MSc (Statistics) / Department of Statistics / This study explores the use of exible link functions in discrete survival models through a simulation study and an application to the Swaziland Demographic and Health Survey (SDHS) data. The objective of the research study is to perform simulation exercises in order to compare the e ectiveness of di erent families of link functions and to construct a discrete multilevel survival model for age at rst marriage among women in Swaziland using a exible link function. The Pareto hazard model, Pregibon and Gosset families of link functions were considered in models with and without unobserved heterogeneity. The Pareto model where the family parameter is estimated from the data was found to outperform the other models, followed by the Pregibon and the Gosset family of link functions. The results from both simulation study and real data analysis of the SDHS data illustrated that, misspecication of the link function causes bias on the estimation of results. This demonstrates the importance of choosing the right link. The ndings of this study reveal that women who are highly educated, stay in the Manzini and Shiselweni region, those who reside in urban areas were more likely to marry later compared to their counterparts in Swaziland. The results also reveal that the proportion of early rst marriages is declining since the di erence among birth cohorts is found to be very high, with women of younger cohorts getting married later compared to older women. / NRF

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This thesis shows that consumers' behaviour has a decisive impact on the innovative behaviour of firms and on the development of industry. As a framework, an evolutionary simulation model is chosen, and market interactions are modelled according to a search theoretic approach.

Indiana University-Purdue University Indianapolis (IUPUI) / Protein malfunction can cause human diseases, which makes the protein a target in the process of drug discovery. In-depth knowledge of how protein functions can widely contribute to the understanding of the mechanism of these diseases. Protein functions are determined by protein structures and their dynamic properties. Protein dynamics refers to the constant physical movement of atoms in a protein, which may result in the transition between different conformational states of the protein. These conformational transitions are critically important for the proteins to function. Understanding protein dynamics can help to understand and interfere with the conformational states and transitions, and thus with the function of the protein. If we can understand the mechanism of conformational transition of protein, we can design molecules to regulate this process and regulate the protein functions for new drug discovery. Protein Dynamics can be simulated by Molecular Dynamics (MD) Simulations. The MD simulation data generated are spatial-temporal and therefore very high dimensional. To analyze the data, distinguishing various atomic interactions within a protein by interpreting their 3D coordinate values plays a significant role. Since the data is humongous, the essential step is to find ways to interpret the data by generating more efficient algorithms to reduce the dimensionality and developing user-friendly visualization tools to find patterns and trends, which are not usually attainable by traditional methods of data process. The typical allosteric long-range nature of the interactions that lead to large conformational transition, pin-pointing the underlying forces and pathways responsible for the global conformational transition at atomic level is very challenging. To address the problems, Various analytical techniques are performed on the simulation data to better understand the mechanism of protein dynamics at atomic level by developing a new program called Probing Long-distance interactions by Tapping into Paired-Distances (PLITIP), which contains a set of new tools based on analysis of paired distances to remove the interference of the translation and rotation of the protein itself and therefore can capture the absolute changes within the protein. Firstly, we developed a tool called Decomposition of Paired Distances (DPD). This tool generates a distance matrix of all paired residues from our simulation data. This paired distance matrix therefore is not subjected to the interference of the translation or rotation of the protein and can capture the absolute changes within the protein. This matrix is then decomposed by DPD using Principal Component Analysis (PCA) to reduce dimensionality and to capture the largest structural variation. To showcase how DPD works, two protein systems, HIV-1 protease and 14-3-3 σ, that both have tremendous structural changes and conformational transitions as displayed by their MD simulation trajectories. The largest structural variation and conformational transition were captured by the first principal component in both cases. In addition, structural clustering and ranking of representative frames by their PC1 values revealed the long-distance nature of the conformational transition and locked the key candidate regions that might be responsible for the large conformational transitions. Secondly, to facilitate further analysis of identification of the long-distance path, a tool called Pearson Coefficient Spiral (PCP) that generates and visualizes Pearson Coefficient to measure the linear correlation between any two sets of residue pairs is developed. PCP allows users to fix one residue pair and examine the correlation of its change with other residue pairs. Thirdly, a set of visualization tools that generate paired atomic distances for the shortlisted candidate residue and captured significant interactions among them were developed. The first tool is the Residue Interaction Network Graph for Paired Atomic Distances (NG-PAD), which not only generates paired atomic distances for the shortlisted candidate residues, but also display significant interactions by a Network Graph for convenient visualization. Second, the Chord Diagram for Interaction Mapping (CD-IP) was developed to map the interactions to protein secondary structural elements and to further narrow down important interactions. Third, a Distance Plotting for Direct Comparison (DP-DC), which plots any two paired distances at user’s choice, either at residue or atomic level, to facilitate identification of similar or opposite pattern change of distances along the simulation time. All the above tools of PLITIP enabled us to identify critical residues contributing to the large conformational transitions in both HIV-1 protease and 14-3-3σ proteins. Beside the above major project, a side project of developing tools to study protein pseudo-symmetry is also reported. It has been proposed that symmetry provides protein stability, opportunities for allosteric regulation, and even functionality. This tool helps us to answer the questions of why there is a deviation from perfect symmetry in protein and how to quantify it.

Phylogenetics is the research of ancestor-descendant relationships among different groups of organisms, for example, species or populations of interest. The datasets involved are usually sequence alignments of various subsets of taxa for various genes. A major task of phylogenetics is often to combine estimated gene trees from many loci sampled from the genes into an overall estimate species tree topology. Eventually, one can construct the tree of life that depicts the ancestor-descendant relationships for all known species around the world. If there is missing data or incomplete sampling in the datasets, then supertree methods can be used to assemble gene trees with different subsets of taxa into an estimated overall species tree topology. In this study, we assume that gene tree discordance is solely due to incomplete lineage sorting under the multispecies coalescent model (Degnan and Rosenberg, 2009). If there is missing data or incomplete sampling in the datasets, then supertree methods can be used to assemble gene trees with different subsets of taxa into an estimated species tree topology. In addition, we examine the performance of the most commonly used supertree method (Wilkinson et al., 2009), namely matrix representation with parsimony (MRP), to explore its statistical properties in this setting. In particular, we show that MRP is not statistically consistent. That is, an estimated species tree topology other than the true species tree topology is more likely to be returned by MRP as the number of gene trees increases. For some situations, using longer branch lengths, randomly deleting taxa or even introducing mutation can improve the performance of MRP so that the matching species tree topology is recovered more often. In conclusion, MRP is a supertree method that is able to handle large amounts of conflict in the input gene trees. However, MRP is not statistically consistent, when using gene trees arise from the multispecies coalescent model to estimate species trees.

Dans ce mémoire, nous étudions le problème de l'estimation de la variance pour les estimateurs par double dilatation et de calage pour l'échantillonnage à deux phases. Nous proposons d'utiliser une décomposition de la variance différente de celle habituellement utilisée dans l'échantillonnage à deux phases, ce qui mène à un estimateur de la variance simplifié. Nous étudions les conditions sous lesquelles les estimateurs simplifiés de la variance sont valides. Pour ce faire, nous considérons les cas particuliers suivants : (1) plan de Poisson à la deuxième phase, (2) plan à deux degrés, (3) plan aléatoire simple sans remise aux deux phases, (4) plan aléatoire simple sans remise à la deuxième phase. Nous montrons qu'une condition cruciale pour la validité des estimateurs simplifiés sous les plans (1) et (2) consiste à ce que la fraction de sondage utilisée pour la première phase soit négligeable (ou petite). Nous montrons sous les plans (3) et (4) que, pour certains estimateurs de calage, l'estimateur simplifié de la variance est valide lorsque la fraction de sondage à la première phase est petite en autant que la taille échantillonnale soit suffisamment grande. De plus, nous montrons que les estimateurs simplifiés de la variance peuvent être obtenus de manière alternative en utilisant l'approche renversée (Fay, 1991 et Shao et Steel, 1999). Finalement, nous effectuons des études par simulation dans le but d'appuyer les résultats théoriques. / In this thesis we study the problem of variance estimation for the double expansion estimator and the calibration estimators in the case of two-phase designs. We suggest to use a variance decomposition different from the one usually used in two-phase sampling, which leads to a simplified variance estimator. We look for the necessary conditions for the simplified variance estimators to be appropriate. In order to do so, we consider the following particular cases : (1) Poisson design at the second phase, (2) two-stage design, (3) simple random sampling at each phase, (4) simple random sampling at the second phase. We show that a crucial condition for the simplified variance estimator to be valid in cases (1) and (2) is that the first phase sampling fraction must be negligible (or small). We also show in cases (3) and (4) that the simplified variance estimator can be used with some calibration estimators when the first phase sampling fraction is negligible and the population size is large enough. Furthermore, we show that the simplified estimators can be obtained in an alternative way using the reversed approach (Fay, 1991 and Shao and Steel, 1999). Finally, we conduct some simulation studies in order to validate the theoretical results.

Ce mémoire porte sur la présentation des estimateurs de Bernstein qui sont des alternatives récentes aux différents estimateurs classiques de fonctions de répartition et de densité. Plus précisément, nous étudions leurs différentes propriétés et les comparons à celles de la fonction de répartition empirique et à celles de l'estimateur par la méthode du noyau. Nous déterminons une expression asymptotique des deux premiers moments de l'estimateur de Bernstein pour la fonction de répartition. Comme pour les estimateurs classiques, nous montrons que cet estimateur vérifie la propriété de Chung-Smirnov sous certaines conditions. Nous montrons ensuite que l'estimateur de Bernstein est meilleur que la fonction de répartition empirique en terme d'erreur quadratique moyenne. En s'intéressant au comportement asymptotique des estimateurs de Bernstein, pour un choix convenable du degré du polynôme, nous montrons que ces estimateurs sont asymptotiquement normaux. Des études numériques sur quelques distributions classiques nous permettent de confirmer que les estimateurs de Bernstein peuvent être préférables aux estimateurs classiques. / This thesis focuses on the presentation of the Bernstein estimators which are recent alternatives to conventional estimators of the distribution function and density. More precisely, we study their various properties and compare them with the empirical distribution function and the kernel method estimators. We determine an asymptotic expression of the first two moments of the Bernstein estimator for the distribution function. As the conventional estimators, we show that this estimator satisfies the Chung-Smirnov property under conditions. We then show that the Bernstein estimator is better than the empirical distribution function in terms of mean squared error. We are interested in the asymptotic behavior of Bernstein estimators, for a suitable choice of the degree of the polynomial, we show that the Bernstein estimators are asymptotically normal. Numerical studies on some classical distributions confirm that the Bernstein estimators may be preferable to conventional estimators.

Kognitive Diagnosemodelle (DCMs) sind konfirmatorische probabilistische Modelle mit kategorialen latenten Variablen, die Mehrfachladungsstrukturen erlauben. Sie ermöglichen die Abbildung der Kompetenzen in mehrdimensionalen Profilen, die zur Erstellung informativer Rückmeldungen dienen können. Diese Dissertation untersucht in zwei Anwendungsstudien und einer Simulationsstudie wichtige methodische Aspekte bei der Schätzung der DCMs. In der Arbeit wurde ein neuer Mathematiktest entwickelt basierend auf theoriegeleiteten vorab definierten Q-Matrizen. In den Anwendungsstudien (a) illustrierten wir die Anwendung der DCMs für empirische Daten für den neu entwickelten Mathematiktest, (b) verglichen die DCMs mit konfirmatorischen Faktorenanalysemodellen (CFAs), (c) untersuchten die inkrementelle Validität der mehrdimensionalen Profile und (d) schlugen eine Methode zum Vergleich konkurrierender DCMs vor. Ergebnisse der Anwendungsstudien zeigten, dass die geschätzten DCMs meist einen nicht akzeptablen Modellfit aufwiesen. Zudem fanden wir nur eine vernachlässigbare inkrementelle Validität der mehrdimensionalen Profile nach der Kontrolle der Personenparameter bei der Vorhersage der Mathematiknote. Zusammengenommen sprechen diese Ergebnisse dafür, dass DCMs per se keine zusätzliche Information über die mehrdimensionalen CFA-Modelle hinaus bereitstellen. DCMs erlauben jedoch eine andere Aufbereitung der Information. In der Simulationsstudie wurde die Präzision der Parameterschätzungen in log-linearen DCMs sowie die Sensitivität ausgewählter Indizes der Modellpassung auf verschiedene Formen der Fehlspezifikation der Interaktionsterme oder der Q-Matrix untersucht. Die Ergebnisse der Simulationsstudie zeigen, dass die Parameterwerte für große Stichproben korrekt geschätzt werden, während die Akkuratheit der Parameterschätzungen bei kleineren Stichproben z. T. beeinträchtigt ist. Ein großer Teil der Personen wird in Modellen mit fehlspezifizierten Q-Matrizen falsch klassifiziert. / Cognitive diagnostic classification models (DCMs) have been developed to assess the cognitive processes underlying assessment responses. Current dissertation aims to provide theoretical and practical considerations for estimation of DCMs for educational applications by investigating several important underexplored issues. To avoid problems related to retrofitting of DCMs to an already existing data, test construction of the newly mathematics assessment for primary school DMA was based on a-priori defined Q-matrices. In this dissertation we compared DCMs with established psychometric models and investigated the incremental validity of DCMs profiles over traditional IRT scores. Furthermore, we addressed the issue of the verification of the Q-matrix definition. Moreover, we examined the impact of invalid Q-matrix specification on item, respondent parameter recovery, and sensitivity of selected fit measures. In order to address these issues one simulation study and two empirical studies illustrating applications of several DCMs were conducted. In the first study we have applied DCMs in general diagnostic modelling framework and compared those models to factor analysis models. In the second study we implemented a complex simulation study and investigated the implications of Q-matrix misspecification on parameter recovery and classification accuracy for DCMs in log-linear framework. In the third study we applied results of the simulation study to a practical application based on the data for 2032 students for the DMA. Presenting arguments for additional gain of DCMs over traditional psychometric models remains challenging. Furthermore, we found only a negligible incremental validity of multivariate proficiency profiles compared to the one-dimensional IRT ability estimate. Findings from the simulation study revealed that invalid Q-matrix specifications led to decreased classification accuracy. Information-based fit indices were sensitive to strong model misspecifications.

It has previously been determined that using 3 or 4 points on a categorized response scale will fail to produce a continuous distribution of scores. However, there is no evidence, thus far, revealing the number of scale points that may indeed possess an approximate or sufficiently continuous distribution. This study provides the evidence to suggest the level of categorization in discrete scales that makes them directly comparable to continuous scales in terms of their measurement properties. To do this, we first introduced a novel procedure for simulating discretely scaled data that was both informed and validated through the principles of the Classical True Score Model. Second, we employed a measurement invariance (MI) approach to confirmatory factor analysis (CFA) in order to directly compare the measurement quality of continuously scaled factor models to that of discretely scaled models. The simulated design conditions of the study varied with respect to item-specific variance (low, moderate, high), random error variance (none, moderate, high), and discrete scale categorization (number of scale points ranged from 3 to 101). A population analogue approach was taken with respect to sample size (N = 10,000). We concluded that there are conditions under which response scales with 11 to 15 scale points can reproduce the measurement properties of a continuous scale. Using response scales with more than 15 points may be, for the most part, unnecessary. Scales having from 3 to 10 points introduce a significant level of measurement error, and caution should be taken when employing such scales. The implications of this research and future directions are discussed.

In the residential and commercial buildings, most of the energy is used to provide the thermal comfort environment to the occupants. The recent research towards Green Buildings is focusing on reduction of energy consumption by air-conditioners and fans used for producing the thermal comfort environment. The thermal comfort is defined as the condition of mind which expresses human satisfaction with the thermal environment. The human body is continuously producing metabolic heat and it should be maintained within the narrow range of core temperature. The heat generated inside the body should be lost to the environment to maintain the thermal equilibrium with each other. The heat loss from the body is taking place in different modes such as conduction, convection, radiation and evaporation through the skin and respiration. These heat losses are influenced by the environmental factors (air temperature, air velocity, relative humidity and mean radiant temperature), physiological factors (activity level, posture and sweat rate) and clothing factors (thermal insulation value, evaporative resistance and microenvironment volume). When the body is in thermally equilibrium with its surrounding environment, the heat production should be equal to heat loss to maintain the thermal comfort. The level of thermal comfort can be measured by the different indices which combine many parameters. Of these, the Fanger’s PMV (Predicted Mean Vote) – PPD (Percentage of People Dissatisfied) index was universally suggested by ASHRAE and ISO. The PMV – PPD index was derived based on the experiment conducted on acclimated European and American subjects. Many researchers have criticized that the PMV – PPD index is not valid for tropical regions and some researchers have well agreed with this index for the same region. The validation of PMV – PPD index for thermal comfort Indians has not yet been examined. The validation of PMV – PPD index can be done by the human heat balance experiment and the individual heat losses have to be calculated from the measured parameters. In the human heat balance, the convective heat transfer plays the major role when the air movement exists around the human body. The convective heat loss is dependent on the convective heat transfer coefficient which is the function of the driving force of the convection. Using Computational Fluid Dynamics techniques, an attempt has been made in this work to determine the convective heat transfer coefficient of the human body at standing posture in natural convection. The CFD technique has been used to analyze the heat and fluid flow around the human body as follows: The anthropometric digital human manikin was modeled in GAMBIT with a test room. This model was meshed by tetrahedral elements and exported to FLUENT software to perform the analysis. The simulation was done at different ambient temperatures (16 oC to 32 oC with increment of 2 oC). The Boussinesq approximation was used to simulate the natural convection and the Surface to Surface model was used to simulate the radiation. The surrounding wall temperature was assigned equal to the ambient temperature. The sum of convective and radiative heat losses calculated based on the ASHRAE model was set as heat flux from the manikin’s surface. From the simulation, the local skin temperatures have been taken, and the temperature and velocity distributions analyzed. The result shows that the skin temperature is increasing with an increase in ambient temperature and the thickness of the hydrodynamic and thermodynamic boundary layers is increasing with height of the manikin. From the Nusselt number analogy, the convective heat transfer coefficients of the individual manikin’s segments have been calculated and the relation with respect to the temperature differences has been derived by the regression analysis. The relation obtained for the convective heat transfer coefficient has been validated with previous experimental results cited in literature for the same conditions. The result shows that the present relation agrees well with the previous experimental relations. The characteristics of the human thermal plume have been studied and the velocity of this plume is found to increase with the ambient temperature. Using the Grashof number, the flow around the human manikin has been examined and it is observed to be laminar up to abdomen level and turbulent from shoulder level. In between these two levels, the flow is found to be in transition. The validation of PMV model for tropical countries, especially for Indians, was done by heat balance experiment on Indian subjects. The experiment was conducted on forty male subjects at different ambient temperatures in a closed room in which low air movement exists. The local skin temperature, relative humidity, air velocity and globe temperature were measured. The sensation vote was received from all the subjects at all the conditions. The convective heat loss was calculated from its coefficient obtained from the present computational simulation. The radiation heat loss was calculated for two cases: In case one, the mean radiant temperature was taken equal to the ambient temperature and in case two, the mean radiant temperature was calculated from the globe temperature. The other heat losses were calculated from the basic formulae and the relations given by ASHRAE based on Fanger’s assumption. From these calculations, the validity of the Fanger’s assumption was examined. The collected sensation votes and the calculated PMV were compared to validate the PMV – PPD index for Indians. The experimental results show that there was much variation in the calculated comfort level using the measured parameters and the Fanger’s assumption. For the case of mean radiant temperature equal to the ambient temperature for indoor condition, the comfort level was varying more than the actual. In addition, the calculated comfort level from the globe temperature agreed well with the comfort level from the collected sensation votes. So it was concluded that the ASHRAE model is valid for Indians if the radiation was measured exactly. Using the ASHRAE model, the required wall emissivity of the surrounding wall at different ambient temperatures was determined from the CFD simulation. In the ASHRAE model, the surrounding wall emissivity plays the major role in the radiative heat loss from the human body. Hence in recent years, research on low emissive wall paints is focused. The computational study was done to determine the required wall emissivity to obtain the thermal comfort of the occupant at low energy consumption. The simulation was done with the different ambient temperatures (16 oC to 40 oC with increment of 4 oC) with the different surrounding wall emissivity (0.0 to 1.0 with increment of 0.2). From this simulation, the change in mean skin temperature with respect to wall emissivity was obtained for all ambient temperature conditions. The required mean skin temperature for a particular activity level was compared with the simulation results and from that, the required wall emissivity at the different ambient conditions was determined. If the surrounding walls are having the required emissivity, it leads to decrease in heat/cold strain on the human body, and the thermal comfort can be obtained with low energy consumption.(please note that title in the CD is given as COMPUTATION OF REQUIRED WALL EMISSIVITY FOR LOW ENERGY CONSUMPTION IN BUILDINGS USING ASHRAE MODEL VALIDATED FOR INDIAN THERMAL COMFORT)