Dr. Heiko Großmann

Dr. Heiko Großmann

Fakultät für Mathematik (FMA)
Institut für Mathematische Stochastik (IMST)
Universitätsplatz 2, 39106, Magdeburg, G18-405
Projekte
Publikationen

2017

Begutachteter Zeitschriftenartikel

Zhang, Bairu;  Twycross-Lewis, Richard;  Großmann, Heiko;  Morrissey, Dylan 

Testing gait with ankle-foot orthoses in children with cerebral palsy by using functional mixed-effects analysis of variance
In: Scientific reports - [London]: Macmillan Publishers Limited, part of Springer Nature, Vol. 7.2017, Art. 11081, insgesamt 12 S.; http://dx.doi.org/10.1038/s41598-017-11282-1

2016

Begutachteter Zeitschriftenartikel

Großmann, Heiko 

Partial-profile choice designs for estimating main effects and interactions of two-level attributes from paired comparison data
In: Journal of statistical theory and practice - London [u.a.]: Taylor & Francis, Bd. 11.2016, 2, S. 236-253; http://dx.doi.org/10.1080/15598608.2016.1197868

Buchbeitrag

Zhang, Bairu;  Großmann, Heiko 

Functional data analysis in designed experiments
In: mODa 11 - advances in model-oriented design and analysis : proceedings of the 11th International Workshop in Model-Oriented Design and Analysis held in Hamminkeln, Germany, June 12-17, 2016. - Switzerland : Springer, S. 235-242

2015

Begutachteter Zeitschriftenartikel

Großmann, Heiko 

Automating the analysis of variance of orthogonal designs
In: Computational statistics & data analysis. - Amsterdam : Elsevier Science, Bd. 70.2014, S. 1-18

Buchbeitrag

Grossmann, Heiko;  Schwabe, Rainer 

Design for discrete choice experiments
In: Dean, Angela: : Handbook of design and analysis of experiments. - Hoboken : CRC Press, S. 787-832, 2015 - (CRC Handbooks of Modern Statistical Methods; 7)

Nicht begutachteter Zeitschriftenartikel

Großmann, Heiko 

Partial-profile choise designs for estimating main and interaction effects of two-level attributes from paired comparison data
In: Magdeburg: Univ., Fak. für Mathematik, 2015; 24 S. - (Preprint / Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2015,15)

2014

Begutachteter Zeitschriftenartikel

Großmann, Heiko;  Graßhoff, Ulrike;  Schwabe, Rainer 

A catalogue of designs for partial profiles in paired comparison experiments with three groups of factors
In: Statistics. - London [u.a.] : Taylor & Francis, Bd. 48.2014, 6, S. 1268-1281

2013

Begutachteter Zeitschriftenartikel

Graßhoff, Ulrike;  Großmann, Heiko;  Holling, Heinz;  Schwabe, Rainer 

Optimal design for discrete choice experiments
In: Journal of statistical planning and inference. - Amsterdam : North-Holland Publ. Co, Bd. 143.2013, 1, S. 167-175

2012

Originalartikel in begutachteter internationaler Zeitschrift

Großmann, Heiko;  Schwabe, Rainer;  Gilmour, Steven G. 

Designs for first-order interactions in paired comparison experiments with two-level factors
In: Journal of statistical planning and inference. - Amsterdam : Elsevier, Bd. 142.2012, 8, S. 2395-2401

2010

Begutachteter Zeitschriftenartikel

Muller, Helene;  Großmann, Heiko;  Chittka, Lars 

Personality in bumblebees - individual consistency in responses to novel colours?
In: Animal behaviour. - Amsterdam [u.a.] : Elsevier, Bd. 80.2016, 6, S. 1065-1074, 2010

2009

Originalartikel in begutachteter internationaler Zeitschrift

Großmann, Heiko;  Graßhoff, Ulrike;  Schwabe, Rainer 

Approximate and exact optimal designs for paired comparisons of partial profiles when there are two groups of factors
In: Journal of statistical planning and inference . - Amsterdam : Elsevier, Bd. 139.2009, 3, S. 1171-1179

Originalartikel in begutachteter zeitschriftenartiger Reihe

Großmann, Heiko;  Schwabe, Rainer;  Gilmour, Steven G. 

Some new design for first-order interactions in 2[K] paired comparison experiments
In: 6th St. Petersburg Workshop on Simulation; 1: . - St. Petersburg : VVM com. Ltd., ISBN 978-5-9651035-4-6, S. 394-399, 2009 ; Kongress: St. Petersburg Workshop on Simulation; 6 (St. Petersburg) : 2009.06.28-07.04

2007

Buchbeitrag

Großmann, Heiko;  Brocke, Michaela;  Holling, Heinz 

A conjoint measurement based rationale for inducing preferences
In: Abdellaoui, Mohammed: : Uncertainty and Risk : Mental, Formal, Experimental Representations. - Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, S. 243-260, 2007 - (Theory and Decision Library C, Series C: Game Theory, Mathematical Programming and Operations Research; 41)

Originalartikel in begutachteter internationaler Zeitschrift

Graßhoff, Ulrike;  Großmann, Heiko;  Holling, Heinz;  Schwabe, Rainer 

Design optimality in multi-factor generalized linear models in the presence of an unrestricted quantitative factor
In: Journal of statistical planning and inference . - Amsterdam : Elsevier, Bd. 137.2007, 12, S. 3882-3893

Originalartikel in begutachteter zeitschriftenartiger Reihe

Großmann, Heiko;  Holling, Heinz;  Graßhoff, Ulrike;  Schwabe, Rainer 

A comparison of efficient designs for choices between two options
In: mODa 8 - Advances in model oriented design and analysis . - Heidelberg [u.a.] : Physica-Verl., ISBN 3-7908-1951-4, S. 83-90; Contributions to Statistics, 2007

2006

Originalartikel in begutachteter internationaler Zeitschrift

Großmann, Heiko;  Holling, Heinz;  Graßhoff, Ulrike;  Schwabe, Rainer 

Optimal designs for asymmetric linear paired comparisons with a profile strength constraint
In: Metrika . - Berlin : Springer, Bd. 64.2006, 1, S. 109-119; Abstract unter URL: http://springerlink.metapress.com/(4nyazl45wbmk2g554f4v2j55)/app/home/contribution.asp?referrer=parent&backto=issue,8,12;journal,2,67;linkingpublicationresults,1:102509,1

2005

Buchbeitrag

Grossmann, Heiko (ext.);  Holling, Heinz (ext.);  Brocke, Michaela (ext.);  Grasshoff, Ulrike;  Schwabe, Rainer 

On the empirical relevance of optimal designs for the measurement of preferences.
In: Berger, Martijn P. F. (Hrsg.) ; Wong, Weng Kee (Hrsg.): Applications of optimal designs. Hoboken, NJ : Wiley, 2005, S. 45 - 65

Schwabe, Rainer;  Grasshoff, Ulrike;  Grossmann, Heiko (ext.);  Holling, Heinz (ext.) 

Utility balance and design optimality in logistic models with one unrestricted quantitative factor.
In: Ermakov, S. M. (Hrsg.) ; Melas, V. B. (Hrsg.) ; Pepelyshev, A. N. (Hrsg.): Simulation 2005 (5th Workshop St. Petersburg, Russia June 26 - July 2, 2005). - proceedings. St. Petersburg : Univ., 2005, S. 605 - 610

2004

Originalartikel in begutachteter internationaler Zeitschrift

Grasshoff, Ulrike;  Grossmann, Heiko (ext.);  Holling, Heinz (ext.);  Schwabe, Rainer 

Optimal designs for main effects in linear paired comparison models.
In: Journal of statistical planning and inference [Amsterdam] 126(2004), S. 361 - 376

2003

Originalartikel in begutachteter internationaler Zeitschrift

Grasshoff, Ulrike;  Grossmann, Heiko (ext.);  Holling, Heinz (ext.);  Schwabe, Rainer 

Optimal paired comparison design for first-order interactions.
In: Statistics [Basingstoke] 37(2003), Nr. 5, S. 373 - 386

Originalartikel in begutachteter zeitschriftenartiger Reihe

Schwabe, Rainer;  Grasshoff, Ulrike;  Grossmann, Heiko (ext.);  Holling, Heinz (ext.) 

Optimal 2(K) paired comparison designs for partial profiles.
In: Tatra mountains mathematical publications [Bratislava] 26(2003), S. 79 - 86

2002

Originalartikel in begutachteter zeitschriftenartiger Reihe

Grossmann, Heiko (ext.);  Holling, Heinz (ext.);  Schwabe, Rainer 

Advances in optimum experimental design for conjoint analysis and discrete choice models.
In: Franses, P. H. (Hrsg.) ; Montgomery, A. L. (Hrsg.): Econometric models in marketing. Amsterdam : JAI, 2002, S. 93 - 117 (Advances in econometrics 16)

Lehrveranstaltungen

Sommersemester 2018

Design und Analyse von Experimenten: LSF

Introduction to Probability and Statistics: LSF Elearning

  • Introduction to Probability and Statistics (Tutorial): LSF

Oberseminar zur Stochastik: LSF

Wintersemester 2017/18

Explorative Datenanalyse und Wahrscheinlichkeit: LSF Elearning

In dieser Veranstaltung werden Grundlagen der beschreibenden (deskriptiven) Statistik und der Wahrscheinlichkeitsrechung behandelt.

Mathematische Statistik: LSF Elearning

Ausgehend von der statistischen Modellierung wird die Theorie grundlegender Konzepte der parametrischen Statistik entwickelt: Statistische Modelle, Schätztheorie, Konfidenzbereiche, Testtheorie.

Statistical Methods: LSF Elearning

Statistical Inference: - Statistical Modelling - Point estimation - Confidence intervals - Testing of statistical hypotheses (parametric tests) - Non-parametric tests (goodness of fit, independence, homogeneity)

Oberseminar zur Stochastik: LSF

Vorträge zu Forschungs- und Abschlussarbeiten.

Sommersemester 2017

Statistische Methoden

Grundlegende statistische Schätz- und Testverfahren bei normalverteilten Daten, einfache Varianzanalyse, Regressions- und Korrelationsanalyse, Anpassungstests, Tests auf Homogenität und Unabhängigkeit, nichtparametrische Verfahren, Methode der Kleinsten Quadrate, Maximum-Likelihood und Bayes-Verfahren, Mulitiples Testen und multiple Konfidenzbereiche.

Die verschiedenen Verfahren und Methoden werden anhand realer Datensätze aus Biologie, Medizin und Wirtschaft illustriert, die mit Hilfe von Statistik-Software unter Computer-Einsatz ausgewertet werden. Gegebenenfalls werden Daten selbst erhoben.

Seminar zur Stochastik

Die Teilnehmerinnen und Teilnehmer sollen ein Thema selbstständig bearbeiten und in einem Vortrag präsentieren.

Introduction to Probability and Statistics

Descriptive Statistics: data, graphical representation, measures of location and variability, empirical quantiles, measures of relationship for bivariate data. Basic Probability: discrete and continuous probability spaces, random variables, expectation and variance, quantiles, covariance and correlation, conditional probability, independence.

Aim: Fundamental understanding of concepts and basic properties, ability to interpret and communicate data.

Oberseminar zur Stochastik

Vorträge zu Forschungs- und Abschlussarbeiten.

Material

Bibliothek optimaler Designs

Sammlung optimaler Designs für gepaarte Vergleiche

Summary

This page provides optimal designs for paired comparisons of partial profiles for choice experiments and conjoint analysis (ACA like graded paired comparisons). It is assumed that the set of attributes used to describe options can be partitioned into two groups such that the attributes in each group have the same number of levels. The total number of attributes considered ranges from four to six. The common number of levels for attributes in the first group is between two and four and attributes in the second group can have up to five levels. The number of attributes on which the two options in a pair differ is either two or three. In order to be practical, only optimal designs with up to 100 paired comparisons are presented.

Construction methods are described in:
Großmann, H., Graßhoff, U. and Schwabe, R. (2009). Approximate and exact optimal designs for paired comparisons of partial profiles when there are two groups of factors. Journal of Statistical Planning and Inference 139, 1171-1179.

How to read the table

    • Design: Click on name to display design in a new window
    • Parameters
      • K: Total number of attributes used to describe options
      • K1: Number of attributes in the first group
      • K2: Number of attributes in the second group
      • u1: Common number of levels for all attributes in the first group
      • u2: Common number of levels for all attributes in the second group
      • S: The profile strength, that is, the number of attributes for which the two options in each pair have different levels
    • Pairs: The required number of paired comparisons or choice sets
Optimal designs
 Parameters  Parameters 
DesignKK1K2u1u2SPairsDesignKK1K2u1u2SPairs
PP01 4 1 3 2 3 3 42 PP26 5 3 2 3 4 3 96
PP02 4 2 2 2 3 2 18 PP27 5 4 1 2 3 2 36
PP03 4 2 2 2 3 3 12 PP28 5 4 1 2 3 3 24
PP04 4 2 2 2 4 2 16 PP29 5 4 1 2 4 2 28
PP05 4 2 2 2 4 3 24 PP30 5 4 1 2 4 3 24
PP06 2 2 2 5 2 50 PP31 5 4 1 2 5 2 40
PP07 4 2 2 2 5 3 40 PP32 5 4 1 2 5 3 40
PP08 4 2 2 3 4 2 60 PP33 6 2 4 2 3 2 30
PP09 4 2 2 3 5 2 90 PP34 6 2 4 2 4 2 28
PP10 4 3 1 2 3 2 30 PP35 6 2 4 2 5 2 90
PP11 4 3 1 2 3 3 36 PP36 6 2 4 3 4 2 96
PP12 4 3 1 2 4 2 12 PP37 6 3 3 2 3 2 54
PP13 4 3 1 2 4 3 72 PP38 6 3 3 2 3 3 36
PP14 4 3 1 2 5 2 60 PP39 6 3 3 2 4 2 48
PP15 4 3 1 3 4 2 54 PP40 6 3 3 2 4 3 32
PP16 5 1 4 2 3 3 36 PP41 6 3 3 2 5 3 100
PP17 5 2 3 2 3 2 24 PP42 6 4 2 2 3 2 24
PP18 5 2 3 2 3 3 96 PP43 6 4 2 2 3 3 32
PP19 5 2 3 2 4 2 44 PP44 6 4 2 2 4 2 20
PP20 5 2 3 2 5 2 70 PP45 6 4 2 2 4 3 80
PP21 5 3 2 2 3 2 42 PP46 6 4 2 2 5 2 60
PP22 5 3 2 2 3 3 28 PP47 6 4 2 2 5 3 40
PP23 5 3 2 2 4 2 18 PP48 6 4 2 3 4 2 84
PP24 5 3 2 2 4 3 24 PP49 6 5 1 2 4 2 80
PP25 5 3 2 3 4 2 72 PP50 6 5 1 2 5 2 90

 

Using the designs

    • The designs presume that only main effects (part-worth utilities) are to be estimated; they are not suitable for models with interactions
    • Attributes are labeled with capital letters: A, B, C,...
    • The first K1 attributes have u1 levels and the remaining K2 attributes have u2 levels. Levels are numbered 1, 2,...
      • Example: Design PP01
        Since K1=1, K2=3, u1=2 and u2=3, attribute A has 2 levels whereas attributes B, C and D have 3 levels each
    • Meaning of the star symbol (*)
      • A * indicates that the level of an attribute is the same for both options in a pair
        • Example: Design PP02
          The options in the first two pairs of the design have common levels for attributes C and D
           Option 1Option 2
          PairABCDABCD
          1 1 1 * * 2 2 * *
          2 1 2 * * 2 1 * *
      • In practice, common levels are often not shown when pairs are presented for evaluation
        • Example: Design PP02
          When the two pairs in the above table are presented, often only levels of attributes A and B are used
      • Alternatively, if the level of an attribute is a * for both options in a pair, this can be replaced with the same (arbitrarily chosen) level of the attribute.
        • Example: Design PP02
          Attributes C and D both have 3 levels. So in the above table in the first pair the * for C can be replaced with the level 1 and the * star for D with the level 3. In the second pair, the shared level for C could be 2 and the common level for D could be 1 to give
           Option 1Option 2
          PairABCDABCD
          1 1 1 1 3 2 2 1 3
          2 1 2 2 1 2 1 2 1
    • Randomization
      • The pairs should be presented in random order
      • Within each pair it should be decided at random which option is presented first.
        Similarly, if the two options in each pair are presented simultaneously on a computer screen, use a random mechanism to decide which one appears on the left respectively right side of the screen.
        • Example: Design PP01
          The first two pairs of the design in the table are
           Option 1Option 2
          PairABCDABCD
          1 1 1 1 * 2 2 2 *
          2 1 2 2 * 2 3 3 *
          A possible outcome of the randomization could be that in the first pair options 1 and 2 are swapped while in the second pair their order remains unchanged:
           Option 1Option 2
          PairABCDABCD
          1 2 2 2 * 1 1 1 *
          2 1 2 2 * 2 3 3 *
      • Designs remain optimal after randomizing pairs and options within pairs
      • Do not randomize attribute levels within options
    • The designs can be easily pasted into a text editor such as notepad, winedt etc.

Letzte Änderung: 16.04.2018 - Ansprechpartner:

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