randomLCA {randomLCA}

Fits a Latent Class Model including a Random Effect

Description

Fit latent class models, which may include a random effect.

Usage

randomLCA(patterns, freq = NULL, nclass = 2, calcSE = TRUE, notrials = 20, 
  random = FALSE, byclass = FALSE, quadpoints = 21, constload = TRUE,
  blocksize = dim(patterns)[2], level2 = FALSE, probit = FALSE,
  level2size = blocksize, qniterations = 5, penalty = 0.01, EMtol = 1.0e-5,
  verbose = FALSE, seed = as.integer(runif(1, 0, .Machine$integer.max)),
  cores =  max(detectCores() %/% 2, 1))

Arguments

patterns

Data frame or matrix of 0 and 1 defining the outcome patterns. May also include missing values, with randomLCA using maximum likelihood to fit the models using all available data.

freq

Frequency for each outcome pattern, if missing this is calculated from the patterns, and the patterns are summarised to remove duplicate values.

nclass

Number of classes to be fitted

calcSE

Calculate standard errors for parameters. Useful for bootstrapping.

notrials

For a standard latent class model, the number of random starting values used

random

Include random effect?

byclass

Vary random effect loading(s) by class?

quadpoints

Number of quadrature points for adaptive quadrature

constload

Outcome loadings are constant for random effects model?

blocksize

Where a random effects (single level) model is broken into blocks, that is the loadings are repeated, this defines the size of the blocks

probit

Probit model for random effect?

level2

Fit 2 level random effects model (further details to follow)?

level2size

Size of level 2 blocks if fitting 2 level models

qniterations

Number of Quasi-Newton iterations within each EM/adaptive cycle. Decrease if there is a failure to converge

penalty

penalty applied to likelihood for outcome probabilities. Shrinks outcome probabilities in slightly and can prevent extreme values. Setting penalty to 0 will produce an unpenalized fit.

EMtol

convergence tolerance for EM algorithm for fixed effect latent class

verbose

Prints fit progress if true

seed

Initial random seed for generating starting values. This can be set to guarantee that the fit is the same each time, including the order of the classes.

cores

Number of cores to be used for parallel evaluation of starting values

Details

The structure of the patterns is assumed to be a number of blocks of different outcomes each of level2size, allowing outcomes to be repeated. Each outcome is assumed to have it's own loading. An example is the width of the patterns is n and the level2size is n, resulting in n outcomes and therefore n loadings. Alternatively if the level2size is 1, then there are n repeats of the same outcome (but with different probabilities) with the same loading. In practice they may not be the same type of outcome, but usually will be.

The algorithm used is EM for the standard latent class and adaptive (in the sense of moving the location of the quadrature points) Gauss-Hermite quadrature for the random effects models. The number of quadrature points defaults to 21.

Value

randomLCA object This contains

fit

Fit object from optim

nclass

Number of classes

classp

Class probabilities

outcomep

Outcome probability

lambdacoef

Loadings

se

Standard errors corresponding to results returned by optim

np

Number of parameters

nobs

Number of observations in total

logLik

log likelihood for fitted model

penlogLik

Penalised log likelihood for fitted model

observed

Observed numbers corresponding to each pattern

fitted

Fitted number corresponding to each pattern

deviance

Deviance

classprob

Posterior class probability for each pattern

bics

BIC obtained for each trial when fitting initial latent class models

call

call to randomLCA

random

random parameter to randomLCA

constload

constload parameter to randomLCA

level2

level2 parameter to randomLCA

level2size

level2size parameter to randomLCA

byclass

byclass parameter to randomLCA

probit

probit parameter to randomLCA

quadpoints

quadpoints parameter to randomLCA

blocksize

blocksize parameter to randomLCA

freq

frequency of each pattern

qniterations

qniterations parameter to randomLCA

penalty

penalty parameter to randomLCA

Note

In the returned object there a fields for patterns and frequencies. If frequencies are not supplied then the patterns and frequencies are constructed. If frequencies are supplied then zero rows are removed. When frequencies are supplied it is assumed that the data has been simplified. The returned fitted, posterior class probabilities etc, all correspond to the simplified patterns, not to the original data.

Author(s)

Ken Beath

References

Beath KJ (2017). randomLCA: An R Package for Latent Class with Random Effects Analysis. Journal of Statistical Software, 81(13), pp. 1-25. doi:10.18637/jss.v081.i13

Examples

# standard latent class with 2 classes
dentistry.lca2 <- randomLCA(dentistry[, 1:5], freq = dentistry$freq, nclass = 2, cores = 1)
# random effects model with constant random effect loading
dentistry.lca2random <- randomLCA(dentistry[, 1:5], freq = dentistry$freq, 
	nclass = 2, random = TRUE, constload = TRUE, probit = TRUE, cores = 1)
# allow loading to vary by dentist
# this is the 2LCR model from Qu et al (1996)
dentistry.lca2random1 <- randomLCA(dentistry[, 1:5], freq = dentistry$freq, 
	nclass = 2, random = TRUE, constload = FALSE, probit = TRUE, cores = 1)