OpenMx {OpenMx}

OpenMx: An package for Structural Equation Modeling and Matrix Algebra Optimization

Description

OpenMx is a package for structural equation modeling, matrix algebra optimization and other statistical estimation problems. Try the example below. We try and have useful help files: for instance help(mxRun) to learn more. Also the reference manual

Details

OpenMx solves algebra optimization and statistical estimation problems using matrix algebra. Most users use it for Structural equation modeling.

The core function is mxModel, which makes a model. Models are containers for mxData, matrices, mxPaths algebras, mxBounds, confidence intervals, and mxConstraints. Most models require an expectation (see the list below) to calculate the expectations for the model. Models also need a fit function, several of which are built-in (see below). OpenMx also allows user-defined fit functions for purposes not covered by the built-in functions. (e.g., mxFitFunctionR or mxFitFunctionAlgebra).

Note, for mxModels of type="RAM", the expectation and fit-function are set for you automatically.

Running and summarizing a model

Once built, the resulting mxModel can be run (i.e., optimized) using mxRun. This returns the fitted model.

You can summarize the results of the model using summary(yourModel)

Additional overview of model making and getting started

The OpenMx manual is online (see references below). However, mxRun, mxModel, mxMatrix all have working examples that will help get you started as well.

The main OpenMx functions are: mxAlgebra, mxBounds, mxCI, mxConstraint, mxData, mxMatrix, mxModel, and mxPath.

Expectation functions include mxExpectationNormal, mxExpectationRAM, mxExpectationLISREL, and mxExpectationStateSpace;

Fit functions include mxFitFunctionML, mxFitFunctionAlgebra, mxFitFunctionRow and mxFitFunctionR.

Datasets built into OpenMx

OpenMx comes with over a dozen useful datasets built-in. Discover them using data(package="OpenMx"), and open them with, for example, data("jointdata", package ="OpenMx", verbose= TRUE)

Please cite the 'OpenMx' package in any publications that make use of it:

Michael C. Neale, Michael D. Hunter, Joshua N. Pritikin, Mahsa Zahery, Timothy R. Brick Robert M. Kirkpatrick, Ryne Estabrook, Timothy C. Bates, Hermine H. Maes, Steven M. Boker. (2016). OpenMx 2.0: Extended structural equation and statistical modeling. Psychometrika, 81, 535–549. DOI: 10.1007/s11336-014-9435-8

Steven M. Boker, Michael C. Neale, Hermine H. Maes, Michael J. Wilde, Michael Spiegel, Timothy R. Brick, Jeffrey Spies, Ryne Estabrook, Sarah Kenny, Timothy C. Bates, Paras Mehta, and John Fox. (2011) OpenMx: An Open Source Extended Structural Equation Modeling Framework. Psychometrika, 306-317. DOI:10.1007/s11336-010-9200-6

Steven M. Boker, Michael C. Neale, Hermine H. Maes, Michael J. Wilde, Michael Spiegel, Timothy R. Brick, Ryne Estabrook, Timothy C. Bates, Paras Mehta, Timo von Oertzen, Ross J. Gore, Michael D. Hunter, Daniel C. Hackett, Julian Karch, Andreas M. Brandmaier, Joshua N. Pritikin, Mahsa Zahery, Robert M. Kirkpatrick, Yang Wang, and Charles Driver. (2016) OpenMx 2 User Guide. http://openmx.ssri.psu.edu/docs/OpenMx/latest/OpenMxUserGuide.pdf

References

The OpenMx User's guide can be found at https://openmx.ssri.psu.edu/documentation

Examples

library(OpenMx)
data(demoOneFactor)
# ===============================
# = Make and run a 1-factor CFA =
# ===============================

latents  = c("G") # the latent factor
manifests = names(demoOneFactor) # manifest variables to be modeled
# ====================
# = Make the MxModel =
# ====================
m1 <- mxModel("One Factor", type = "RAM", 
	manifestVars = manifests, latentVars = latents, 
	mxPath(from = latents, to = manifests),
	mxPath(from = manifests, arrows = 2),
	mxPath(from = latents, arrows = 2, free = FALSE, values = 1.0),
	mxData(cov(demoOneFactor), type = "cov", numObs = 500)
)

# ===============================
# = mxRun it and get a summary! =
# ===============================

m1 = mxRun(m1)
summary(m1)