Generate data based on an MxModel object

Description

This function creates a randomly sampled data set based on the model.

Usage

mxGenerateData(model, nrows)

Arguments

Details

This function looks inside the MxModel object to extract the model-implied means and covariance. It then generates data with the same mean and covariance. Data can be generated based on Normal (mxExpectationNormal), RAM (mxExpectationRAM), LISREL (mxExpectationLISREL), and state space (mxExpectationStateSpace) models.

Thresholds and ordinal data are implemented by generating continuous data and then using cut and mxFactor to break the continous data at the thresholds into an ordered factor.

If the model has definition variables, then a data set must be included in the model object and the number of rows requested must match the number of rows in the model data. In this case the means, covariance, and thresholds are reevaluated for each row of data, potentially creating a a different mean, covariance, and threshold structure for every generated row of data.

For state space models (i.e. models with an mxExpectationStateSpace or mxExpectationStateSpaceContinuousTime expectation), the data are generated based on the autoregressive structure of the model. The rows of data in a state space model are not independent replicates of a stationary process. Rather, they are the result of a latent (possibly non-stationary) autoregressive process. For state space models different rows of data often correspond to different times. As alluded to above, data generation works for discrete time state space models and hybrid continuous-discrete time state space models. The latter have a continous process that is measured as discrete times.

Value

A data.frame with nrows rows.

References

The OpenMx User's guide can be found at http://openmx.psyc.virginia.edu/documentation.

Examples

#----------
# Create data based on state space model.
require(OpenMx)
nvar <- 5
varnames <- paste("x", 1:nvar, sep="")
ssModel <- mxModel(model="State Space Manual Example",
    mxMatrix("Full", 1, 1, TRUE, .3, name="A"),
    mxMatrix("Zero", 1, 1, name="B"),
    mxMatrix("Full", nvar, 1, TRUE, .6, name="C", dimnames=list(varnames, "F1")),
    mxMatrix("Zero", nvar, 1, name="D"),
    mxMatrix("Diag", 1, 1, FALSE, 1, name="Q"),
    mxMatrix("Diag", nvar, nvar, TRUE, .2, name="R"),
    mxMatrix("Zero", 1, 1, name="x0"),
    mxMatrix("Diag", 1, 1, FALSE, 1, name="P0"),
    mxMatrix("Zero", 1, 1, name="u"),
    mxExpectationStateSpace("A", "B", "C", "D", "Q", "R", "x0", "P0", "u"),
    mxFitFunctionML()
)

ssData <- mxGenerateData(ssModel, 200) # 200 time points

# Add simulated data to model
ssModel <- mxModel(ssModel, mxData(ssData, 'raw'))

# Fit model to simulated data
ssRun <- mxRun(ssModel)

# Compare parameters estimated from random data to
#  their true generating values
cbind(Rand=omxGetParameters(ssRun), Gen=omxGetParameters(ssModel))
# Note the parameters should be "close" (up to sampling error)
# to the generating values


#----------
require(OpenMx)
manifests <- paste("x", 1:5, sep="")
latents <- c("G")
factorModel <- mxModel("One Factor",
      type="RAM",
      manifestVars = manifests,
      latentVars = latents,
      mxPath(from=latents, to=manifests, values=.8),
      mxPath(from=manifests, arrows=2, values=.2),
      mxPath(from=latents, arrows=2,
            free=FALSE, values=1.0),
      mxPath(from = 'one', to = manifests))

factorData <- mxGenerateData(factorModel, 100)

factorModel <- mxModel(factorModel,
                       mxData(observed=cov(factorData), type="cov",
                              numObs=nrow(factorData),
                              means = colMeans(factorData)))
factorRun <- mxRun(factorModel)
cbind(Rand=omxGetParameters(factorRun), Gen=omxGetParameters(factorModel))