mxComputeEM: Fit a model using DLR's (1977) Expectation-Maximization (EM) algorithm

Description

The EM algorithm constitutes the following steps: Start with an initial parameter vector. Predict the missing data to form a completed data model. Optimize the completed data model to obtain a new parameter vector. Repeat these steps until convergence criteria are met.

Usage

mxComputeEM(expectation, predict, mstep, observedFit = "fitfunction", ...,
  maxIter = 500L, tolerance = 1e-09, verbose = 0L,
  freeSet = NA_character_, accel = "varadhan2008",
  information = NA_character_, infoArgs = list())

Arguments

expectation

a vector of expectation names

predict

what to predict from the observed data (available options depend on the expectation)

mstep

a compute plan to optimize the completed data model

observedFit

the name of the observed data fit function (defaults to "fitfunction")

...

Not used. Forces remaining arguments to be specified by name.

maxIter

maximum number of iterations

tolerance

optimization is considered converged when the maximum relative change in fit is less than tolerance

verbose

level of diagnostic output

freeSet

names of matrices containing free variables

accel

name of acceleration method ("varadhan2008" or "ramsay1975")

information

name of information matrix approximation method

infoArgs

arguments to control the information matrix method

Details

This compute plan does not work with any and all expectations. It requires a special kind of expectation that can predict its missing data to create a completed data model.

The EM algorithm does not produce a parameter covariance matrix for standard errors. S-EM, an implementation of Meng & Rubin (1991), is included.

Ramsay (1975) was recommended in Bock, Gibbons, & Muraki (1988).

References

Bock, R. D., Gibbons, R., & Muraki, E. (1988). Full-information item factor analysis. Applied Psychological Measurement, 6(4), 431-444.

Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 1-38.

Meng, X.-L. & Rubin, D. B. (1991). Using EM to obtain asymptotic variance-covariance matrices: The SEM algorithm. Journal of the American Statistical Association, 86 (416), 899-909.

Ramsay, J. O. (1975). Solving implicit equations in psychometric data analysis. Psychometrika, 40 (3), 337-360.

Varadhan, R. & Roland, C. (2008). Simple and globally convergent methods for accelerating the convergence of any EM algorithm. Scandinavian Journal of Statistics, 35, 335-353.