Minimal average degree aberration and the state polytope for experimental designs

For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Groebner bases provide a systematic way of doing this. The algebraic method does not in general produce all estimable models but it can be shown that it yields models which have minimal average degree in a well-defined sense and in both a weighted and unweighted version. This provides an alternative measure to that based on "aberration" and moreover is applicable to any experimental design. A simple algorithm is given and bounds are derived for the criteria, which may be used to give asymptotic Nyquist-like estimability rates as model and sample sizes increase

Bridiging designs for conjoint analysis: The issue of attribute importance.

Abstract: Conjoint analysis studies involving many attributes and attribute levels often occur in practice. Because such studies can cause respondent fatigue and lack of cooperation, it is important to design data collection tasks that reduce those problems. Bridging designs, incorporating two or more task subsets with overlapping attributes, can presumably lower task difficulty in such cases. In this paper, we present results of a study examining the effects on predictive validity of bridging design decisions involving important or unimportant attributes as links (bridges) between card-sort tasks and the degree of balance and consistency in estimated attribute importance across tasks. We also propose a new symmetric procedure, Symbridge, to scale the bridged conjoint solutions.Studies; Cooperation; Data; Problems; Effects; Decisions;

Joint optimization of allocation and release policy decisions for surgical block time under uncertainty

The research presented in this dissertation contributes to the growing literature on applications of operations research methodology to healthcare problems through the development and analysis of mathematical models and simulation techniques to find practical solutions to fundamental problems facing nearly all hospitals. In practice, surgical block schedule allocation is usually determined regardless of the stochastic nature of case demand and duration. Once allocated, associated block time release policies, if utilized, are often simple rules that may be far from optimal. Although previous research has examined these decisions individually, our model considers them jointly. A multi-objective model that characterizes financial, temporal, and clinical measures is utilized within a simulation optimization framework. The model is also used to test “conventional wisdom” solutions and to identify improved practical approaches. Our result from scheduling multi-priority patients at the Stafford hospital highlights the importance of considering the joint optimization of block schedule and block release policy on quality of care and revenue, taking into account current resources and performance. The proposed model suggests a new approach for hospitals and OR managers to investigate the dynamic interaction of these decisions and to evaluate the impact of changes in the surgical schedule on operating room usage and patient waiting time, where patients have different sensitivities to waiting time. This study also investigated the performance of multiple scheduling policies under multi-priority patients. Experiments were conducted to assess their impacts on the waiting time of patients and hospital profit. Our results confirmed that our proposed threshold-based reserve policy has superior performance over common scheduling policies by preserving a specific amount of OR time for late-arriving, high priority demand

Archives of Data Science, Series A. Vol. 1,1: Special Issue: Selected Papers of the 3rd German-Polish Symposium on Data Analysis and Applications

The first volume of Archives of Data Science, Series A is a special issue of a selection of contributions which have been originally presented at the {\em 3rd Bilateral German-Polish Symposium on Data Analysis and Its Applications} (GPSDAA 2013). All selected papers fit into the emerging field of data science consisting of the mathematical sciences (computer science, mathematics, operations research, and statistics) and an application domain (e.g. marketing, biology, economics, engineering)

The Impact of Role Conceptualization on the Process and Outcomes of Decision Making in an Educational Context

Research has shown that the traditional conceptualization of Organizational Citizenship Behaviors (OCBs) is not tenable because some employees perceive OCBs to be part of their job or in-role behaviors (Morrison, 1994). Conceptualizing behaviors as in-role has been shown to increase the frequency of the behaviors but no study has investigated whether conceptualization of these behaviors influences the manner in which they are conducted. This study combined findings from OCB research with the Judgment and Decision Making literature in order to identify the impact that role conceptualization had on an ambiguous decision making exercise where the act of making the decision could have been considered an OCB. It was hypothesized that role conceptualization would influence the decision-making process used and outcomes associated with the decision. This influence was hypothesized to result in decisions that are more systematic if participants perceived the task as part of their job. Additionally, it was hypothesized that personal characteristics or work context would influence decisions and that effect would be moderated by role conceptualization. Results indicate that role conceptualization was not significantly related to the use of relevant student characteristics. Teachers who considered the decision-making task as an important part of their jobs were actually less consistent in their decisions to recommend college. Finally, while there was evidence that personal and work characteristics influenced the decision outcomes and processes, there was no support for the moderating effects of role conceptualization

Multivariat analyse som verktøy til forståelse og reduksjon av kompleksitet av matematiske modeller i systembiologi

In the area of systems biology, technologies develop very fast, which allows us to collect massive amounts of various data. The main interest of scientists is to receive an insight into the obtained data sets and discover their inherent properties. Since the data often are rather complex and intimidating equations may be required for modelling, data analysis can be quite challenging for the majority of bio-scientists who do not master advanced mathematics. In this thesis it is proposed to use multivariate statistical methods as a tool for understanding the properties of complex models used for describing biological systems. The methods of multivariate analysis employed in this thesis search for latent variables that form a basis of all processes in a system. This often reduces dimensions of the system and makes it easier to get the whole picture of what is going on. Thus, in this work, methods of multivariate analysis were used with a descriptive purpose in Papers I and IV to discover effects of input variables on a response. Often it is necessary to know a functional form that could have generated the collected data in order to study the behaviour of the system when one or another parameter is tuned. For this purpose, we propose the Direct Look-Up (DLU) approach that is claimed here to be a worthy alternative to the already existing fitting methods due to its high computational speed and ability to avoid many problems such as subjectivity, choice of initial values, local optima and so on (Papers II and III). Another aspect covered in this thesis is an interpretation of function parameters by the custom human language with the use of multivariate analysis. This would enable mathematicians and bio-scientists to understand each other when describing the same object. It was accomplished here by using the concept of a metamodel and sensory analysis in Paper IV. In Paper I, a similar approach was used even though the main focus of the paper was slightly different. The original aim of the article was to show the advantages of the multi-way GEMANOVA analysis over the traditional ANOVA analysis for certain types of data. However, in addition, the relationship between human profiling of data samples and function parameters was discovered. In situations when funds for conducting experiments are limited and it is unrealizable to study all possible parameter combinations, it is necessary to have a smart way of choosing a few but most representative conditions for a particular system. In Paper V Multi-level Binary Replacement design (MBR) was developed as such, which can also be used for searching for a relevant parameter range. This new design method was applied here in Papers II and IV for selection of samples for further analyses.Teknologiutviklingen innenfor systembiologien er nå så rask at det gir mulighet til å samle svært store datamengder på kort tid og til relativ lav pris. Hovedinteressen til forskerne er typisk å få innsikt i dataene og deres iboende egenskaper. Siden data kan være ganske komplekse og ofte beskrives ved kompliserte, gjerne ikke-lineære, funksjoner, kan dataanalyse være ganske utfordrende for mange bioforskere som ikke behersker avansert matematikk. I dette arbeidet er det foreslått å bruke multivariat statistisk analyse for å komme nærmere en forståelse av egenskapene av kompliserte modeller som blir brukt for å beskrive biologiske systemer. De multivariate metodene som er benyttet i denne avhandlingen søker etter latente variabler som utgjør en lineær basis og tilnærming til de komplekse prosessene i et system. Dermed kan man oppnå en forenkling av systemet som er lettere å tolke. I dette arbeidet ble multivariate analysemetoder brukt i denne beskrivende hensikten i Artikler (Papers) I og IV til å oppdage effekter av funksjonsparametre på egenskapene til komplekse matematiske modeller. Ofte er det nødvendig å finne en matematisk funksjon som kunne ha generert de innsamlede dataene for å studere oppførselen av systemet. Med den hensikt foreslår vi en metode for modelltilpasning ved DLU-metoden (the Direct Look-Up) som her påstås å være et verdifullt alternativ til de eksisterende estimeringsmetodene på grunn av høy fart og evne til å unngå typiske problemer som for eksempel subjektivitet, valg av initialverdier, lokale optima, m.m (Artikler II og III). Et annet aspekt dekket i denne avhandlingen er bruken av multivariat analyse til å gi tolking av matematiske funksjonsparametre ved hjelp av et dagligdags vokabular. Dette kan gjøre det enklere for matematikere og bioforskere å forstå hverandre når de beskriver det samme objektet. Det var utført her ved å benytte ideen om en metamodell og sensorisk analyse i Artikkel IV. I Artikkel I var en lignende metode også brukt for å få sensoriske beskrivelser av bilder generert fra differensiallikninger. Hovedfokuset i Artikkel I var imidlertid et annet, nemlig å vise fordelen ved multi-way GEMANOVA-analyse fremfor den tradisjonelle ANOVA-analysen for visse datatyper. I denne artikkelen ble GEMANOVA brukt til å avdekke sammenhengen mellom kompliserte kombinasjoner av funksjonsparametrene og bildedeskriptorer. I situasjoner der ressurser til å utføre eksperimenter er begrenset og det er umulig å prøve ut alle kombinasjoner av parametre, er det behov for metoder som kan bestemme et fåtall av parameterinnstillinger som er mest mulig representative for et bestemt system. I Artikkel V ble derfor Multi-level Binary Replacement (MBR) design utviklet som en sådan, og den kan også brukes for å søke etter et relevant parameterrom for datasimuleringer. Den nye designmetoden ble anvendt i Artikler II og IV for utvelgelse av parameterverdier for videre analyser

Understanding student travel preferences in Mahikeng: A hybrid choice modelling approach within the theory of planned behaviour

University student mobility is not reflected in the National Learner Transport Policy although some formal operators make provisions for identifiable post-school learners. South African universities do not accommodate the majority of students and they tend to have scattered campuses and residences. Only a few (6/26) public universities have contracts with scheduled bus and shuttle services specifically for students. Literature reveals that the characteristics of university student mobility are distinct from the general population. A segment specific approach to redress the potentially problematic results of aggregation could guide the treatment and inclusion of post-matric mobility needs in the National Learner Transport Policy. Research Problem In the broader sense of university student mobility, the level of service preferences of students is unknown in South Africa, or poorly specified in order for appropriate services to be developed. This study presents evidence of behavioural heterogeneity in the context of university student travel behaviour. It fills a policy and research gap by exploring university student travel behaviour and making a unique contribution to stated choice literature and applications in Africa. Hypothesis Tested Two hypotheses are tested. First, students have unique compositions of behaviour influencing their intention to use bus and minibus taxi. Secondly, there are level of service (LOS) preference differences between students who have high, medium or low intent to use any public transport mode. Methodology In navigating toward these hypotheses, the Theory of Planned Behaviour is used to theoretically reflect student behavioural inclinations toward bus and minibus taxi services in Mahikeng. In order to represent the choices students make between two modes the Hybrid Choice Modelling framework is adopted and applied. Therefore the hypotheses mentioned above are tested by means of grouping student responses based on a certain level of intention to use a mode, namely: high (P), neutral (N) or low (Z). To supplement the intention construct, perceived control to use bus or minibus taxi is also used to group university student level of service preferences. Behaviour specific latent class choice models (LCCM) are developed to estimate the probability of a student choosing a specific level of service related to bus and minibus taxi. Utilities are estimated in the form of multinomial logit models that are group (class) specific. An unlabelled d-optimal survey is developed based on observation and literature. Distributed at the North West University’s Mahikeng site of delivery, the survey had 121 properly completed responses of 150 printed copies, only 81 surveys were used in the study. Results Three findings are made. The theory of planned behaviour ratings indicate that students are much more favourable to minibus taxi use than bus use. Behavioural latent classes for intention and perceived behavioural control are distinct from the base model. The latent variable model reveals that students are willing to pay to avoid using bus and maintaining their current dispositions towards it. The relationship between intention and perceived behavioural control in the public transport context implies that control over a behaviour is a prerequisite to intention. Through this argument, three behavioural segments that are consistent with literature and theory were identified: choice users (neutral intention and high control), captive users(low control and low intention), and public transport lifestyle users (high intention and neutral control). Further research is needed to validate these relationships. Conclusions and recommendations The study accepts both null hypotheses based on the findings that there are class specific level of service preferences, and the behavioural dispositions within these classes are unique. It is recommended that the Learner Transport Policy be expanded to include university student mobility, and that higher education institutions in SA need to manage student travel demand. The main limitations in this study is the insignificance of demographic variables, potentially due to the homogeneity of the sample