com.imsl.datamining.decisionTree

Class CHAID

java.lang.Object

com.imsl.datamining.PredictiveModel

com.imsl.datamining.decisionTree.DecisionTree

com.imsl.datamining.decisionTree.CHAID

All Implemented Interfaces:

Serializable, Cloneable

public class CHAID
extends DecisionTree
implements Serializable, Cloneable

Generates a decision tree using CHAID for categorical or discrete ordered predictor variables. Due to Kass (1980), CHAID is an acronym for chi-square automatic interaction detection. At each node, CHAID looks for the best splitting variable using the following steps: given a predictor variable X, perform a 2-way chi-squared test of association between each possible pair of categories of X with the categories of Y. The least significant result is noted and, if a threshold is met, the two categories of X are merged.

Next, treating this merged category as a single category, CHAID repeats the series of tests to determine if there is further merging possible. If a merged category consists of three or more of the original categories of X, CHAID calls for a step to test whether the merged categories should be split. This is done by forming all binary partitions of the merged category and testing each one against Y in a 2-way test of association. If the most significant result meets a threshold, then the merged category is split accordingly. As long as the threshold in this step is smaller than the threshold in the merge step, the splitting step and the merge step will not cycle back and forth.

Once each predictor is processed in this manner, the predictor with the most significant qualifying 2-way test with Y is selected as the splitting variable, and its last state of merged categories defines the split at the given node. If none of the tests qualify (by having an adjusted p-value smaller than a threshold), then the node is not split. This growing procedure continues until one or more stopping conditions are met.

See Also:

Example, Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class com.imsl.datamining.decisionTree.DecisionTree

DecisionTree.MaxTreeSizeExceededException, DecisionTree.PruningFailedToConvergeException, DecisionTree.PureNodeException

Nested classes/interfaces inherited from class com.imsl.datamining.PredictiveModel

PredictiveModel.CloneNotSupportedException, PredictiveModel.PredictiveModelException, PredictiveModel.StateChangeException, PredictiveModel.SumOfProbabilitiesNotOneException, PredictiveModel.VariableType

Constructor Summary

Constructors

Constructor and Description
CHAID(CHAID chaidModel) Constructs a copy of the input CHAID decision tree.
CHAID(double[][] xy, int responseColumnIndex, PredictiveModel.VariableType[] varType) Constructs a CHAID object for a single response variable and multiple predictor variables.

Method Summary

Modifier and Type	Method and Description
CHAID	clone() Clones a CHAID decision tree.
double	getMergeCategoriesSigLevel() Returns the significance level for merging categories.
double	getSplitMergedCategoriesSigLevel() Returns the significance level for splitting previously merged categories.
double	getSplitVariableSignificanceLevel() Returns the significance level for split variable selection.
protected int	selectSplitVariable(double[][] xy, double[] classCounts, double[] parentFreq, double[] splitValue, double[] splitCriterionValue, int[] splitPartition) Selects the split variable for the current node using CHAID (chi-square automatic interaction detection).
protected void	setConfiguration(PredictiveModel pm) Sets the configuration of PredictiveModel to that of the input model.
void	setMergeCategoriesSignificanceLevel(double mergeAlpha) Sets the significance level for merging categories.
void	setSplitMergedCategoriesSigLevel(double splitMergedAlpha) Sets the significance level for splitting previously merged categories.
void	setSplitVariableSignificanceLevel(double splitVariableSelectionAlpha) Sets the significance level for split variable selection.

Methods inherited from class com.imsl.datamining.decisionTree.DecisionTree

fitModel, getCostComplexityValues, getDecisionTree, getFittedMeanSquaredError, getMaxDepth, getMaxNodes, getMeanSquaredPredictionError, getMinCostComplexityValue, getMinObsPerChildNode, getMinObsPerNode, getNodeAssigments, getNumberOfComplexityValues, getNumberOfRandomFeatures, isAutoPruningFlag, isRandomFeatureSelection, predict, predict, predict, printDecisionTree, printDecisionTree, pruneTree, setAutoPruningFlag, setCostComplexityValues, setMaxDepth, setMaxNodes, setMinCostComplexityValue, setMinObsPerChildNode, setMinObsPerNode, setNumberOfRandomFeatures, setRandomFeatureSelection

Methods inherited from class com.imsl.datamining.PredictiveModel

getClassCounts, getClassErrors, getClassLabels, getClassProbabilities, getCostMatrix, getMaxNumberOfCategories, getMaxNumberOfIterations, getNumberOfClasses, getNumberOfColumns, getNumberOfMissing, getNumberOfPredictors, getNumberOfRows, getNumberOfUniquePredictorValues, getPredictorIndexes, getPredictorTypes, getPrintLevel, getPriorProbabilities, getRandomObject, getResponseColumnIndex, getResponseVariableAverage, getResponseVariableMostFrequentClass, getResponseVariableType, getTotalWeight, getVariableType, getWeights, getXY, isConstantSeries, isMustFitModel, isUserFixedNClasses, setClassCounts, setClassLabels, setClassProbabilities, setCostMatrix, setMaxNumberOfCategories, setMaxNumberOfIterations, setMustFitModel, setNumberOfClasses, setPredictorIndex, setPredictorTypes, setPrintLevel, setPriorProbabilities, setRandomObject, setResponseColumnIndex, setTrainingData, setVariableType, setWeights

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

CHAID

public CHAID(double[][] xy,
             int responseColumnIndex,
             PredictiveModel.VariableType[] varType)

Constructs a CHAID object for a single response variable and multiple predictor variables.

Parameters:

xy - a double matrix containing the training data and associated response values

responseColumnIndex - an int specifying the column index of the response variable

varType - a PredictiveModel.VariableType array containing the type of each variable

CHAID

public CHAID(CHAID chaidModel)

Constructs a copy of the input CHAID decision tree.

Parameters:

chaidModel - a CHAID decision tree

Method Detail

clone

public CHAID clone()

Clones a CHAID decision tree.

Specified by:

clone in class PredictiveModel

Returns:

a clone of the CHAID decision tree

getMergeCategoriesSigLevel

public double getMergeCategoriesSigLevel()

Returns the significance level for merging categories.

Returns:

a double, the significance level for merging categories

setMergeCategoriesSignificanceLevel

public final void setMergeCategoriesSignificanceLevel(double mergeAlpha)

Sets the significance level for merging categories.

Parameters:

mergeAlpha - a double, specifying the significance level for merging categories

mergeAlpha must be between 0.0 and 1.0. In addition, if splitMergeAlpha is set to enable splitting of previously merged categories, then mergeAlpha \( \le \) splitMergeAlpha.

Default: mergeAlpha = 0.05.

getSplitMergedCategoriesSigLevel

public double getSplitMergedCategoriesSigLevel()

Returns the significance level for splitting previously merged categories.

Returns:

a double, the significance level for splitting merged categories

setSplitMergedCategoriesSigLevel

public final void setSplitMergedCategoriesSigLevel(double splitMergedAlpha)

Sets the significance level for splitting previously merged categories.

Parameters:

splitMergedAlpha - a double specifying the significance level for splitting merged categories

splitMergeAlpha must be greater than or equal to CHAID.getMergeCategoriesSigLevel() unless disabled using splitMergeAlpha=-1. Default: splitMergeAlpha = -1.0 disables splitting of merged categories.

getSplitVariableSignificanceLevel

public double getSplitVariableSignificanceLevel()

Returns the significance level for split variable selection.

Returns:

a double, the significance level for split variable selection

setSplitVariableSignificanceLevel

public final void setSplitVariableSignificanceLevel(double splitVariableSelectionAlpha)

Sets the significance level for split variable selection.

Parameters:

splitVariableSelectionAlpha - a double specifying the significance level for split variable selection

splitVariableSelectionAlpha must be between 0.0 and 1.0.

Default: splitVariableSelectionAlpha = 0.05.

setConfiguration

protected final void setConfiguration(PredictiveModel pm)

Sets the configuration of PredictiveModel to that of the input model.

Overrides:

setConfiguration in class DecisionTree

Parameters:

pm - a PredictiveModel object which is to have its attributes duplicated in this instance

selectSplitVariable

protected int selectSplitVariable(double[][] xy,
                                  double[] classCounts,
                                  double[] parentFreq,
                                  double[] splitValue,
                                  double[] splitCriterionValue,
                                  int[] splitPartition)

Selects the split variable for the current node using CHAID (chi-square automatic interaction detection).

Specified by:

selectSplitVariable in class DecisionTree

Parameters:

xy - a double matrix containing the data

classCounts - a double array containing the counts for each class of the response variable, when it is categorical

parentFreq - a double array used to indicate which subset of the observations belong in the current node

splitValue - a double array representing the resulting split point if the selected variable is quantitative

splitCriterionValue - a double, the value of the criterion used to determine the splitting variable

splitPartition - an int array indicating the resulting split partition if the selected variable is categorical

Returns:

an int specifying the column index of the split variable in this.getPredictorIndexes()