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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