R: Fit a model using DLR's (1977) Expectation-Maximization (EM)...

mxComputeEM {OpenMx} | R Documentation

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

### Arguments

`expectation` | a vector of expectation names (DEPRECATED)
`predict` | what to predict from the observed data (DEPRECATED)
`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
`estep` | a compute plan to perform the expectation step

### 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. The Oakes (1999) direct method and S-EM, an implementation of Meng & Rubin (1991), are 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.

Oakes, D. (1999). Direct calculation of the information matrix via the EM algorithm. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61(2), 479-482.

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.

[Package OpenMx version 2.11.4 Index]