Letteratura scientifica selezionata sul tema "Mixed variables"

Latent variable models are widely used in social sciences in which interest is centred on entities such as attitudes, beliefs or abilities for which there e)dst no direct measuring instruments. Latent modelling tries to extract these entities, here described as latent (unobserved) variables, from measurements on related manifest (observed) variables. Methodology already exists for fitting a latent variable model to manifest data that is either categorical (latent trait and latent class analysis) or continuous (factor analysis and latent profile analysis). In this thesis a latent trait and a latent class model are presented for analysing the relationships among a set of mixed manifest variables using one or more latent variables. The set of manifest variables contains metric (continuous or discrete) and binary items. The latent dimension is continuous for the latent trait model and discrete for the latent class model. Scoring methods for allocating individuals on the identified latent dimen-sions based on their responses to the mixed manifest variables are discussed. ' Item nonresponse is also discussed in attitude scales with a mixture of binary and metric variables using the latent trait model. The estimation and the scoring methods for the latent trait model have been generalized for conditional distributions of the observed variables given the vector of latent variables other than the normal and the Bernoulli in the exponential family. To illustrate the use of the naixed model four data sets have been analyzed. Two of the data sets contain five memory questions, the first on Thatcher's resignation and the second on the Hillsborough football disaster; these five questions were included in BMRBI's August 1993 face to face omnibus survey. The third and the fourth data sets are from the 1990 and 1991 British Social Attitudes surveys; the questions which have been analyzed are from the sexual attitudes sections and the environment section respectively.

The location model is a potential basis for discriminating between groups of objects with mixed types of variables. The model specifies a parametric form for the conditional distribution of the continuous variables given each pattern of values of the categorical variables, thus leading to a theoretical discriminant function between the groups. To conduct a practical discriminant analysis, the objects must first be sorted into the cells of a multinomial table generated from the categorical values, and the model parameters must then be estimated from the data. However, in many practical situations some of the cells are empty, which prevents simple implementation of maximum likelihood estimation and restricts the feasibility of linear model estimators to cases with relatively few categorical variables. This deficiency was overcome by non-parametric smoothing estimation proposed by Asparoukhov and Krzanowski (2000). Its usual implementation uses exponential and piece-wise smoothing functions for the continuous variables, and adaptive weighted nearest neighbour for the categorical variables. Despite increasing the range of applicability, the smoothing parameters that are chosen by maximising the leave-one-out pseudo-likelihood depend on distributional assumptions, while, the smoothing method for the categorical variables produces erratic values if the number of variables is large. This thesis rectifies these shortcomings, and extends location model methodology to situations where there are large numbers of mixed categorical and continuous variables. Chapter 2 uses the simplest form of the exponential smoothing function for the continuous variables and describes how the smoothing parameters can instead be chosen by minimising either the leave-one-out error rate or the leave-one-out Brier score, neither of which make distributional assumptions. Alternative smoothing methods, namely a kernel and a weighted form of the maximum likelihood, are also investigated for the categorical variables. Numerical evidence in Chapter 3 shows that there is little to choose among the strategies for estimating smoothing parameters and among the smoothing methods for the categorical variables. However, some of the proposed smoothing methods are more feasible when the number of parameters to be estimated is reduced. Chapter 4 reviews previous work on problems of high dimensional feature variables, and focuses on selecting variables on the basis of the distance between groups. In particular, the Kullback-Leibler divergence is considered for the location model, but existing theory based on maximum likelihood estimators is not applicable for general cases. Chapter 5 therefore describes the implementation of this distance for smoothed estimators, and investigates its asymptotic distribution. The estimated distance and its asymptotic distribution provide a stopping rule in a sequence of searching processes, either by forward, backward or stepwise selections, following the test for no additional information. Simulation results in Chapter 6 exhibit the feasibility of the proposed variable selection strategies for large numbers of variables, but limitations in several circumstances are identified. Applications to real data sets in Chapter 7 show how the proposed methods are competitive with, and sometimes better than other existing classification methods. Possible future work is outlined in Chapter 8.

Dans le cadre de la conception de systèmes complexes, tels que les aéronefs et les lanceurs, la présence de fonctions d'objectifs et/ou de contraintes à forte intensité de calcul (e.g., modèles d'éléments finis) couplée à la dépendance de choix de conception technologique discrets et non ordonnés entraîne des problèmes d'optimisation difficiles. De plus, une partie de ces choix technologiques est associée à un certain nombre de variables de conception continues et discrètes spécifiques qui ne doivent être prises en considération que si des choix technologiques spécifiques sont faits. Par conséquent, le problème d'optimisation qui doit être résolu afin de déterminer la conception optimale du système présente un espace de recherche et un domaine de faisabilité variant de façon dynamique. Les algorithmes existants qui permettent de résoudre ce type particulier de problèmes ont tendance à exiger une grande quantité d'évaluations de fonctions afin de converger vers l'optimum réalisable, et sont donc inadéquats lorsqu'il s'agit de résoudre les problèmes à forte intensité de calcul. Pour cette raison, cette thèse explore la possibilité d'effectuer une optimisation de l'espace de conception contraint à variables mixtes et de taille variable en s'appuyant sur des méthodes d’optimisation à base de modèles de substitution créés à l'aide de processus Gaussiens, également connue sous le nom d'optimisation Bayésienne. Plus spécifiquement, 3 axes principaux sont discutés. Premièrement, la modélisation de substitution par processus gaussien de fonctions mixtes continues/discrètes et les défis qui y sont associés sont discutés en détail. Un formalisme unificateur est proposé afin de faciliter la description et la comparaison entre les noyaux existants permettant d'adapter les processus gaussiens à la présence de variables discrètes non ordonnées. De plus, les performances réelles de modélisation de ces différents noyaux sont testées et comparées sur un ensemble de benchmarks analytiques et de conception ayant des caractéristiques et des paramétrages différents. Dans la deuxième partie de la thèse, la possibilité d'étendre la modélisation de substitution mixte continue/discrète à un contexte d'optimisation Bayésienne est discutée. La faisabilité théorique de cette extension en termes de modélisation de la fonction objectif/contrainte ainsi que de définition et d'optimisation de la fonction d'acquisition est démontrée. Différentes alternatives possibles sont considérées et décrites. Enfin, la performance de l'algorithme d'optimisation proposé, avec diverses paramétrisations des noyaux et différentes initialisations, est testée sur un certain nombre de cas-test analytiques et de conception et est comparée aux algorithmes de référence.Dans la dernière partie de ce manuscrit, deux approches permettant d'adapter les algorithmes d'optimisation bayésienne mixte continue/discrète discutés précédemment afin de résoudre des problèmes caractérisés par un espace de conception variant dynamiquement au cours de l’optimisation sont proposées. La première adaptation est basée sur l'optimisation parallèle de plusieurs sous-problèmes couplée à une allocation de budget de calcul basée sur l'information fournie par les modèles de substitution. La seconde adaptation, au contraire, est basée sur la définition d'un noyau permettant de calculer la covariance entre des échantillons appartenant à des espaces de recherche partiellement différents en fonction du regroupement hiérarchique des variables dimensionnelles. Enfin, les deux alternatives sont testées et comparées sur un ensemble de cas-test analytiques et de conception.Globalement, il est démontré que les méthodes d'optimisation proposées permettent de converger vers les optimums des différents types de problèmes considérablement plus rapidement par rapport aux méthodes existantes. Elles représentent donc un outil prometteur pour la conception de systèmes complexes<br>Within the framework of complex system design, such as aircraft and launch vehicles, the presence of computationallyintensive objective and/or constraint functions (e.g., finite element models and multidisciplinary analyses)coupled with the dependence on discrete and unordered technological design choices results in challenging optimizationproblems. Furthermore, part of these technological choices is associated to a number of specific continuous anddiscrete design variables which must be taken into consideration only if specific technological and/or architecturalchoices are made. As a result, the optimization problem which must be solved in order to determine the optimalsystem design presents a dynamically varying search space and feasibility domain.The few existing algorithms which allow solving this particular type of problems tend to require a large amountof function evaluations in order to converge to the feasible optimum, and result therefore inadequate when dealingwith the computationally intensive problems which can often be encountered within the design of complex systems.For this reason, this thesis explores the possibility of performing constrained mixed-variable and variable-size designspace optimization by relying on surrogate model-based design optimization performed with the help of Gaussianprocesses, also known as Bayesian optimization. More specifically, 3 main axes are discussed. First, the Gaussianprocess surrogate modeling of mixed continuous/discrete functions and the associated challenges are extensivelydiscussed. A unifying formalism is proposed in order to facilitate the description and comparison between theexisting kernels allowing to adapt Gaussian processes to the presence of discrete unordered variables. Furthermore,the actual modeling performances of these various kernels are tested and compared on a set of analytical and designrelated benchmarks with different characteristics and parameterizations.In the second part of the thesis, the possibility of extending the mixed continuous/discrete surrogate modeling toa context of Bayesian optimization is discussed. The theoretical feasibility of said extension in terms of objective/-constraint function modeling as well as acquisition function definition and optimization is shown. Different possiblealternatives are considered and described. Finally, the performance of the proposed optimization algorithm, withvarious kernels parameterizations and different initializations, is tested on a number of analytical and design relatedtest-cases and compared to reference algorithms.In the last part of this manuscript, two alternative ways of adapting the previously discussed mixed continuous/discrete Bayesian optimization algorithms in order to solve variable-size design space problems (i.e., problemscharacterized by a dynamically varying design space) are proposed. The first adaptation is based on the paralleloptimization of several sub-problems coupled with a computational budget allocation based on the informationprovided by the surrogate models. The second adaptation, instead, is based on the definition of a kernel allowingto compute the covariance between samples belonging to partially different search spaces based on the hierarchicalgrouping of design variables. Finally, the two alternatives are tested and compared on a set of analytical and designrelated benchmarks.Overall, it is shown that the proposed optimization methods allow to converge to the various constrained problemoptimum neighborhoods considerably faster when compared to the reference methods, thus representing apromising tool for the design of complex systems

Dans cette thèse, nous nous intéressons à l'étude des programmes polynomiaux, c'est à dire les problème d'optimisation dont la fonction objectif et/ou les contraintes font intervenir des polynômes de plusieurs variables. Ces problèmes ont de nombreuses applications pratiques et constituent actuellement un champ de recherche très actif. Différentes méthodes permettent de les résoudre de façon exacte ou approchée, en utilisant par exemple des relaxationssemidéfinies positives du type "moments-somme de carrés". Mais ces problèmes restent très difficiles et on ne sait résoudre en toute généralité que des instances de petite taille.Dans le cas quadratique, une approche de résolution exacte efficace a été initialement proposée à travers la méthode QCR. Elle se base sur une reformulation quadratique convexe "optimale" au sens de la borne par relaxation continue.Une des motivations de cette thèse est de généraliser cette approche pour le cas des problèmes polynomiaux. Dans la majeure partie de ce manuscrit, nous étudions les problèmes d'optimisation en variables binaires. Nous proposons deux familles de reformulations convexes pour ces problèmes: des reformulations "directes" et des reformulations passant par la quadratisation.Pour les reformulations directes, nous nous intéressons tout d'abord aux linéarisations. Nous introduisons le concept de q-linéarisation, une linéarisation utilisant q variables additionnelles, et comparons les bornes obtenues par relaxation continue pour différentes valeurs de q. Ensuite, nous appliquons la reformulation convexe au problème polynomial, en ajoutant des termes supplémentaires à la fonction objectif, mais sans ajouter de variables ou de contraintes additionnelles.La deuxième famille de reformulations convexes vise à étendre la reformulation quadratique convexe au cas polynomial. Nous proposons plusieurs nouvelles reformulations alternatives que nous comparons aux méthodes existantes sur des instances de la littérature. En particulier nous présentons l'algorithme PQCR pour résoudre des problèmes polynomiaux binaires sans contrainte. La méthode PQCR permet de résoudre des instances jusqu'ici non résolues. En plus des expérimentations numériques, nous proposons aussi une étude théorique visant à comparer les différentes reformulations quadratiques de la littérature puis à leur appliquer une reformulation convexe.Enfin nous considérons des cas plus généraux et nous proposons une méthode permettant de calculer des relaxations convexes pour des problèmes continus<br>In this thesis, we are interested in the study of polynomial programs, that is optimization problems for which the objective function and/or the constraints are expressed by multivariate polynomials. These problems have many practical applications and are currently actively studied. Different methods can be used to find either a global or a heuristic solution, using for instance, positive semi-definite relaxations as in the "Moment/Sum of squares" method. But these problems remain very difficult and only small instances are addressed. In the quadratic case, an effective exact solution approach was initially proposed in the QCR method. It is based on a quadratic convex reformulation, which is optimal in terms of continuous relaxation bound.One of the motivations of this thesis is to generalize this approach to the case of polynomial programs. In most of this manuscript, we study optimization problems with binary variables. We propose two families of convex reformulations for these problems: "direct" reformulations and quadratic ones.For direct reformulations, we first focus on linearizations. We introduce the concept of q-linearization, that is a linearization using q additional variables, and we compare the bounds obtained by continuous relaxation for different values of q. Then, we apply convex reformulation to the polynomial problem, by adding additional terms to the objective function, but without adding additional variables or constraints.The second family of convex reformulations aims at extending quadratic convex reformulation to the polynomial case. We propose several new alternative reformulations that we compare to existing methods on instances of the literature. In particular we present the algorithm PQCR to solve unconstrained binary polynomial problems. The PQCR method is able to solve several unsolved instances. In addition to numerical experiments, we also propose a theoretical study to compare the different quadratic reformulations of the literature and then apply a convex reformulation to them.Finally, we consider more general problems and we propose a method to compute convex relaxations for continuous problems

Nous nous intéressons à desméthodes statistiques pour estimer l'héritabilitéd'un caractère biologique, qui correspond à lapart des variations de ce caractère qui peut êtreattribuée à des facteurs génétiques. Nousproposons dans un premier temps d'étudierl'héritabilité de traits biologiques continus àl'aide de modèles linéaires mixtes parcimonieuxen grande dimension. Nous avons recherché lespropriétés théoriques de l'estimateur du maximumde vraisemblance de l'héritabilité : nousavons montré que cet estimateur était consistantet vérifiait un théorème central limite avec unevariance asymptotique que nous avons calculéeexplicitement. Ce résultat, appuyé par des simulationsnumériques sur des échantillons finis,nous a permis de constater que la variance denotre estimateur était très fortement influencéepar le ratio entre le nombre d'observations et lataille des effets génétiques. Plus précisément,quand le nombre d’observations est faiblecomparé à la taille des effets génétiques (ce quiest très souvent le cas dans les étudesgénétiques), la variance de l’estimateur était trèsgrande. Ce constat a motivé le développementd'une méthode de sélection de variables afin dene garder que les variants génétiques les plusimpliqués dans les variations phénotypiques etd’améliorer la précision des estimations del’héritabilité.La dernière partie de cette thèse est consacrée àl'estimation d'héritabilité de données binaires,dans le but d'étudier la part de facteursgénétiques impliqués dans des maladies complexes.Nous proposons d'étudier les propriétésthéoriques de la méthode développée par Golanet al. (2014) pour des données de cas-contrôleset très efficace en pratique. Nous montronsnotamment la consistance de l’estimateur del’héritabilité proposé par Golan et al. (2014)<br>We study statistical methods toestimate the heritability of a biological trait,which is the proportion of variations of thistrait that can be explained by genetic factors.First, we propose to study the heritability ofquantitative traits using high-dimensionalsparse linear mixed models. We investigate thetheoretical properties of the maximumlikelihood estimator for the heritability and weshow that it is a consistent estimator and that itsatisfies a central limit theorem with a closedformexpression for the asymptotic variance.This result, supported by an extendednumerical study, shows that the variance of ourestimator is strongly affected by the ratiobetween the number of observations and thesize of the random genetic effects. Moreprecisely, when the number of observations issmall compared to the size of the geneticeffects (which is often the case in geneticstudies), the variance of our estimator is verylarge. This motivated the development of avariable selection method in order to capturethe genetic variants which are involved themost in the phenotypic variations and providemore accurate heritability estimations. Wepropose then a variable selection methodadapted to high dimensional settings and weshow that, depending on the number of geneticvariants actually involved in the phenotypicvariations, called causal variants, it was a goodidea to include or not a variable selection stepbefore estimating heritability.The last part of this thesis is dedicated toheritability estimation for binary data, in orderto study the proportion of genetic factorsinvolved in complex diseases. We propose tostudy the theoretical properties of the methoddeveloped by Golan et al. (2014) for casecontroldata, which is very efficient in practice.Our main result is the proof of the consistencyof their heritability estimator

Intensive selection for increased milk production over many generations has led to growing genetic similarity and increased relationships in dairy population. In the current study, inbreeding depression was estimated for number of days to first service, summit milk, conception by 70 days non-return, and calving rate with a linear mixed model (LMM) approach and for calving difficulty, calf mortality with a Bayesian threshold model (BTM) for categorical traits. Effectiveness of classical and unknown parentage group procedures to estimate inbreeding coefficients was evaluated depending on completeness of a 5-generation pedigree. A novel method derived from the classical formula to estimate inbreeding was utilized to evaluate completeness of pedigrees. Two different estimates of maternal inbreeding were fitted in separate models as a linear covariate in combined LMM analyses (Holstein registered and grade cows and Jersey cows) or separate analyses (registered Holstein cows) by parity (1-4) with fetal inbreeding. Impact of inbreeding type, model, data structure, and treatment of herd-year-season (HYS) on magnitude and size of inbreeding depression were assessed. Grade Holstein datasets were sampled and analyzed by percentage of pedigree present (0-30%, 30-70% and 70-100%). BTM analyses (sire-mgs) were performed using Gibbs sampling for parities 1, 2 and 3 fitting maternal inbreeding only. In LMM analyses of grade data, the least pedigree and diagonal A matrix performed the worst. Significant inbreeding effects were obtained in most traits in cows of parity 1. Fetal inbreeding depression was mostly lower than that from maternal inbreeding. Inbreeding depression in binary traits was the most difficult to evaluate. Analyses with non-additive effects included in LMM, for data by inbreeding level and by age group should be preferred to estimate inbreeding depression. In BTM inbreeding effects were strongly related to dam parity and calf sex. Largest effects were obtained from parity 1 cows giving birth to male calves (0.417% and 0.252% for dystocia and calf mortality) and then births to female calves (0.300% and 0.203% for dystocia and calf mortality). Female calves from mature cows were the least affected (0.131% and 0.005% for dystocia and calf mortality). Data structure was found to be a very important factor to attainment of convergence in distribution.<br>Ph. D.

In this article we propose a new mixed effects regression model for fractional bounded response variables. Our model allows us to incorporate covariates directly to the expected value, so we can quantify exactly the influence of these covariates in the mean of the variable of interest rather than to the conditional mean. Estimation is carried out from a Bayesian perspective and due to the complexity of the augmented posterior distribution we use a Hamiltonian Monte Carlo algorithm, the No-U-Turn sampler, implemented using Stan software. A simulation study for comparison, in terms of bias and RMSE, was performed showing that our model has a better performance than other traditional longitudinal models for bounded variables. Finally, we applied our Beta Inflated mixed-effects regression model to real data which consists of utilization of credit lines in the peruvian financial system.<br>En este artículo proponemos un nuevo modelo de regresión con efectos mixtos para variables acotadas fraccionarias. Este modelo nos permite incorporar covariables directamente al valor esperado, de manera que podemos cuantificar exactamente la influencia de estas covariables en la media de la variable de interés en vez de en la media condicional. La estimación se llevó a cabo desde una perspectiva bayesiana y debido a la complejidad de la distribución aumentada a posteriori usamos un algoritmo de Monte Carlo Hamiltoniano, el muestreador No-U-Turn, que se encuentra implementado en el software Stan. Se realizó un estudio de simulación que compara, en términos de sesgo y RMSE, el modelo propuesto con otros modelos tradicionales longitudinales para variables acotadas, resultando que el primero tiene un mejor desempeño. Finalmente, aplicamos nuestro modelo de regresión Beta Inflacionada con efectos mixtos a datos reales los cuales consistían en información de la utilización de las líneas de crédito en el sistema financiero peruano.<br>Tesis

Bon nombre de problèmes d'optimisation rencontrés dans l'industrie font appel à des systèmes complexes et n'ont pas de formulation analytique explicite : ce sont des problèmes d'optimisation de type boîte noire (ou blackbox en anglais). Ils peuvent être dits “mixtes”, auquel cas ils impliquent des variables de différentes natures (continues et discrètes), et avoir de nombreuses contraintes à satisfaire. De plus, les évaluations de l'objectif et des contraintes peuvent être numériquement coûteuses.Dans cette thèse, nous étudions des méthodes de résolution de tels problèmes complexes, à savoir des problèmes d'optimisation boîte noire avec contraintes et variables mixtes, pour lesquels les évaluations des fonctions sont très coûteuses en temps de calcul.Puisque l'utilisation de dérivées n'est pas envisageable, ce type de problèmes est généralement abordé par des approches sans dérivées comme les algorithmes évolutionnaires, les méthodes de recherche directe et les approches basées sur des métamodèles.Nous étudions les performances de telles méthodes déterministes et stochastiques dans le cadre de l'optimisation boîte noire, y compris sur un cas test en éléments finis que nous avons conçu. En particulier, nous évaluons les performances de la variante ORTHOMADS de l'algorithme de recherche directe MADS sur des problèmes d'optimisation continus et à variables mixtes issus de la littérature.Nous proposons également une nouvelle méthode d'optimisation boîte noire, nommée BOA, basée sur des approximations par métamodèles. Elle comporte deux phases dont la première vise à trouver un point réalisable tandis que la seconde améliore itérativement la valeur de l'objectif de la meilleure solution réalisable trouvée. Nous décrivons des expériences utilisant des instances de la littérature et des applications de l'industrie automobile. Elles incluent des tests de notre algorithme avec différents types de métamodèles, ainsi que des comparaisons avec ORTHOMADS<br>Numerous industrial optimization problems are concerned with complex systems and have no explicit analytical formulation, that is they are blackbox optimization problems. They may be mixed, namely involve different types of variables (continuous and discrete), and comprise many constraints that must be satisfied. In addition, the objective and constraint blackbox functions may be computationally expensive to evaluate.In this thesis, we investigate solution methods for such challenging problems, i.e constrained mixed-variable blackbox optimization problems involving computationally expensive functions.As the use of derivatives is impractical, problems of this form are commonly tackled using derivative-free approaches such as evolutionary algorithms, direct search and surrogate-based methods.We investigate the performance of such deterministic and stochastic methods in the context of blackbox optimization, including a finite element test case designed for our research purposes. In particular, the performance of the ORTHOMADS instantiation of the direct search MADS algorithm is analyzed on continuous and mixed-integer optimization problems from the literature.We also propose a new blackbox optimization algorithm, called BOA, based on surrogate approximations. It proceeds in two phases, the first of which focuses on finding a feasible solution, while the second one iteratively improves the objective value of the best feasible solution found. Experiments on instances stemming from the literature and applications from the automotive industry are reported. They namely include results of our algorithm considering different types of surrogates and comparisons with ORTHOMADS

This thesis examines corporate taxpayers’ compliance variables and analyses the influence of business characteristics on compliance behaviour. A two-phase exploratory mixed methods approach was employed to explore participants’ views of corporate taxpayers’ compliance variables, with the intention of using this information to develop a survey instrument. The method comprised eight focus group interviews with 60 tax auditors from the Inland Revenue Board of Malaysia (IRBM), and a mixed-mode survey among selected Malaysian corporate taxpayers. Thematic analysis and descriptive and inferential analysis were mainly used to examine the qualitative and quantitative data.The results suggest that the main corporate taxpayers’ compliance variables are: tax knowledge, tax complexity, tax agents and tax audits. The main business characteristics that are found to have significant influence on compliance variables are the length of time the business has been operational, size and industry. Continuous tax education and tax audit programmes are thus vital, and should focus more closely on specific groups of taxpayers, namely smaller and more newly established companies, companies in rural areas, and business industries that are more inclined to use cash transactions. Moreover, as many corporate taxpayers perceive the probability of an audit as low, the IRBM should publicise its audit activities more prolifically through available media channels. Tax simplification, especially on laws regarding estimation of income tax, is also an important consideration.This study extends the scope of tax compliance research to corporate taxpayers, and builds upon the limited international and Malaysian literature in this area. Most of the research findings of this thesis yield consistent results with respect to particular tax compliance variables. In a tax policy context, this study enables international tax authorities in general, and Malaysian tax authorities in particular, to have greater confidence in developing and administering tax laws and policies to maintain and/or increase the overall level of corporate compliance.