/**
* Calculates the sample likelihood and BIC score for i given its parents in a simple SEM model.
*/
private double localSemScore(int i, int[] parents) {
try {
ICovarianceMatrix cov = getCovMatrix();
double varianceY = cov.getValue(i, i);
double residualVariance = varianceY;
int n = sampleSize();
int p = parents.length;
int k = (p * (p + 1)) / 2 + p;
// int k = (p + 1) * (p + 1);
// int k = p + 1;
TetradMatrix covxx = cov.getSelection(parents, parents);
TetradMatrix covxxInv = covxx.inverse();
TetradVector covxy = cov.getSelection(parents, new int[] {i}).getColumn(0);
TetradVector b = covxxInv.times(covxy);
residualVariance -= covxy.dotProduct(b);
if (residualVariance <= 0 && verbose) {
out.println(
"Nonpositive residual varianceY: resVar / varianceY = "
+ (residualVariance / varianceY));
return Double.NaN;
}
double c = getPenaltyDiscount();
// return -n * log(residualVariance) - 2 * k; //AIC
return -n * Math.log(residualVariance) - c * k * Math.log(n);
// return -n * log(residualVariance) - c * k * (log(n) - log(2 * PI));
} catch (Exception e) {
e.printStackTrace();
throw new RuntimeException(e);
// throwMinimalLinearDependentSet(parents, cov);
}
}
/**
* @return Returns the error covariance matrix of the model. i.e. [a][b] is the covariance of E_a
* and E_b, with [a][a] of course being the variance of E_a. THESE ARE NOT PARAMETERS OF THE
* MODEL; THEY ARE CALCULATED. Note that elements of this matrix may be Double.NaN; this
* indicates that these elements cannot be calculated.
*/
private TetradMatrix errCovar(Map<Node, Double> errorVariances) {
List<Node> variableNodes = getVariableNodes();
List<Node> errorNodes = new ArrayList<Node>();
for (Node node : variableNodes) {
errorNodes.add(semGraph.getExogenous(node));
}
TetradMatrix errorCovar = new TetradMatrix(errorVariances.size(), errorVariances.size());
for (int index = 0; index < errorNodes.size(); index++) {
Node error = errorNodes.get(index);
double variance = getErrorVariance(error);
errorCovar.set(index, index, variance);
}
for (int index1 = 0; index1 < errorNodes.size(); index1++) {
for (int index2 = 0; index2 < errorNodes.size(); index2++) {
Node error1 = errorNodes.get(index1);
Node error2 = errorNodes.get(index2);
Edge edge = semGraph.getEdge(error1, error2);
if (edge != null && Edges.isBidirectedEdge(edge)) {
double covariance = getErrorCovariance(error1, error2);
errorCovar.set(index1, index2, covariance);
}
}
}
return errorCovar;
}
private TetradMatrix subMatrix(Node x, Node y, List<Node> z) {
int dim = z.size() + 2;
int[] indices = new int[dim];
indices[0] = variables.indexOf(x);
indices[1] = variables.indexOf(y);
for (int k = 0; k < z.size(); k++) {
indices[k + 2] = variables.indexOf(z.get(k));
}
TetradMatrix submatrix = new TetradMatrix(dim, dim);
for (int i = 0; i < dim; i++) {
for (int j = 0; j < dim; j++) {
int i1 = indices[i];
int i2 = indices[j];
submatrix.set(i, j, covMatrix.getDouble(i1, i2));
}
}
return submatrix;
}
/**
* @return The edge coefficient matrix of the model, a la SemIm. Note that this will normally need
* to be transposed, since [a][b] is the edge coefficient for a-->b, not b-->a. Sorry.
* History. THESE ARE PARAMETERS OF THE MODEL--THE ONLY PARAMETERS.
*/
public TetradMatrix edgeCoef() {
List<Node> variableNodes = getVariableNodes();
TetradMatrix edgeCoef = new TetradMatrix(variableNodes.size(), variableNodes.size());
for (Edge edge : edgeParameters.keySet()) {
if (Edges.isBidirectedEdge(edge)) {
continue;
}
Node a = edge.getNode1();
Node b = edge.getNode2();
int aindex = variableNodes.indexOf(a);
int bindex = variableNodes.indexOf(b);
double coef = edgeParameters.get(edge);
edgeCoef.set(aindex, bindex, coef);
}
return edgeCoef;
}
/**
* 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);
}
}
/**
* Constructs a new standardized SEM IM from the freeParameters in the given SEM IM.
*
* @param im Stop asking me for these things! The given SEM IM!!!
* @param initialization CALCULATE_FROM_SEM if the initial values will be calculated from the
* given SEM IM; INITIALIZE_FROM_DATA if data will be simulated from the given SEM,
* standardized, and estimated.
*/
public StandardizedSemIm(SemIm im, Initialization initialization) {
this.semPm = new SemPm(im.getSemPm());
this.semGraph = new SemGraph(semPm.getGraph());
semGraph.setShowErrorTerms(true);
if (semGraph.existsDirectedCycle()) {
throw new IllegalArgumentException("The cyclic case is not handled.");
}
if (initialization == Initialization.CALCULATE_FROM_SEM) {
// This code calculates the new coefficients directly from the old ones.
edgeParameters = new HashMap<Edge, Double>();
List<Node> nodes = im.getVariableNodes();
TetradMatrix impliedCovar = im.getImplCovar(true);
for (Parameter parameter : im.getSemPm().getParameters()) {
if (parameter.getType() == ParamType.COEF) {
Node a = parameter.getNodeA();
Node b = parameter.getNodeB();
int aindex = nodes.indexOf(a);
int bindex = nodes.indexOf(b);
double vara = impliedCovar.get(aindex, aindex);
double stda = Math.sqrt(vara);
double varb = impliedCovar.get(bindex, bindex);
double stdb = Math.sqrt(varb);
double oldCoef = im.getEdgeCoef(a, b);
double newCoef = (stda / stdb) * oldCoef;
edgeParameters.put(Edges.directedEdge(a, b), newCoef);
} else if (parameter.getType() == ParamType.COVAR) {
Node a = parameter.getNodeA();
Node b = parameter.getNodeB();
Node exoa = semGraph.getExogenous(a);
Node exob = semGraph.getExogenous(b);
double covar = im.getErrCovar(a, b) / Math.sqrt(im.getErrVar(a) * im.getErrVar(b));
edgeParameters.put(Edges.bidirectedEdge(exoa, exob), covar);
}
}
} else {
// This code estimates the new coefficients from simulated data from the old model.
DataSet dataSet = im.simulateData(1000, false);
TetradMatrix _dataSet = dataSet.getDoubleData();
_dataSet = DataUtils.standardizeData(_dataSet);
DataSet dataSetStandardized = ColtDataSet.makeData(dataSet.getVariables(), _dataSet);
SemEstimator estimator = new SemEstimator(dataSetStandardized, im.getSemPm());
SemIm imStandardized = estimator.estimate();
edgeParameters = new HashMap<Edge, Double>();
for (Parameter parameter : imStandardized.getSemPm().getParameters()) {
if (parameter.getType() == ParamType.COEF) {
Node a = parameter.getNodeA();
Node b = parameter.getNodeB();
double coef = imStandardized.getEdgeCoef(a, b);
edgeParameters.put(Edges.directedEdge(a, b), coef);
} else if (parameter.getType() == ParamType.COVAR) {
Node a = parameter.getNodeA();
Node b = parameter.getNodeB();
Node exoa = semGraph.getExogenous(a);
Node exob = semGraph.getExogenous(b);
double covar = -im.getErrCovar(a, b) / Math.sqrt(im.getErrVar(a) * im.getErrVar(b));
edgeParameters.put(Edges.bidirectedEdge(exoa, exob), covar);
}
}
}
this.measuredNodes = Collections.unmodifiableList(semPm.getMeasuredNodes());
}
