Dr. Heiko Großmann
Dr. Heiko Großmann
Institute for Mathematical Stochastics (IMST)
Current projects
Optimal Design for Thurstonian IRT Models
Duration: 01.10.2024 bis 30.09.2027
The main aim of the present project is the development of optimal designs for Thurstonian IRT modes in the case of metric, binary, or ordinal responses which provide a sufficiently good estimation of the trait scores. In addition, binary paired comparisons will be considered which are derived from ranking more than two alternatives. In the present situation, optimal designs are characterized by combinations of those values of item parameters, factor loadings and intercepts which optimize prior determined criteria, as correlation between estimated and true trait scores. In order to apply these models in the selection of personnel, only positive factor loadings are admitted. This condition is supported by simulation studies and requires the development of novel types of optimal designs. Beyond properties of optimal designs developed in the literature so far, three more requirements have to be particularly taken into account: (a) the specific form of the non-linearity, (b) the restriction of the design region, and © the constraint that alternatives have to load on mutually distinct factors, respectively. To implement the findings of the project in practical applications, a user-friendly program in R is to be developed using a shiny app.
Completed projects
Explaining osteoarthritis: development and implementation of a multimedia Patient Explanation Package (PEP-OA)
Duration: 01.04.2019 bis 31.03.2021
Grant number: NIHRDH-PB-PG-0817-20031. Osteoarthritis (OA) is a common, debilitating and painful condition, particularly when patients move the affected joint. Core-management approaches (exercise and weight control) reduce pain and improve function, but exercise-induced pain creates anxiety and confusion about such self-management. Common, unhelpful, misconceptions about OA exist and currently professionals do not have the language to explain OA in a way that reflects current scientific understanding. The overarching aim of the project is to improve OA explanations through the development and implementation of a multimedia Patient Explanation Package (PEP-OA). A partial-profile conjoint analysis study with patients will estimate the extent to which new, prioritised, explanation statements are preferred over currently used/available statements. Suitable OA explanations identified in this study will be used in the further development of the multimedia package. The corresponding work package requires the development of an efficient experimental design for the choice experiment which will be carried out at the University of Magdeburg.
Funktionale Datenanalyse von Ganganalyse-Daten
Duration: 06.01.2014 bis 06.01.2018
Bestimmte neurologische Erkrankungen beeinträchtigen die Gehfähigkeit der betroffenen Individuen. In diesem Projekt werden Verfahren der funktionalen Datenanalyse entwickelt, um Daten zu analysieren, die mit Hilfe bildgebender Verfahren in einem Ganglabor bei Kindern und Jugendlichen erhoben werden. Im angewandten Teil des Projekts wird unter anderem untersucht, wie sich bestimmte medizinische Hilfsmittel (Orthesen) auf das Gehverhalten auswirken.
A Small-Sample Randomization Based Approach to Semi-Parametric Estimation and Misspecification in Generalized Linear Mixed Models
Duration: 01.11.2012 bis 01.11.2016
Verallgemeinerte lineare Modelle mit festen und zufälligen Effekten bieten eine elegante Möglichkeit zur Modellierung abhängiger Beobachtungen. Bei der Schätzung der Modellparameter wird in der Regel angenommen, dass die zufälligen Parameter eine multivariate Normalverteilung besitzen. In diesem Projekt wird ein alternativer und speziell für kleine Stichprobenumfänge geeigneter Ansatz betrachtet, bei dem zwar, wie üblich, die bedingte Verteilung der abhängigen Variable bei gegebenen Werten der zufälligen Parameter zur Exponentialfamilie gehört, die Verteilung der zufälligen Effekte jedoch aus Randomisierungsüberlegungen abgeleitet ist. Für das sich ergebende semiparametrische Modell wird ein Schätzalgorithmus entwickelt. Weiterhin wird in Simulationsstudien numerisch untersucht, wie sich Verletzungen der Normalverteilungsannahme auf die Schätzungen auswirken.
2021
Peer-reviewed journal article
Optimal design for probit choice models with dependent utilities
Graßhoff, Ulrike; Großmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Statistics - London [u.a.] : Taylor & Francis, Bd. 55 (2021), Heft 1, S. 173-194
Partially orthogonal blocked three-level response surface designs
Großmann, Heiko; Gilmour, Steven G.
In: Econometrics and statistics - Amsterdam [u.a.] : Elsevier B.V . - 2021
2020
Peer-reviewed journal article
Enhanced normograms and pregnancy outcome analysis in nonhuman primate developmental toxicity studies
Großmann, Heiko; Weinbauer, Gerhard F.; Baker, Ann; Fuchs, Antje; Luetjens, C. Marc
In: Reproductive toxicology - Amsterdam [u.a.]: Elsevier Science, Bd. 95.2020, S. 29-36
On the meaning of block effects in paired comparison choice experimentsand a relationship with blocked 2(K) main effects plans
Großmann, Heiko
In: Journal of statistical planning and inference: JSPI - Amsterdam: North-Holland Publ. Co., Bd. 209.2020, S. 76-84
Non-peer-reviewed journal article
Optimal design for probit choice models with dependent utilities
Graßhoff, Ulrike; Großmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: De.arxiv.org - [S.l.]: Arxiv.org, 2020, article 2001.09036, insgesamt 26 Seiten
2018
Peer-reviewed journal article
A practical approach to designing partial-profile choice experiments with two alternatives for estimating main effects and interactions of many two-level attributes
Großmann, Heiko
In: Journal of choice modelling - Amsterdam ˜[u.a.]œ: Elsevier, 2008 . - 2018[Online first]
2017
Peer-reviewed journal article
Testing gait with ankle-foot orthoses in children with cerebral palsy by using functional mixed-effects analysis of variance
Zhang, Bairu; Twycross-Lewis, Richard; Großmann, Heiko; Morrissey, Dylan
In: Scientific reports - [London]: Macmillan Publishers Limited, part of Springer Nature, Vol. 7.2017, Art. 11081, insgesamt 12 S.
2016
Book chapter
Functional data analysis in designed experiments
Zhang, Bairu; Großmann, Heiko
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[Kongress: 11th International Workshop in Model-Oriented Design and Analysis, Hamminkeln, Germany, June 12-17, 2016]
Peer-reviewed journal article
Partial-profile choice designs for estimating main effects and interactions of two-level attributes from paired comparison data
Großmann, Heiko
In: Journal of statistical theory and practice - Cham: Springer International Publishing, Bd. 11.2016, 2, S. 236-253
2015
Book chapter
Design for discrete choice experiments
Grossmann, Heiko; Schwabe, Rainer
In: Handbook of design and analysis of experiments - Boca Raton: CRC Press, a Chapman & Hall book . - 2015, S. 787-832 - (CRC Handbooks of Modern Statistical Methods; 7)
Peer-reviewed journal article
Automating the analysis of variance of orthogonal designs
Großmann, Heiko
In: Computational statistics & data analysis - Amsterdam: Elsevier Science, Bd. 70 (2014), S. 1-18
Non-peer-reviewed journal article
Partial-profile choise designs for estimating main and interaction effects of two-level attributes from paired comparison data
Großmann, Heiko
In: Magdeburg: Univ., Fak. für Mathematik, 2015, 24 S. - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2015,15)
2014
Peer-reviewed journal article
A catalogue of designs for partial profiles in paired comparison experiments with three groups of factors
Großmann, Heiko; Graßhoff, Ulrike; Schwabe, Rainer
In: Statistics. - London [u.a.] : Taylor & Francis, Bd. 48.2014, 6, S. 1268-1281
2013
Peer-reviewed journal article
Optimal design for discrete choice experiments
Graßhoff, Ulrike; Großmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Journal of statistical planning and inference. - Amsterdam : North-Holland Publ. Co, Bd. 143.2013, 1, S. 167-175
2012
Original article in peer-reviewed international journal
Designs for first-order interactions in paired comparison experiments with two-level factors
Großmann, Heiko; Schwabe, Rainer; Gilmour, Steven G.
In: Journal of statistical planning and inference. - Amsterdam : Elsevier, Bd. 142.2012, 8, S. 2395-2401
2010
Peer-reviewed journal article
Personality in bumblebees - individual consistency in responses to novel colours?
Muller, Helene; Großmann, Heiko; Chittka, Lars
In: Animal behaviour - Amsterdam [u.a.] : Elsevier, Bd. 80.2016, 6, S. 1065-1074
2009
Original article in peer-reviewed international journal
Approximate and exact optimal designs for paired comparisons of partial profiles when there are two groups of factors
Großmann, Heiko; Graßhoff, Ulrike; Schwabe, Rainer
In: Journal of statistical planning and inference . - Amsterdam : Elsevier, Bd. 139.2009, 3, S. 1171-1179
Original article in peer-reviewed periodical-type series
Some new design for first-order interactions in 2[K] paired comparison experiments
Großmann, Heiko; Schwabe, Rainer; Gilmour, Steven G.
In: 6th St. Petersburg Workshop on Simulation; 1: . - St. Petersburg : VVM com. Ltd., ISBN 978-5-9651035-4-6, S. 394-399, 2009Kongress: St. Petersburg Workshop on Simulation; 6 (St. Petersburg) : 2009.06.28-07.04
2007
Book chapter
A conjoint measurement based rationale for inducing preferences
Großmann, Heiko; Brocke, Michaela; Holling, Heinz
In: Uncertainty and Risk - Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg ; Abdellaoui, Mohammed . - 2007, S. 243-260 - (Theory and Decision Library C, Series C: Game Theory, Mathematical Programming and Operations Research; 41)
Original article in peer-reviewed international journal
Design optimality in multi-factor generalized linear models in the presence of an unrestricted quantitative factor
Graßhoff, Ulrike; Großmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Journal of statistical planning and inference - Amsterdam : Elsevier, Bd. 137 (2007), Heft 12, S. 3882-3893
Original article in peer-reviewed periodical-type series
A comparison of efficient designs for choices between two options
Großmann, Heiko; Holling, Heinz; Graßhoff, Ulrike; Schwabe, Rainer
In: mODa 8 - advances in model-oriented design and analysis - Heidelberg [u.a.] : Physica-Verl. , 2007, S. 83-90 - (Contributions to Statistics)
A comparison of efficient designs for choices between two options
Großmann, Heiko; Holling, Heinz; Graßhoff, Ulrike; Schwabe, Rainer
In: mODa 8 - Advances in model oriented design and analysis - Heidelberg [u.a.] : Physica-Verl. , 2007, S. 83-90 - (Contributions to Statistics)
2006
Original article in peer-reviewed international journal
Optimal designs for asymmetric linear paired comparisons with a profile strength constraint
Großmann, Heiko; Holling, Heinz; Graßhoff, Ulrike; Schwabe, Rainer
In: Metrika . - Berlin : Springer, Bd. 64.2006, 1, S. 109-119; Abstract
2005
Book chapter
On the empirical relevance of optimal designs for the measurement of preferences.
Grossmann, Heiko; Holling, Heinz; Brocke, Michaela; Grasshoff, Ulrike; Schwabe, Rainer
In: Berger, Martijn P. F. (Hrsg.) ; Wong, Weng Kee (Hrsg.): Applications of optimal designs. Hoboken, NJ : Wiley, 2005, S. 45 - 65
Utility balance and design optimality in logistic models with one unrestricted quantitative factor.
Schwabe, Rainer; Grasshoff, Ulrike; Grossmann, Heiko; Holling, Heinz
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
Original article in peer-reviewed international journal
Optimal designs for main effects in linear paired comparison models.
Grasshoff, Ulrike; Grossmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Journal of statistical planning and inference [Amsterdam] 126(2004), S. 361 - 376
2003
Original article in peer-reviewed international journal
Optimal paired comparison design for first-order interactions.
Grasshoff, Ulrike; Grossmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Statistics [Basingstoke] 37(2003), Nr. 5, S. 373 - 386
Original article in peer-reviewed periodical-type series
Optimal 2(K) paired comparison designs for partial profiles.
Schwabe, Rainer; Grasshoff, Ulrike; Grossmann, Heiko; Holling, Heinz
In: Tatra mountains mathematical publications [Bratislava] 26(2003), S. 79 - 86
2002
Original article in peer-reviewed periodical-type series
Advances in optimum experimental design for conjoint analysis and discrete choice models.
Grossmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Franses, P. H. (Hrsg.) ; Montgomery, A. L. (Hrsg.): Econometric models in marketing. Amsterdam : JAI, 2002, S. 93 - 117 (Advances in econometrics 16)
Sommer Semester 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
Winter Semester 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.
Sommer Semester 2017
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.
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.
Vorträge zu Forschungs- und Abschlussarbeiten.
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
| Parameters | Parameters | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Design | K | K1 | K2 | u1 | u2 | S | Pairs | Design | K | K1 | K2 | u1 | u2 | S | Pairs |
| 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 | 4 | 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
- Example: Design PP01
- 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 1 Option 2 Pair A B C D A B C D 1 1 1 * * 2 2 * * 2 1 2 * * 2 1 * *
- Example: Design PP02
- 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
- Example: Design PP02
- 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 giveOption 1 Option 2 Pair A B C D A B C D 1 1 1 1 3 2 2 1 3 2 1 2 2 1 2 1 2 1
- Example: Design PP02
- A * indicates that the level of an attribute is the same for both options in a pair
- 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
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 1 Option 2 Pair A B C D A B C D 1 1 1 1 * 2 2 2 * 2 1 2 2 * 2 3 3 *
Option 1 Option 2 Pair A B C D A B C D 1 2 2 2 * 1 1 1 * 2 1 2 2 * 2 3 3 *
- Example: Design PP01
- 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.