Statistical modeling for management

255 Pages·2008·1.123 MB·English

by  Hutcheson, Graeme D.;Moutinho, Luiz

iv
SSttaattiissttiiccaall
MMooddeelliinngg ffoorr
MMaannaaggeemmeenntt
iv
TSo a ntumaber otf veirys pattienti pceoplea (Youl know who you are), Andrea,
Alex, …and all Portuguese waiters.
Graeme Hutcheson
Modeling for
Luiz Moutinho
Management
iv
Statistical
Modeling for
Management
Graeme D. Hutcheson
Luiz Moutinho
iv
© Graeme D Hutcheson and Luiz Moutinho2008
First published 2008
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Contents
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
1 MeasurementScales 1
1.1 ContinuousData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Theunderlyingdistribution . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Recordingthedata . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3 Applyingmathematicaloperations . . . . . . . . . . . . . . . . . 5
1.2 OrderedCategoricalData . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Theunderlyingdistribution . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Recordingthedata . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.3 Applyingmathematicaloperations . . . . . . . . . . . . . . . . . 11
1.3 UnorderedCategoricalData. . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.1 Theunderlyingdistribution . . . . . . . . . . . . . . . . . . . . . 13
1.3.2 Recordingthedata . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.3 Applyingmathematicaloperations . . . . . . . . . . . . . . . . . 14
1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 ModelingContinuousData 17
2.1 TheGeneralizedLinearModel . . . . . . . . . . . . . . . . . . . . . . 17
2.2 TheOrdinaryLeast-SquaresModel . . . . . . . . . . . . . . . . . . . . 19
2.2.1 SimpleOLSregression . . . . . . . . . . . . . . . . . . . . . . . 19
Computingandinterpretingmodelparameters. . . . . . . . . . . 21
Predictingtheresponsevariable . . . . . . . . . . . . . . . . . . 22
Goodness-of-fitstatistics . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2 MultipleOLSregression . . . . . . . . . . . . . . . . . . . . . . 29
Computingandinterpretingmodelparameters. . . . . . . . . . . 29
Predictingtheresponsevariable . . . . . . . . . . . . . . . . . . 31
Goodness-of-fitstatistics . . . . . . . . . . . . . . . . . . . . . . 31
2.3 CategoricalExplanatoryVariables . . . . . . . . . . . . . . . . . . . . 35
2.4 AnalyzingSimpleExperimentalDesignsforContinuousData. . . . . . 36
2.4.1 Unrelatedgroupsdesign . . . . . . . . . . . . . . . . . . . . . . 36
ComparingtwogroupsusingOLSregression . . . . . . . . . . . 36
vi CONTENTS
ComparingmorethantwogroupsusingOLSregression . . . . . 42
Comparingtwogroupsusingat-test . . . . . . . . . . . . . . . . 46
ComparingmorethantwogroupsusingANOVA . . . . . . . . . 47
2.4.2 Relatedgroupsdesigns . . . . . . . . . . . . . . . . . . . . . . . 47
ComparingtwogroupsusingOLSregression . . . . . . . . . . . 48
ComparingmorethantwogroupsusingOLSregression . . . . . 53
Comparingtwogroupsusingat-test . . . . . . . . . . . . . . . . 54
ComparingmorethantwogroupsusingANOVA . . . . . . . . . 55
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3 ModelingDichotomousData 57
3.1 TheGeneralizedLinearModel . . . . . . . . . . . . . . . . . . . . . . 57
3.2 TheLogisticRegressionModel . . . . . . . . . . . . . . . . . . . . . . 62
3.2.1 Simplelogisticregression . . . . . . . . . . . . . . . . . . . . . 62
ComputingandInterpretingModelParameters . . . . . . . . . . 63
Predictedprobabilities . . . . . . . . . . . . . . . . . . . . . . . 65
Goodness-of-fitstatistics . . . . . . . . . . . . . . . . . . . . . . 66
3.2.2 MultipleLogisticRegression . . . . . . . . . . . . . . . . . . . . 69
Computingandinterpretingmodelparameters. . . . . . . . . . . 71
Predictedprobabilities . . . . . . . . . . . . . . . . . . . . . . . 73
Goodness-of-fitstatistics . . . . . . . . . . . . . . . . . . . . . . 73
3.2.3 Categoricalexplanatoryvariables . . . . . . . . . . . . . . . . . 76
Computingandinterpretingmodelparameters. . . . . . . . . . . 77
Predictedprobabilities . . . . . . . . . . . . . . . . . . . . . . . 78
Goodness-of-fitstatistics . . . . . . . . . . . . . . . . . . . . . . 80
3.3 AnalyzingSimpleExperimentalDesignsforDichotomousData . . . . 82
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4 ModelingOrderedData 83
4.1 TheGeneralizedLinearModel . . . . . . . . . . . . . . . . . . . . . . 83
4.2 TheProportionalOddsModel. . . . . . . . . . . . . . . . . . . . . . . 83
4.2.1 Simpleproportionalodds . . . . . . . . . . . . . . . . . . . . . . 85
Checkingtheproportionaloddsassumption . . . . . . . . . . . . 86
Computingandinterpretingmodelparameters. . . . . . . . . . . 88
Predictedprobabilities . . . . . . . . . . . . . . . . . . . . . . . 89
Goodness-of-fitstatistics . . . . . . . . . . . . . . . . . . . . . . 90
4.2.2 Multipleproportionalodds . . . . . . . . . . . . . . . . . . . . . 93
Checkingtheproportionaloddsassumption . . . . . . . . . . . . 94
Computingandinterpretingmodelparameters. . . . . . . . . . . 94
Predictedprobabilities . . . . . . . . . . . . . . . . . . . . . . . 96
Goodness-of-fitstatistics . . . . . . . . . . . . . . . . . . . . . . 97
4.2.3 Categoricalexplanatoryvariables . . . . . . . . . . . . . . . . . 100
4.3 AnalyzingSimpleExperimentalDesignsforOrderedData . . . . . . . 106
4.3.1 Unrelatedgroupsdesign . . . . . . . . . . . . . . . . . . . . . . 107
4.3.2 Relatedgroupsdesign . . . . . . . . . . . . . . . . . . . . . . . 113
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
CONTENTS vii
5 ModelingUnorderedData 121
5.1 TheGeneralizedLinearModel . . . . . . . . . . . . . . . . . . . . . . 121
5.2 TheMulti-nomialLogisticRegressionModel . . . . . . . . . . . . . . 122
5.2.1 Simplemulti-nomiallogisticregression . . . . . . . . . . . . . . 123
Computingandinterpretingmodelparameters. . . . . . . . . . . 123
Predictedprobabilities . . . . . . . . . . . . . . . . . . . . . . . 126
Goodness-of-fitstatistics . . . . . . . . . . . . . . . . . . . . . . 127
5.2.2 Multiplemulti-nomiallogisticregressionincluding
categoricalvariables . . . . . . . . . . . . . . . . . . . . . . . . 130
Computingandinterpretingmodelparameters. . . . . . . . . . . 131
Predictedprobabilities . . . . . . . . . . . . . . . . . . . . . . . 133
Goodness-of-fitstatistics . . . . . . . . . . . . . . . . . . . . . . 134
5.3 AnalyzingSimpleExperimentalDesignsforUnorderedData . . . . . . 137
5.3.1 Unrelatedgroupsdesign . . . . . . . . . . . . . . . . . . . . . . 137
5.3.2 Relatedgroupsdesign . . . . . . . . . . . . . . . . . . . . . . . 145
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6 NeuralNetworks 153
6.1 CognitiveTheory–NodesandLinks–MentalManipulationofData . . 153
6.1.1 Roots: Aparallelmodelofthebrain . . . . . . . . . . . . . . . . 153
6.1.2 Neuralnetworksembodyaprocessoflearning . . . . . . . . . . 154
6.1.3 ImplementationofNNs . . . . . . . . . . . . . . . . . . . . . . . 157
6.1.4 Thebackpropagationalgorithm(BP) . . . . . . . . . . . . . . . . 158
Detailsofthealgorithm. . . . . . . . . . . . . . . . . . . . . . . 161
6.1.5 BasicpropertiesoftheSOM . . . . . . . . . . . . . . . . . . . . 164
6.1.6 Potentialbenefitsoftheapproach . . . . . . . . . . . . . . . . . 167
6.1.7 Businessapplications . . . . . . . . . . . . . . . . . . . . . . . . 167
6.2 Example-Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.2.1 Theresearchmodel . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.2.2 Analysisofthedata . . . . . . . . . . . . . . . . . . . . . . . . . 170
6.2.3 Labelingofhiddennodes: malebuyers . . . . . . . . . . . . . . 171
6.2.4 Labelingofhiddennodes: femalebuyers . . . . . . . . . . . . . 172
6.2.5 Findings: malecarbuyers . . . . . . . . . . . . . . . . . . . . . 172
6.2.6 Findings: femalecarbuyers . . . . . . . . . . . . . . . . . . . . 174
6.2.7 Conclusionsandimplications . . . . . . . . . . . . . . . . . . . 175
7 ApproximateAlgorithmsforManagementProblems 177
7.1 GeneticAlgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
7.1.1 Sitelocationanalysisusinggeneticalgorithms . . . . . . . . . . 179
7.1.2 Chromosomerepresentation . . . . . . . . . . . . . . . . . . . . 180
7.1.3 Fitnessfunction . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.1.4 Geneticoperators . . . . . . . . . . . . . . . . . . . . . . . . . . 181
7.1.5 Simpleillustration . . . . . . . . . . . . . . . . . . . . . . . . . 181
7.2 TabuSearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
7.2.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
viii CONTENTS
7.2.2 Applicationoftabusearchtosegmentation . . . . . . . . . . . . 183
7.3 SimulatedAnnealing . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
7.3.1 Salesterritorydesignusingsimulatedannealing . . . . . . . . . . 185
7.3.2 InformationaboutasingleSCU . . . . . . . . . . . . . . . . . . 186
7.3.3 Themodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.3.4 Contiguity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
7.3.5 Equalworkload . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
7.3.6 Equalityofsalespotential . . . . . . . . . . . . . . . . . . . . . 188
7.3.7 Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
7.3.8 Applicationofsimulatedannealing . . . . . . . . . . . . . . . . 190
8 OtherStatistical,MathematicalandCo-patternModelingTechniques 191
8.1 DiscriminantAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 191
8.2 AutomaticInteractionDetection(AID) . . . . . . . . . . . . . . . . . 191
8.3 LogicalTypeDiscriminantModels: TheC5Algorithm . . . . . . . . 192
8.4 MultidimensionalScaling . . . . . . . . . . . . . . . . . . . . . . . . 198
8.5 ConjointAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
8.6 CorrespondenceAnalysis . . . . . . . . . . . . . . . . . . . . . . . . 200
8.7 LatentAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
8.8 FuzzySets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
8.9 FuzzyDecisionTrees . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8.10 ArtificialIntelligence . . . . . . . . . . . . . . . . . . . . . . . . . . 206
8.11 ExpertSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
8.11.1 Methodbasedonmarketingmainadvantagesmain
limitationsapplications . . . . . . . . . . . . . . . . . . . . . 207
8.12 FuzzyLogicandFuzzyExpertSystems. . . . . . . . . . . . . . . . . 208
8.13 RoughSetTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
8.14 VariablePrecisionRoughSets(VPRS) . . . . . . . . . . . . . . . . . 210
8.14.1 AnoverviewofVPRS . . . . . . . . . . . . . . . . . . . . . . 210
8.15 Dempster-ShaferTheory. . . . . . . . . . . . . . . . . . . . . . . . . 212
8.16 ChaosTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
8.17 DataMining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
8.17.1 Miningandrefiningdata . . . . . . . . . . . . . . . . . . . . . 217
8.17.2 Siftware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
8.17.3 Invasionofthedatasnatchers . . . . . . . . . . . . . . . . . . 218
8.17.4 Miningwithquerytools . . . . . . . . . . . . . . . . . . . . . 219
8.18 DataMining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
8.18.1 Acomputingperspectiveondatamining . . . . . . . . . . . . 221
8.18.2 Dataminingtools . . . . . . . . . . . . . . . . . . . . . . . . 221
8.18.3 Trynewdata-miningtechniques–theycanovercome,
augmenttraditionalstatanalysis . . . . . . . . . . . . . . . . . 221
References 223
Index 231
List of Tables
1 MeasurementScales 1
1.1 Examplesofintervalandratioscales . . . . . . . . . . . . . . . . . . 4
1.2 Anexampleofcategorizedcontinuousdata . . . . . . . . . . . . . . 5
1.3 Orderedcategoricalcodingofarmyrank: exampleI . . . . . . . . . 7
1.4 Orderedcategoricalcodingofarmyrank: exampleII . . . . . . . . . 8
1.5 Unorderedcategoricalcodingofarmyrank . . . . . . . . . . . . . . 8
1.6 Continuousvariablescodedasorderedcategories . . . . . . . . . . . 9
1.7 Acontinuousvariablecodedasorderedcategoricaldata . . . . . . . 10
1.8 Representingageusingorderedcategories . . . . . . . . . . . . . . . 10
1.9 Mis-codinganorderedcategoricalvariable . . . . . . . . . . . . . . 11
1.10 Highesteducationalattainment . . . . . . . . . . . . . . . . . . . . . 12
1.11 Unorderedcategoricaldata: codingexampleI . . . . . . . . . . . . . 13
1.12 Unorderedcategoricaldata: codingexampleII . . . . . . . . . . . . 14
1.13 Numberofcarssoldinayear . . . . . . . . . . . . . . . . . . . . . 14
2 ModelingContinuousData 17
SimpleOLSregression . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Data: icecreamconsumption . . . . . . . . . . . . . . . . . . . . . 20
2.2 Regressionparameters . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Predictionsofconsumption. . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Computingthedevianceforthemodel“consumption=α” . . . . . . 25
2.5 Computing the deviance for the model “consumption = α +
β temperature” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 Assessingsignificancebycomparingmodeldeviances . . . . . . . . 27
2.7 Analysisofdeviancetable: thesignificanceofvariables . . . . . . . 28
2.8 Estimatingthesignificanceofindividualparametersusing
t-statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
MultipleOLSregression . . . . . . . . . . . . . . . . . . . . . . . 29
2.9 Regressionparameters . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.10 Confidenceintervals . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.11 Predictionsofconsumption. . . . . . . . . . . . . . . . . . . . . . . 32