Chapter 1 Basic Mathematical Concepts



Section I: Mathematical Fundamentals

Section II: The General Linear Model

References

Mosteller, Frederick and John W. Tukey (1977) Data Analysis and Regression. Reading, MA: Addison-Wesley.

R. Darrell Bock (1975) Multivariate Statistical Methods in Behavioral Research. New York: McGraw-Hill.

Box, George E. P., William G. Hunter, J. Stuart Hunter (1978) Statistics for Experimenters. New York: Wiley.

Glantz, Stanton A. and Bryan K. Slinker (1990) Primer of Applied Regression and Analysis of Variance. New York: McGraw-Hill.

Kirk, Roger E. (1982) Experimental Design. Second Edition. Pacific Grove, CA: Brooks/Cole.

Mendenhall, William (1968) The Design and Analysis of Experiments. Belmont,CA: Duxbury.

Section III: Covariance Structure

Section IV: Consumer Judgment and Choice

Psychophysics

Batchelor, R.A. (1986) "The Psychophysics of Inflation," Journal of Economic Psychology, 7 (September), 269-90.

Monroe, Kent B. (1977) "Objective and Subjective Contextual Influences on Price Perception." In Arch G. Woodside, Jagdish Sheth, and Peter D. Bennet (Eds.) Consumer and Industrial Buying Behavior. NY: Elsevier-North Holland.

Sinn, Hans-Werner (1985) "Psychophysical Laws in Risk Theory," Journal of Economic Psychology, 6, 185-206.

Kamen, Joseph M. and Robert J. Toman (1970) "Psychophysics of Prices," Journal of Marketing Research, 7 (February), 27-35.

Gabor, Andre, Clive W. J. Granger and Anthony P. Sowter (1971) "Comments on 'Psychophysics of Prices', Journal of Marketing Research, 8 (May), 251-2.

Comparative Judgement

Thurstone, L.L. (1927) "A Law of Comparative Judgement," Psychological Review, 38, 368-89.

Freiden, Jon B. and Douglas S. Bible (1982) "The Home Purchase Process: Measurement of Evaluative Criteria through Pairwise Measures," Journal of the Academy of Marketing Science, 10 (Fall, 359-76

Signal Detection and Categorical Judgement

Cradit, J. Dennis., Armen Taschian and Charles Hofacker (1994) "Signal Detection Theory and Single Observation Designs: Methods and Indices for Advertising Recognition Testing," Journal of Marketing Research, (February), 117-27.

Parducci, Allen (1963) "Category Judgement: A Range-Frequency Model," Psychological Review, 72 (6), 407-18.

Tashchian, Armen J., J. Dennis White, and Sukgoo Pak (1988) "Signal Detection Analysis and Advertising Recognition: An Introduction Measurement and Interpretation Issues," Journal of Marketing Research 25 (November), 397-404.

Srinivasan, V. and Amiya K. Basu (1989) "The Metric Quality of Ordered Categorical Data," Marketing Science, 8 (Summer), 205-30.

Functional Measurement

Anderson, Norman H. (1982) "Cognitive Algebra and Social Psychophysics" in Bernd Wegener (Ed.) Social Attitudes and Psychophysical Measurement, Hillsdale, NJ: Lawrence Erlbaum.

Levin, Irwin P., Richard D. Johnson and Patricia J.Deldin (1985) "Framing Effects in Judgement Tasks with Varying Amounts of Information," Organization Behavior and Human Decision Processes, 36 (December), 362-77.

Levin, Irwin P. (1985) "How Changes in Price and Salary Affect Economic Satisfaction: Information Integration Models and Inference Processes," Journal of Economic Psychology, 6 (June), 143-55.

Johnson, Richard D. and Irwin P. Levin (1985) "More than Meets the Eye: The Effect of Missing Information of Purchase Evaluations," Journal of Consumer Research, 12 (September), 169-77.

White J. Dennis and Elise L. Truly (1989) "Price-Quality Integration and Warranty Evaluation: A Preliminary Test of Alternative Models f or Risk Assessment," Journal of Business Research, 19, 109-25.

Birnbaum, Michael H. (1982) "Controversies in Psychological Measurement," in Bernd Wegener (Ed.) Social Attitudes and Psychophysical Measurement, Hillsdale, NJ: Lawrence Erlbaum.

Lynch, John G., Jr. (1985) "Uniqueness Issues in the Decompositional Modeling of Multiattribute Overall Evaluations: An Information Integration Perspective," Journal of Marketing Research, 22 (February), 1-19

McFadden, Daniel (1986) "The Choice Theory Approach to Market Research," Marketing Science 5 (Fall), 275-97.

Logit Models

Green, Paul E., Frank J. Carmone and David P. Wachspress (1977) "On the Analysis of Qualitative Data in Marketing Research," Journal of Marketing Research, 14 (February), 52-9.

Malhotra, Noresh K. (1984) "The Use of Linear Logit Models in Marketing Research," Journal of Marketing Research, 21 (February), 20-31.

Gensch, Dennis H. and Wilfred W. Recker (1979) "The Multinomial Multiattribute Logit Choice Model," Journal of Marketing Research, 16 (February), 124-32.

Flath, David and E.W. Leonard (1979) "A comparison of Two Logit Models in the Analysis of Qualitative Marketing Data." Journal of Marketing Research 16, (November), 533-8.

Bunche, David S. and Richard R. Batsell (1989) " A Monte Carlo Comparison of Estimators for the Multinomial Logit Model," Journal of Marketing Research, 26 (February), 56-68.

Probit Models

Malhotra, Naresh K. (1983) "A Threshold Model of Store Choice," Journal of Retailing, 59, (Summer), 3-21.

Hofacker, Charles F. (1990) "Derivation of Covariance Probit Elasticities," Management Science, 36 (April), 500-4.

Currim, Imran S., (1982) "Predictive Testing of Consumer Choice Models Not Subject to Independence of Irrelevant Alternatives, "Journal of Marketing Research, 21 (November), 20-31.

Kamakura, Wagner A. and Rajendra Srivastava (1984) "Predicting Choice Shares under Conditions of Brand Interdependence," Journal of Marketing Research, 21 (November), 20-31.

Nested Logit Models and Extensions of the MNL Mode

Louviere, Jordan J. and George Woodworth (1983) "Design and Analysis of Simulated Consumer Choice or Allocation Experiments: An Approach Based on Aggregate Data," Journal of Marketing Research, 20 (November), 350-67.

Moore, William L. and Donald R. Lehman (1989) "A Paired Comparison Nested Logit Model of Individual Preference Structures," Journal of Marketing Research¸26 (November), 420-8.

Elasticities and Competition

Mahajan, Vijay, Paul E. Green and Stephen M. Goldberg (1982) " A Conjoint Model for Measuring Self-and Cross-Price/Demand Relationships," 19 (August), 334-42.

Gupta, Sunil (1988) "Impact of Sales Promotions on When, What and How Much to Buy," Journal of Marketing Research, 25 (November), 342-55.

Noncompensatory Choice

Manrai, Ajay K. and Prabhakant Sinha (1989) "Elimination by Cutoffs," Marketing Science, 8 (Spring), 133-52.

Rotondo, John (1986) "Price as an Aspect of Choice in EBA," Marketing Science , 5 (Fall), 391-402.

Johnson, Eric J. and Robert J. Meyer (1984) "Compensatory Choice Models of Noncompensatory Processes: The Effect of Varying Context," Journal of Consumer Research 11 (June), 528-41.

Grether, David and Louis Wilde (1984) "An Analysis of Conjunctive Choice: Theory and Experiments," Journal of Consumer Research, 10 (March) 373-85

References

Conjoint Measurement

Green, Paul E. and V. Srinivasan (1978) "Conjoint Analysis in Consumer Research: Issues and Outlook," Journal of Consumer Research, 5 (September), 103-21.

Green, Paul E. and V. Srinivasan (1990) "Conjoint Analysis in Marketing: New Developments with Implication for Research and Practice," Journal of Marketing, 54 (October), 3-19.

Jaccard, James, David Brinberg and Lee J. Ackerman (1986) "Assessing Attribute Importance: A Comparison of Six Methods," Journal of Consumer Research, 12 (March), 463-8.

Validity and Conjoint Measurement

Green, Paul E., Wayne S. DeSarbe and Pradeep K. Kedia (1980) "On the Insensitivity of Brand-Choice Simulations to Attribute Importance Weights," Decision Sciences, 11, 439-50.

Green, Paul E., Kristiaan Helsen and Bruce Shandler (1988) "Conjoint Internal Validity under Alternative Profile Presentations," Journal of Consumer Research, 15 (December), 392-7.

Green, Paul E., Abba M. Kreiger, and Pradep Bansal (1988) "Complete Unacceptable Levels in Conjoint Analysis: A Cautionary Note," Journal of Marketing Research, 25 (August), 293-300.

Hagerty, Michael R. (1986) "The Cost of Simplifying Preference Models," Marketing Science, 5 (Fall), 298-319.

Moore, William L. and Morris B. Holbrook (1990) "Conjoint Analysis on Object with Environmentally Correlated Attributes: The Questionable Importance of Representative Design," Journal of Consumer Research 16 (March), 490-7.

Reibstein, David, John E.G. Bateson and William Boulding (1988) "Conjoint Analysis Reliability: Empirical Findings," Marketing Science, 7 (Summer), 271-86.

Safizadeh, M. Hossein (1989) "The Internal Validity of the Trade-off Method of Conjoint Analysis," Decision Sciences 20 (Summer), 451-61.

Teas R. Kenneth (1985) "An Analysis of the Temporal Stability and Structural Reliability of Metric Conjoint Analysis Procedures," Journal of the Academy of Marketing Science, 13 (Winter/Spring), 122-42.

Wittink, Dick R. and Phillipe Cattin (1981) "Alternative Estimation Methods for Conjoint Analysis: A Monte Carlo Study," Journal of Marketing Research, 18 (February), 101-6

Conjoint: Choice Simulation and Aggregation

Green, Paul E. and Abba M. Krieger (1988) "Choice Rules and Sensitivity Analysis in Conjoint Simulators," Journal of the Academy of Marketing Science, 16 (Spring), 114-27.

Kamakura, Wagner A. (1988) "A Least Squares Procedure for Benefit Segmentation with Conjoint Experiments," Journal of Marketing Research, 25 (May), 157-67.

Wiley, James B. and James T. Low (1983) "A Monte Carlo Simulation of Two Approaches for Aggregation Conjoint Data,"Journal of Marketing Research, 20 (November), 405-16.

Conjoint: Extensions

Green Paul E. (1984) "Hybrid Models for Conjoint Analysis: An Expository Review," Journal of Marketing Research, 21 (May), 155-69.

Tantiwong, Duang Tip and Peter C. Wilton (1985) "Understanding Food Store Preferences among the Elderly Using Hybrid Conjoint Measurement Models," Journal of Retailing, 61 (Winter), 35-64.

Green Paul E., J. Douglas Carroll and Stephen M. Goldberg (1981) "A General Approach to Product Design Optimization Via Conjoint Analysis," Journal of Marketing, 45 (Summer), 17-37.

Green, Paul E. and Abba M. Krieger (1985) "Models and Heuristics for Product Line Selection," Marketing Science 4 (Winter), 1-19

Teas R. Kenneth (1987) "Magnitude Scaling of the Dependent Variable in Decompositional Multiattribute Preference Models," Journal of the Academy of Marketing Science, 15 (Fall), 64-73.

MDS in Marketing Research

Cooper, Lee G. (1983) "A Review of Multidimensional Scaling in Marketing Research," Applied Psychological Measurement, 7 (Fall), 427-50

Green, Paul E. and Frank J. Carmone (1969) "Multidimensional Scaling: An Introduction and comparison of Nonmetric Unfolding Techniques," Journal of Marketing Research, 6 (August), 330-41.

Lehmann, Donald R. (1972) "Judged Similarity and Brand-Switching Data as Similarity Measures," Journal of Marketing Research, 9 (August), 331-4.

Perreault, William D. and Forrest W. Young (1980) "Alternating Lease Squares Optimal Scaling: Analysis of Nonmetric Data in Marketing Research," Journal of Marketing Research, 17 (February), 1-13.

Moore, William L. and Morris B. Holbrook (1982) "On the Predictive Validity of Joint Space Models in Consumer Evaluations of New Concepts," Journal of Consumer Research, 9 (September), 206-10

MacKay, David B. and Joseph L. Zinnes (1986) "A Probabilistic Model for the Multidimensional Scaling of Proximity and Preference Data," Marketing Science, 5 (Fall), 324-44.

Schiffman, Susan S., M. Lance Reynolds and Forrest W. Young (1981) Introduction to Multidimensional Scaling. New York: Academic.

Shocker, Allen D. and V. Srinivasan (1974) "A Consumer Based Methodology for the Identification of New Product Ideas," Management Science, Series B, 20 (February), 921-37.

MDS Models: Applications and Extensions

DeSarbo Wayne S. and Vithala R. Rao (1986) "A Constrained Unfolding Methodology for Product Positioning," Marketing Science, 5 (Winter), 1-19.

Gavish, Bezale, Dan Horsky and Kizhanatham Srikanth (1983) "An Approach to the Optimal Positioning of a New Product," Management Science, 29 (November), 1277-97.

Green, Paul E. and Abba M. Krieger (1989) "Recent Contributions to Optimal Product Positioning and Buyer Segmentation," European Journal of Operational Research, 41 (July), 127-41.

Harshman, Richard A., Paul E. Green, Yorman Wind and Margaret E. Lundy (1982) "A Model for the Analysis of Asymmetric Data in Marketing Research," Marketing Science, 1 (Spring), 205-42.

Holbrook, Morris B. and Duglas V. Holloway (1984) "Marketing Strategy and the Structure of Aggregate, Segment-specific, and Differential Preferences," Journal of Marketing, 48 (Winter), 62-7.

Sudharshan, D., Jerrod H. May and Allan D. Shocker (1987) "A Simulation Comparison of Methods for New Product Location," Marketing Science 6 (Spring), 182-201.

Here we might note certain similarities between the Binomial model in Equation (15.20) and the Negative Binomial in Equation (15.23). In the latter, the role of p is played by [pic]while 1 - p is analogous to [pic] As before, we will be estimating k and m according to the method of moments, or using ML or Minimum Chi Square.

References

Kahn, Barbara E., Manohar U. Kalwani and Donald G. Morrison (1988) "Niching Versus Change -of-Pace Brands: Purchase Frequencies and Penetration Rates to Infer Brand Positionings," Journal of Marketing Research, 25 (November), 384-90.

Kahn, Barbara E., Manohar U. Kalwani and Donald G. Morrison (1984) "Measuring Variety-Seeking and Reinforcement Behaviors Using Panel Data," Journal of Marketing Research 23 (May), 89-100.

Lilien, Gary L. and Philip Kotler (1983) Marketing Decision Making. New York: Harper and Row.

Schmittlein, David C., Albert C. Bemmaor and Donald G. Morrison (1985) "Why Does the NBD Model Work? Robustness in Representing Product Purchases and Imperfectly Recorded Purchases," Marketing Science 4 (Summer), 255-56.

Wheat, Rita D. and Donald G. Morrison (1990) "Assessing Purchase Timing Models: Whether or Not is Preferable to When," Marketing Science, 9 (Spring), 162-70.

Section V: Economics and Econometrics

Appendices

A. The Greek Alphabet

|alpha |α |Α |

|beta |β |Β |

|gamma |γ |Γ |

|delta |δ |Δ |

|epsilon |ε |Ε |

|zeta |ζ |Ζ |

|eta |η |Η |

|theta |θ |Θ |

|iota |ι |Ι |

|kappa |κ |Κ |

|lambda |λ |Λ |

|mu |μ |Μ |

|nu |ν |Ν |

|xi or ksi |ξ |Ξ |

|omicron |ο |Ο |

|phi |π |Π |

|rho |ρ |Ρ |

|sigma |σ |Σ |

|tau |τ |Τ |

|upsilon |υ |Υ |

|phi |φ |Φ |

|chi |χ |Χ |

|psi |ψ |Ψ |

|omega |ω |Ω |

Index

(-equivalent tests 118

2SLS 225

a priori 66, 67, 72, 86

absolute threshold 146

additive conjoint measurement 190

aggregate data 168

algebra for matrices 3

all y models 127

Almon's scheme 235

ALS 191

alternating least squares 191, 193

alternative specific constants 182

alternative specific variables 182

analytical solution 31

angle-preserving transformation 30

ANOVA 76

AR 249

arithmetic mean See

ASC 182

associative property of matrix addition 6

associative property of scalar multiplication 4

ASV 182

asymptotic efficiency 34

attraction 168

autocovariance 242

autoregression 248

autoregressive process 249

backshift operator 235, 245, 251

beta distribution 206

big R squared 70

bilinear form 8

brand switching 204

canonical correlation 99

category rating scale 157

central limit theorem 64

chain rule 22

Chi Square 41

city block metric. 195

classification 104

closed form solution 31

Cobb-Douglas function 221

Cochrane-Orcutt iterative procedure 233

Cochran's theorem 43

coding

dummy 78

effect 77

orthogonal 79

column centering 16

column vector See vector

common factors 111, 137

communalities 137, 138

communality 137

commutative property of matrix addition 6

comparative judgment model 182

conditional logit 182, 183

conditional probability 105, 205

confidence interval 66

confidence intervals 66

conformable for addition 4

congeneric tests 118

congeneric tests. 118

conjoint 190

constant elasticity model 222

contemporaneous correlation 238

correct rejection 160

corrected SSCP matrix 16

corrected sum of square and cross products 16

correlation, squared multiple 70

correlogram 246

covariance 14

covariance structure models 110

cross effects 183

cross product 15

crossing 84

cross-product matrix 9

cross-products 96

cumulated probabilities 158

density function 36, 37

derivative

scalar 20

trace 89

vector 23

derivative of a scalar with respect to a vector 22

derivative of a sum 21

derivative of the transpose 23

determinant 11

determinant of a matrix 11

deviation score 14

Diag function 17

diagonal 18

diagonal matrix 5

dichotomous dependent variable 168

difference thresholds 147

differential effects 183

direct product 90

disaggregate data 169

discrete choice 168

discriminal process 151

discriminant function 104, 107

distances 194

distribution

beta hat 64

chi square 41

F 45

multivariate normal 40

Student's t 43

distribution function 37

distribution function, normal 39

distributive property of scalar multiplication 5

dot product 6

dummy coding 78

Dunn-Bonferroni 86, 99

effect coding 77

efficiency 170

eigenstructure 24, 91, 137

eigenvalue 26

eigenvector 26

eigenvectors

left 92

right 92

elasticity 184, 220

endogenous variables 124

equimax 143

error term 84

error transform 74

error, specification 111, 124

error-in-equations 111

errors-in-equations 124

errors-in-variables 111

estimation 30, 48, 52, 153

estimator 93

euclidean distance 193

exogenous variables 124

expectation 36

expectation of a random variable 36

exponential distribution 214

exponents 20

external unfolding 201

extraction

factor 140

F distribution 45, 69

factor

rotation 140

factor extraction 140

factor loadings 111

factor structure 143

factors 110

false alarm 160

false alarm rate 162

FAR 160, 162

Fechner’s law 146

full information maximum likelihood 225

full rank 28

fully extended model 183

fundamental theorem of market share 181, 182

Fundamental theorem of market share 185

Gauss-Markov assumption 52, 230

generalized least squares 72, 175

generalized Minkowski metric 195

generic variable 182

GFI 120

global minimum 32, 117

GLS 72, 175, 177, 182, 239

goodness of fit 120

goodness of fit index 120

group space 196

Hessian 33

heterogeneity 206

heteroskedasticity 170, 171

hit 160

hit rate 162

Hotelling-Lawleys trace 98

HR 160, 162

hypotheses 66, 67, 68

ideal point model 199

idempotency 74

identity element of matrix addition 6

identity element of matrix multiplication 11

identity matrix 5

IIA 185

income type variable 168, 181

index, goodness of fit 120

INDSCAL 196, 201

information matrix 34

initial state vector 209

inner product 6

instrumental variables 227

interaction 80

intercept-only 58

internal unfolding 201

inverse normal distribution function 153

inverse of a matrix 12, 13

isopreference contours 198, 200

JND 147

joint probability 205

joint space 199

just identified 129

just noticeable difference 147

Koyck's scheme 235

Kronecker product 90

Lagrange multiplier 25

latent variables 110

law of categorical judgment 157

Law of comparative judgment 150

law of total probability 210

learning models 211

least squares 49

least squares regression 48

left eigenvectors 92

length of a vector 7

levels of variables 55

likelihood 208

linear algebra 2

linear combination 6

linearization 173

ln 20

loadings 111

local minimum 32, 117

log 20

logarithms 20

Logarithms 20

logically inconsistent 170

logistic regression 171

logit 171, 173

logit (2 156

logit model 168

logit, conditional 168

logit, polytomous 168

loss function 49

MA(q) 245

Mahalanobis distance 106

manifest variables 111

MANOVA 101

marginal probability 205

marketing instrument 183

markov chains 209

matrices 15

partitioned 8

matrix 2

cross-product 9

determinant 11

inverse 12, 13

multiplication 10

trace 11, 89

matrix addition 4

matrix addition, associative property 6

matrix addition, commutative property 6

matrix addition, identity element 6

matrix algebra 3

matrix conditional 195

matrix multiplication 7

matrix multiplication, identity element 11

matrix notation 2

matrix subtraction 5

matrix transposition 3

matrix, diagonal 5

matrix, identity 5

matrix, null 5

matrix, postmultiplying 7

matrix, premultiplication 7

matrix, rank 28, 137

matrix, scalar 5

matrix, unit 5

matrix, variance-covariance 17

maximum likelihood 32, 156

Maximum Likelihood 32

MCI 183

MDS 192

mean See

mean vector 15

measures, commensurate 83

method of moments 214

metric 194

minimum Pearson (2 154, 177

minimum, local 117

mispecified model 111

miss 160

mixing distribution 204

MNL 180

MNL model 180, 182

MNL, simple effects 183

modes 195

modification index 121

modified minimum (2 156, 177

moving average 245

moving average (q) process 245

multidimensional scaling 192

multi-method multi-trait 118

multinomal logit model 180

multiplication, vector 6

multiplicative competitive interaction 183

multivariate normal distribution 40

n-afc procedure 163

NBD 213

negative binomial 215

negative binomial distribution 213

nesting 84

NIID 52

non-linear optimization 31

nonmetric MDS 192

non-recursive 130

nonrecursive systems 224

normal distribution 37

normal distribution function 39

normal equations 50

null matrix 5

of commensurate variables 83

off-diagonal 5

ogive 39, 172

one-way analysis of variance 76

operator, error See error transform

operator, expectation 36

operator, prediction See prediction transform

operator, variance 37

optimal scaling 191

order of a matrix 2

ordinary least squares 48

orthogonal 6

orthogonal coding 79

orthonormal 29

outer product 8

paired comparisons. 151

parallel tests 118

parameter estimation 30, 32

partial autocorrelations 255

partial derivative 22

partitioned matrices 8

part-worths 192

perception 195

perceptual space 193

Pillai's trace 98

Plim 51

polychoric correlation 159

polytomous dependent variable 168

posterior probability 208

postmultiplying matrix 7

prediction transform 74

preference vector 198

premultiplying matrix 7

price elasticity of market share 184

price type variable 168, 182

pricing 222

principal axis 25

prior distribution 208

prior probability 105

probability

law of total 210

probit 171

probit model 171, 186

projections 198

proximity judgments 193

purchase incidence 213

quadratic equation 27

quadratic form 8

qualitative independent variables 76

quantitative independent variables 82

quartimax 143

rank of a matrix 137

rank of a square matrix 28

rank, full 28

ratings procedure 161

rational consumer 168

raw cross products matrix 16

receiver operating characteristic 162

recursive system 130

reduced form 125

regression 48

repeated measures 83, 101

response bias 159

right eigenvectors 92

rigid transformation 30

ROC 162, 163

root mean square error 121

rotation 140

row vector See vector

Roy's largest root 98

RUM 168

scalar 2

scalar derivative 20

scalar function of a vector 22

scalar matrix 5

scalar multiplication 4

scalar multiplication, distributive property 5

scalar multiplication,associative property 4

scalar product 6

scaling, optimal 191

scree chart 138

seasonality 255

second order

derivative 23

second order derivative 23

seemingly unrelated regression 238

setting a metric 114

Shepard diagram 191

similarity judgment 195

similarity judgments 193

simple effects MNL 183

simple effects model 182

simple structure 142

singular value decomposition 92

SMC 70

specification error 111

specification errors 124

spike 248

square matrix 3

squared multiple correlation 70

SS predictable 54

SS Total 54

SSCP matrix 16

SSCP matrix, corrected 16

SSCP, raw 16

SSE 54

SSErro 54

standard deviation 14

standardized scores 14

starting values 31

stationarity 242

stationary 204

stress 191, 193

Student's t-statistic 43

subscript reduction operator 3

sum constrained 170

sum of square and cross products, corrected 16

sum of squares 14

sum of squares and cross products 93

sum of squares and cross products, raw 16

sum of squares and cross products, uncorrected 16

sum of squares error 54

sum of squares predictable 54

sum of squares total 54

sums of squares 54

superior-inferior model 211

supremum metric 195

symmetric matrix 4

t distribution 43

theory of signal detectability 159, 164

three way data 195

Thurstone model 171, 182

Thurstone’s law 168

trace of a matrix 11, 89

transformation, angle-preserving 30

transformation, rigid 30

transition matrix 206, 209, 211

transpose operator 2

transpose, derivative 23

treatments 76

triangle inequality 195

t-statistic 43

two way data 195

type I error 67

uncorrected SSCP 16

uncorrected sum of squares and cross products 16

unfolding 200

unfolding, external 201

unfolding, internal 201

union-intersection 99

union-Intersection 88

unique factors 111

unit matrix 5

univariate statistics 14

universal logit model 183

unobserved variables 110

unweighted least squares 173

utilities 151, 192

utility 168

variables, commensurate 83

variance 14

variance matrix 17

variance operator 37

variance-covariance matrix 17

variances 36

variety-seeking model 211

varimax procedure 142

vec 91

vector 2

scalar function of a 22

vector derivative 23

vector model 197

vector multiplication 6

vector notation 2

vector outer product 8

vector, length 7

weighted euclidean model 196

weighted least squares 72, 173

weighted nonlinear least squares 154, 155

white noise 231, 243

Wilk's lambda 98

WLS 72

yes/no task 159

Yule-Walker equations 253

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