One-Step Method for Auxiliary Analysis

Estimates a joint latent class and auxiliary-variable model using one-step maximum likelihood. The measurement-model parameters, mixing proportions, and auxiliary-model parameters are estimated simultaneously.

Usage

one_step(x, model = NULL, data, ...)

Arguments

x

A fitted latent class model of class MxModel.

model

An auxiliary model specified as an OpenMx RAM model or a character string that can be converted using as_ram(). May be omitted when data is a single numeric, integer, or factor variable.

data

A data.frame containing the auxiliary variables, or a single numeric, integer, or factor variable. Observations must be in the same order as in the original latent class model.

...

Additional arguments passed to OpenMx::mxRun().

Value

An MxModel containing the jointly estimated measurement and auxiliary models.

Details

The function starts from a previously fitted latent class model and adds an auxiliary model to each latent class.

Unlike two_step(), the measurement-model parameters and mixing proportions are not fixed. Consequently, auxiliary variables can influence the estimated latent class solution.

Classification uncertainty is accounted for by integrating over latent class membership in the joint likelihood.

By default, unlabeled auxiliary parameters are estimated separately across classes. Explicit parameter labels are preserved, allowing users to specify equality constraints within and across classes.

The measurement indicators and auxiliary variables are assumed conditionally independent given latent class membership, unless additional relationships are explicitly specified.

References

Bakk, Z., & Kuha, J. (2018). Two-step estimation of models between latent classes and external variables. Psychometrika, 83, 871–892. doi:10.1007/s11336-017-9592-7

Examples

if (FALSE) { # \dontrun{
library(OpenMx)

dat <- iris[, 1:4]
names(dat) <- c("SL", "SW", "PL", "PW")

set.seed(123)
fit <- mx_profiles(
  data = dat[, c("PL", "PW")],
  classes = 2
)

# Continuous distal outcome
res <- one_step(
  x = fit,
  data = dat$SL
)
table_results(res)

# Equivalent specification using RAM syntax
res <- one_step(
  x = fit,
  model = "SL ~ 1",
  data = dat["SL"]
)

# Ordinal distal outcome
ordinal <- ordered(cut(dat$SL, breaks = 3))
res_ord <- one_step(
  x = fit,
  data = ordinal
)

# Multivariate continuous auxiliary model
res_custom <- one_step(
  x = fit,
  model = "
    SL ~ 1
    SW ~ 1
    SL ~~ SW
  ",
  data = dat[, c("SL", "SW")]
)
} # }