10, I = 5, pri2 = 500, pri1 = 50, priresp = 0.01, priresp2 = 0.01,
     random = TRUE, estimates = FALSE, count = TRUE, plot.loglik = TRUE, prec = 4, scale = 1.0)

# Obtain the dataset completed with the first set of imputations (ind = 1)
complete_data = compData( convData = cd, implev1 = mmLC[[1]], implev2 = mmLC[[2]], ind = 1 )


## End(Not run) 

davidevdt/BMLCimpute documentation built on June 5, 2019, 12:36 a.m.