/**
* Takes a Cholesky decomposition from the Cholesky.cholesky method and a set of data simulated
* using the information in that matrix. Written by Don Crimbchin. Modified June 8, Matt
* Easterday: added a random # seed so that data can be recalculated with the same result in
* Causality lab
*
* @param cholesky the result from cholesky above.
* @param randomUtil a random number generator, if null the method will make a new generator for
* each random number needed
* @return an array the same length as the width or length (cholesky should have the same width
* and length) containing a randomly generate data set.
*/
private double[] exogenousData(TetradMatrix cholesky, RandomUtil randomUtil) {
// Step 1. Generate normal samples.
double exoData[] = new double[cholesky.rows()];
for (int i = 0; i < exoData.length; i++) {
exoData[i] = randomUtil.nextNormal(0, 1);
}
// Step 2. Multiply by cholesky to get correct covariance.
double point[] = new double[exoData.length];
for (int i = 0; i < exoData.length; i++) {
double sum = 0.0;
for (int j = 0; j <= i; j++) {
sum += cholesky.get(i, j) * exoData[j];
}
point[i] = sum;
}
return point;
}
/**
* @param sampleSize The sample size of the desired data set.
* @param latentDataSaved True if latent variables should be included in the data set.
* @return This returns a standardized data set simulated from the model, using the reduced form
* method.
*/
public DataSet simulateDataReducedForm(int sampleSize, boolean latentDataSaved) {
int numVars = getVariableNodes().size();
// Calculate inv(I - edgeCoef)
TetradMatrix edgeCoef = edgeCoef().copy().transpose();
// TetradMatrix iMinusB = TetradAlgebra.identity(edgeCoef.rows());
// iMinusB.assign(edgeCoef, Functions.minus);
TetradMatrix iMinusB = TetradAlgebra.identity(edgeCoef.rows()).minus(edgeCoef);
TetradMatrix inv = iMinusB.inverse();
// Pick error values e, for each calculate inv * e.
TetradMatrix sim = new TetradMatrix(sampleSize, numVars);
// Generate error data with the right variances and covariances, then override this
// with error data for varaibles that have special distributions defined. Not ideal,
// but not sure what else to do at the moment. It's better than not taking covariances
// into account!
TetradMatrix cholesky = MatrixUtils.choleskyC(errCovar(errorVariances()));
for (int i = 0; i < sampleSize; i++) {
TetradVector e = new TetradVector(exogenousData(cholesky, RandomUtil.getInstance()));
TetradVector ePrime = inv.times(e);
sim.assignRow(i, ePrime); // sim.viewRow(i).assign(ePrime);
}
DataSet fullDataSet = ColtDataSet.makeContinuousData(getVariableNodes(), sim);
if (latentDataSaved) {
return fullDataSet;
} else {
return DataUtils.restrictToMeasured(fullDataSet);
}
}
