private double paramValue(SemIm im, Parameter parameter) {
double paramValue = im.getParamValue(parameter);
if (parameter.getType() == ParamType.VAR) {
paramValue = Math.sqrt(paramValue);
}
return paramValue;
}
private String typeString(Parameter parameter) {
ParamType type = parameter.getType();
if (type == ParamType.COEF) {
return "Coef";
}
if (type == ParamType.VAR) {
// return "Variance";
return "StdDev";
}
if (type == ParamType.COVAR) {
return "Covar";
}
throw new IllegalStateException("Unknown param type.");
}
/**
* Computes the maximum likelihood function value for the given freeParameters values as given
* by the optimizer. These values are mapped to parameter values.
*/
public double evaluate(double[] parameters) {
List<Parameter> _parameters = sem.getSemPm().getFreeParameters();
for (int i = 0; i < _parameters.size(); i++) {
Parameter parameter = _parameters.get(i);
if (parameter.getType() == ParamType.VAR && parameters[i] < 0) {
parameters[i] = 0;
}
}
sem.setFreeParamValues(parameters);
// This needs to be FML-- see Bollen p. 109.
// try {
return sem.getScore();
// } catch (Exception e) {
// return Double.NEGATIVE_INFINITY;
// }
}
private static Element makeJointErrorDistribution(SemIm semIm) {
Element jointErrorElement = new Element(SemXmlConstants.JOINT_ERROR_DISTRIBUTION);
Element normal;
Parameter param;
for (Parameter parameter : semIm.getSemPm().getParameters()) {
param = parameter;
if (param.getType() == ParamType.COVAR) {
normal = new Element(SemXmlConstants.NORMAL);
normal.addAttribute(new Attribute(SemXmlConstants.NODE_1, param.getNodeA().getName()));
normal.addAttribute(new Attribute(SemXmlConstants.NODE_2, param.getNodeB().getName()));
normal.addAttribute(
new Attribute(SemXmlConstants.COVARIANCE, Double.toString(param.getStartingValue())));
jointErrorElement.appendChild(normal);
}
}
return jointErrorElement;
}
private static Element makeEdges(SemIm semIm) {
Element edgesElement = new Element(SemXmlConstants.EDGES);
Parameter param;
Element edge;
for (Parameter parameter : semIm.getSemPm().getParameters()) {
param = parameter;
if (param.getType() == ParamType.COEF) {
edge = new Element(SemXmlConstants.EDGE);
edge.addAttribute(new Attribute(SemXmlConstants.CAUSE_NODE, param.getNodeA().getName()));
edge.addAttribute(new Attribute(SemXmlConstants.EFFECT_NODE, param.getNodeB().getName()));
edge.addAttribute(
new Attribute(SemXmlConstants.VALUE, Double.toString(semIm.getParamValue(param))));
edge.addAttribute(
new Attribute(SemXmlConstants.FIXED, Boolean.valueOf(param.isFixed()).toString()));
edgesElement.appendChild(edge);
}
}
return edgesElement;
}
/**
* This method computes the information matrix or Hessian matrix of second order partial
* derivatives of the fitting function (4B_2 on page 135 of Bollen) with respect to the free
* freeParameters of the estimated SEM. It then computes the inverse of the the information matrix
* and calculates the standard errors of the freeParameters as the square roots of the diagonal
* elements of that matrix.
*
* @param estSem the estimated SEM.
*/
public void computeStdErrors(ISemIm estSem) {
// if (!unmeasuredLatents(estSem.getSemPm()).isEmpty()) {
// int n = estSem.getFreeParameters().size();
// stdErrs = new double[n];
//
// for (int i = 0; i < n; i++) {
// stdErrs[i] = Double.NaN;
// }
//
// return;
// }
// this.semIm = estSem;
estSem.setParameterBoundsEnforced(false);
double[] paramsOriginal = estSem.getFreeParamValues();
double delta;
FittingFunction fcn = new SemFittingFunction(estSem);
boolean ridder = false; // Ridder is more accurate but a lot slower.
int n = fcn.getNumParameters();
// Store the free freeParameters of the SemIm so that they can be reset to these
// values. The differentiation methods change them.
double[] params = new double[n];
System.arraycopy(paramsOriginal, 0, params, 0, n);
// If the Ridder method (secondPartialDerivativeRidr) is used to search for
// the best delta it is initially set to 0.1. Otherwise the delta is set to
// 0.005. That value has worked well for those fitting functions tested to
// date.
if (ridder) {
delta = 0.1;
} else {
delta = 0.005;
}
// The Hessian matrix of second order partial derivatives is called the
// information matrix.
TetradMatrix hess = new TetradMatrix(n, n);
List<Parameter> freeParameters = estSem.getFreeParameters();
boolean containsCovararianceParameter = false;
for (Parameter p : freeParameters) {
if (p.getType() == ParamType.COVAR) {
containsCovararianceParameter = true;
break;
}
}
for (int i = 0; i < n; i++) {
for (int j = i; j < n; j++) {
Parameter pi = freeParameters.get(i);
Parameter pj = freeParameters.get(j);
if (!containsCovararianceParameter) {
// Restrict off-diagonal to just collider edge freeParameters.
if (i != j && (pi.getType() != ParamType.COEF || pj.getType() != ParamType.COEF)) {
continue;
}
if (pi.getNodeB() != pj.getNodeB()) {
continue;
}
}
double v;
if (ridder) {
v = secondPartialDerivativeRidr(fcn, i, j, params, delta);
} else {
v = secondPartialDerivative(fcn, i, j, params, delta);
}
if (Math.abs(v) < 1e-7) {
v = 0;
}
// if (Double.isNaN(v)) {
// v = 0;
// }
hess.set(i, j, v);
hess.set(j, i, v);
}
}
ROWS:
for (int i = 0; i < hess.rows(); i++) {
for (int j = 0; j < hess.columns(); j++) {
if (hess.get(i, j) != 0) {
continue ROWS;
}
}
// System.out.println("Zero row for " + freeParameters.get(i));
}
// The diagonal elements of the inverse of the information matrix are the
// squares of the standard errors of the freeParameters. Their order is the
// same as in the array of free parameter values stored in paramsOriginal.
try {
TetradMatrix hessInv = hess.inverse();
// TetradMatrix hessInv = hess.ginverse();
// System.out.println("Inverse: " + hessInv);
// for (int i = 0; i < freeParameters.size(); i++) {
// System.out.println(i + " = " + freeParameters.get(i));
// }
stdErrs = new double[n];
// Hence the standard errors of the freeParameters are the square roots of the
// diagonal elements of the inverse of the information matrix.
for (int i = 0; i < n; i++) {
double v = Math.sqrt((2.0 / (estSem.getSampleSize() - 1)) * hessInv.get(i, i));
if (v == 0) {
System.out.println("v = " + v + " hessInv(i, i) = " + hessInv.get(i, i));
}
if (v == 0) {
stdErrs[i] = Double.NaN;
} else {
stdErrs[i] = v;
}
}
} catch (Exception e) {
e.printStackTrace();
stdErrs = new double[n];
for (int i = 0; i < n; i++) {
stdErrs[i] = Double.NaN;
}
}
// Restore the freeParameters of the estimated SEM to their original values.
estSem.setFreeParamValues(paramsOriginal);
estSem.setParameterBoundsEnforced(true);
}
/**
* 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());
}