Maximum Principle for Survey Data Analysis

• realiabilityrealiability• tuning parametertuning parameter• the principlethe principle• theoretical aspectstheoretical aspects• practical recommendationspractical recommendations• illustrationillustration

Food preferences investigationFood preferences investigation

TableTable 1 1 DairyDairy GrainGrain GreeneryGreenery FishFish MeatMeat TotalTotal

Respond. nr.1Respond. nr.1 XX XX 22

Respond. nr.2Respond. nr.2 XX XX XX XX 44

Respond. nr.3Respond. nr.3 XX XX 22

Respond. nr.4Respond. nr.4 XX XX XX XX 44

Respond. nr.5Respond. nr.5 XX XX 22

Respond nr. 6Respond nr. 6 XX XX XX XX XX 55

Respond. nr.7Respond. nr.7 XX XX 22

TotalTotal 33 55 55 55 33 2121

%% 43%43% 71%71% 71%71% 71%71% 43%43%

Food Food preferencespreferences investigation investigation

TableTable 2 2 DairyDairy GrainGrain GreeneryGreenery FishFish MeatMeat TotalTotal

Respond. nr.2Respond. nr.2 XX XX XX XX 44

Respond. nr.4Respond. nr.4 XX XX XX XX 44

Respond nr. 6Respond nr. 6 XX XX XX XX XX 55

TotalTotal 33 33 11 33 33 1313

TableTable 3 3 DairyDairy GrainGrain FishFish MeatMeat TotalTotal

Respond. nr.2Respond. nr.2 XX XX XX XX 44

Respond. nr.4Respond. nr.4 XX XX XX XX 44

Respond nr. 6Respond nr. 6 XX XX XX XX 44

TotalTotal 33 33 33 33 1313

Some theoretical aspectsSome theoretical aspects For some time I'm working on a problem of sampling a set of KFor some time I'm working on a problem of sampling a set of Kobservations (cases) from a large data set with N >> K cases so thatobservations (cases) from a large data set with N >> K cases so thatthe selected observations are as "different as possible". In morethe selected observations are as "different as possible". In moremathematical terms, I'm interested in locating those K cases whichmathematical terms, I'm interested in locating those K cases whichwill result in a (not necessarily Euclidean) distance matrix in whichwill result in a (not necessarily Euclidean) distance matrix in whichthe smallest off-diagonal entry d_ij is as large as possible.the smallest off-diagonal entry d_ij is as large as possible. I have developed an algorithm which seems to work very well and I have developed an algorithm which seems to work very well andgenerates sets which are either optimal or close to optimality withoutgenerates sets which are either optimal or close to optimality withoutcomputing the entire distance matrix. However, I'm thinking morecomputing the entire distance matrix. However, I'm thinking moreand more that this maybe a known problem to people who work inand more that this maybe a known problem to people who work inCluster Analysis, MDS, or classification. I wonder if anybody onCluster Analysis, MDS, or classification. I wonder if anybody onthis list could point me to some references about this searchthis list could point me to some references about this searchproblem.problem.

Thanks, Wolfgang HartmannThanks, Wolfgang Hartmann

Some theoretical aspectsSome theoretical aspects

In order to find a reliable component In order to find a reliable component K,K, it seems tautological that following it seems tautological that following our maximum principle, we have to solve maximization problem:our maximum principle, we have to solve maximization problem:

K = argmaxK = argmax(x,y)(x,y)FFkk(H)(H)

Positive / NegativePositive / Negative

Indifferent

Excellent Very good Bad Very bad

00 100100

Positive / NegativePositive / Negative

Negative/Positive Scale in the Questionnaire Negative/Positive Scale in the Questionnaire

Negative/Positive Scale in the QuestionnaireNegative/Positive Scale in the Questionnaire

Negative/Positive Scale in the QuestionnaireNegative/Positive Scale in the Questionnaire

Negative/Positive Scale in the QuestionnaireNegative/Positive Scale in the Questionnaire

Respondent 00 A0100038 actualRespondent 00 A0100038 actual

Respondent 00 A0100038 prognosesRespondent 00 A0100038 prognoses

Daglig stress - belastningsreaktioner

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A/B type menneskets adfærd

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Salg

Kostvaner - Motionsvaner - Alkhogol - Kulilte

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Undersøgelse nr. 1

Undersøgelse nr. 2

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P(t)

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Virksomhed A

t = 2,7°

Sundheds-feber for virksomhed ASundheds-feber for virksomhed A

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P(t)

Temperature

Virksomhed B

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Sundheds-feber for virksomhed BSundheds-feber for virksomhed B