blca: Bayesian Latent Class Analysis with one of several methods

In BayesLCA: Bayesian Latent Class Analysis

Description

Latent class analysis (LCA) attempts to find G hidden classes in binary data X. blca utilises one of: an EM algorithm, a variational Bayes approximation, Gibbs sampling or boot-strapping techniques to find maximum a posteriori (MAP), standard error and density estimates of the parameters.

Usage

blca(X, G, method = c("em", "gibbs", "boot", "vb"), ...)

Arguments

X	The data matrix. This may take one of several forms, see data.blca.
G	The number of classes to run lca for.
method	The method with which to perform lca on the data. Four methods are currently available, "em", "gibbs", "boot" or "vb". Defaults to "em", with a warning.
...	Additional arguments to be passed on, depending on the method. See additional help files for details.

Details

The function calls to one of blca.em, blca.boot, blca.gibbs, blca.vb, depending on the method specified.

Value

A list of class "blca" is returned. All methods return the following items:

classprob	The class probabilities.
itemprob	The item probabilities, conditional on class membership.
Z	Estimate of class membership for each unique datapoint.
prior	A list containing the prior values specified for the model.

See additional help files for details.

Note

Earlier versions of this function erroneously referred to posterior standard deviations as standard errors. This also extended to some of the variable names of the returned function, which are now returned with the corrected suffix blca.em.sd (for standard deviation). For backwards compatability reasons, the earlier suffix .se has been retained as a returned argument.

Author(s)

Arthur White

References

Arthur White, Thomas Brendan Murphy (2014). BayesLCA: An R Package for Bayesian Latent Class Analysis." Journal of Statistical Software, 61(13), 1-28. URL: http://www.jstatsoft.org/v61/i13/.

See Also

blca.em, blca.boot, blca.gibbs, blca.vb

Examples

type1 <- c(0.8, 0.8, 0.2, 0.2)
type2 <- c(0.2, 0.2, 0.8, 0.8)
x<- rlca(1000, rbind(type1,type2), c(0.6,0.4))

set.seed(1)
fit <- blca(x, 2) ## EM algorithm used, warning returned
print(fit)	  ## No posterior standard deviations returned
summary(fit)

set.seed(1)
fit2 <- blca(x, 2, method="em", sd=TRUE) ##No warning - same fit
print(fit2) 				 ##Posterior standard deviations returned

set.seed(1)
##Variational Bayes approximation, with priors specified.
fit3 <- blca(x, 2, method="vb", delta=c(5,5), alpha=2, beta=1) 
print(fit3)	##Posterior standard deviations returned also.
par(mfrow=c(3,2))			  
plot(fit3, which=3:4)
par(mfrow=c(1,1))

Example output

Loading required package: e1071
Loading required package: coda
Restart number 1, logpost = -2451.19... 
New maximum found... Restart number 2, logpost = -2451.19... 
Restart number 3, logpost = -2451.19... 
Restart number 4, logpost = -2451.19... 
Restart number 5, logpost = -2451.19... 

MAP Estimates:
 

Item Probabilities:
 
        Col 1 Col 2 Col 3 Col 4
Group 1 0.774 0.798 0.197 0.201
Group 2 0.189 0.159 0.806 0.828

Membership Probabilities:
 
Group 1 Group 2 
  0.596   0.404 
Warning message:
Posterior standard deviations not returned. 
__________________

Bayes-LCA
Diagnostic Summary
__________________

Hyper-Parameters: 

 Item Probabilities:

 alpha: 
        Col 1 Col 2 Col 3 Col 4
Group 1     1     1     1     1
Group 2     1     1     1     1

 beta: 
        Col 1 Col 2 Col 3 Col 4
Group 1     1     1     1     1
Group 2     1     1     1     1

 Class Probabilities:

 delta: 
Group 1 Group 2 
      1       1 
__________________

Method: EM algorithm  

 Number of iterations: 19 

 Log-Posterior Increase at Convergence: 0.0007934346 

 Log-Posterior: -2451.186 

 AIC: -4920.373 

 BIC: -4964.543 
Restart number 1, logpost = -2451.19... 
New maximum found... Restart number 2, logpost = -2451.19... 
Restart number 3, logpost = -2451.19... 
Restart number 4, logpost = -2451.19... 
Restart number 5, logpost = -2451.19... 

MAP Estimates:
 

Item Probabilities:
 
        Col 1 Col 2 Col 3 Col 4
Group 1 0.774 0.798 0.197 0.201
Group 2 0.189 0.159 0.806 0.828

Membership Probabilities:
 
Group 1 Group 2 
  0.596   0.404 

Posterior Standard Deviation Estimates:
 

Item Probabilities:
 
        Col 1 Col 2 Col 3 Col 4
Group 1 0.021 0.021 0.021 0.021
Group 2 0.027 0.026 0.026 0.026

Membership Probabilities:
 
Group 1 Group 2 
  0.024   0.024 
Restart number 1, logpost = -6946.26... 

MAP Estimates:
 

Item Probabilities:
 
        Col 1 Col 2 Col 3 Col 4
Group 1 0.775 0.798 0.198 0.202
Group 2 0.193 0.163 0.805 0.827

Membership Probabilities:
 
Group 1 Group 2 
  0.594   0.406 

Posterior Standard Deviation Estimates:
 

Item Probabilities:
 
        Col 1 Col 2 Col 3 Col 4
Group 1 0.017 0.016 0.016 0.016
Group 2 0.020 0.018 0.020 0.019

Membership Probabilities:
 
Group 1 Group 2 
  0.015   0.015 

BayesLCA documentation built on July 2, 2020, 12:11 a.m.