Regression Models with Heteroscedasticity using Bayesian Approach

In this paper, we compare the performance of two statistical approaches for the analysis of data obtained from the social research area. In the first approach, we use normal models with joint regression modelling for the mean and for the variance heterogeneity. In the second approach, we use hierarchical models. In the first case, individual and social variables are included in the regression modelling for the mean and for the variance, as explanatory variables, while in the second case, the variance at level 1 of the hierarchical model depends on the individuals (age of the individuals), and in the level 2 of the hierarchical model, the variance is assumed to change according to socioeconomic stratum. Applying these methodologies, we analyze a Colombian tallness data set to find differences that can be explained by socioeconomic conditions. We also present some theoretical and empirical results concerning the two models. From this comparative study, we conclude that it is better to jointly modelling the mean and variance heterogeneity in all cases. We also observe that the convergence of the Gibbs sampling chain used in the Markov Chain Monte Carlo method for the jointly modeling the mean and variance heterogeneity is quickly achieved.

Use Multilevel Graph Partitioning Scheme to solve traveling salesman problem

The traveling salesman problem is although looking very simple problem but it is an important combinatorial problem. In this thesis I have tried to find the shortest distance tour in which each city is visited exactly one time and return to the starting city. I have tried to solve traveling salesman problem using multilevel graph partitioning approach.Although traveling salesman problem itself very difficult as this problem is belong to the NP-Complete problems but I have tried my best to solve this problem using multilevel graph partitioning it also belong to the NP-Complete problems. I have solved this thesis by using the k-mean partitioning algorithm which divides the problem into multiple partitions and solving each partition separately and its solution is used to improve the overall tour by applying Lin Kernighan algorithm on it. Through all this I got optimal solution which proofs that solving traveling salesman problem through graph partition scheme is good for this NP-Problem and through this we can solved this intractable problem within few minutes.Keywords: Graph Partitioning Scheme, Traveling Salesman Problem.

Multilevel analysis of the Be Active Eat Well intervention : environmental and behavioural influences on reductions in child obesity risk

Background: The Be Active Eat Well (BAEW) community-based child obesity prevention intervention was successful in modestly reducing unhealthy weight gain in primary school children using a multi-strategy and multi-setting approach.

Objective: To (1) examine the relationship between changes in obesity-related individual, household and school factors and changes in standardised child body mass index (zBMI), and (2) determine if the BAEW intervention moderated these effects.

Methods: The longitudinal relationships between changes in individual, household and school variables and changes in zBMI were explored using multilevel modelling, with measurement time (baseline and follow-up) at level 1, individual (behaviours, n=1812) at level 2 and households (n=1318) and schools (n=18) as higher levels (environments). The effect of the intervention was tested while controlling for child age, gender and maternal education level.

Results: This study confirmed that the BAEW intervention lowered child zBMI compared with the comparison group (−0.085 units, P=0.03). The variation between household environments was found to be a large contributor to the percentage of unexplained change in child zBMI (59%), compared with contributions from the individual (23%) and school levels (1%). Across both groups, screen time (P=0.03), sweet drink consumption (P=0.03) and lack of household rules for television (TV) viewing (P=0.05) were associated with increased zBMI, whereas there was a non-significant association with the frequency the TV was on during evening meals (P=0.07). The moderating effect of the intervention was only evident for the relationship between the frequency of TV on during meals and zBMI, however, this effect was modest (P=0.04).

Conclusions: The development of childhood obesity involves multi-factorial and multi-level influences, some of which are amenable to change. Obesity prevention strategies should not only target individual behaviours but also the household environment and family practices. Although zBMI changes were modest, these findings are encouraging as small reductions can have population level impacts on childhood obesity levels.

A multilevel social network perspective on IT adoption

Adoption of technologies has long been a key area of research in the information systems (IS) discipline, and researchers have thus been interested in the attributes, beliefs, intentions, and behaviors of individuals and organisations that could explain information and communication technology (ICT) adoption. The focal unit of adoption has mainly been individuals and organisations, however, research at group or social network level as well as the inter-organizational level have recently gained increased interest from IS researchers. This recent focus supports the view of the world as being the sum of all relations. Various social network theories exist that seek to emphasize different proficiencies of social networks and explain theoretical mechanisms for behavior in social networks. The core idea of these theories is that social networks are valuable, and the relations among actors affect the behavior of individuals, groups, organizations, industries, and societies. IS researchers have also found that social network theory can help explain technology adoption. Some researchers, in addition, acknowledge that most adoption situations involve phenomena occuring at multiple levels, yet most technology adoption research applies a single level of analysis. Multilevel research can address the levels of theory, measurement, and analysis required to fully examining research questions. This paper therfore adapts the Coleman diagram into the Multi-level Framework of Technology. Adoption in order to explain how social network theory, at the individual and social network level, can help explain adoption of ICT. As Coleman (1990) attempts to create a link between the micro and macro level in a holistic manner, his approach is applicable in explaining ICT adoption

A multilevel trust management framework for service oriented environment

In service-oriented computing applications, trust management systems are emerging as a promising technology to improve the e-commerce consumers and provider's relationship. Both consumers and providers need to evaluate the trust levels of potential partners before engaging in interactions. The accuracy of trust evaluation greatly affects the success rate of the interaction. This paper addresses the threats and challenges that can compromise the reliability of the current trust management system. This paper studies and examines the importance of the trust factors of the trust management framework, specifically in dealing with malicious feedback ratings from e-commerce users. To improve the reliability of the trust management systems, an approach that addresses feedback-related vulnerabilities is paramount. A multilevel trust management system computes trust by combining different types of information. Using this combination, we introduce a multilevel framework for a new interactive trust management to improve the correctness in estimate of trust information.

Time-domain analysis of piezoelectric impedance-based structural health monitoring using multilevel wavelet decomposition

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Multilevel Model with Time Series Components for the Analysis of Tribal Art Prices

In the present work we perform an econometric analysis of the Tribal art market. To this aim, we use a unique and original database that includes information on Tribal art market auctions worldwide from 1998 to 2011. In Literature, art prices are modelled through the hedonic regression model, a classic fixed-effect model. The main drawback of the hedonic approach is the large number of parameters, since, in general, art data include many categorical variables. In this work, we propose a multilevel model for the analysis of Tribal art prices that takes into account the influence of time on artwork prices. In fact, it is natural to assume that time exerts an influence over the price dynamics in various ways. Nevertheless, since the set of objects change at every auction date, we do not have repeated measurements of the same items over time. Hence, the dataset does not constitute a proper panel; rather, it has a two-level structure in that items, level-1 units, are grouped in time points, level-2 units. The main theoretical contribution is the extension of classical multilevel models to cope with the case described above. In particular, we introduce a model with time dependent random effects at the second level. We propose a novel specification of the model, derive the maximum likelihood estimators and implement them through the E-M algorithm. We test the finite sample properties of the estimators and the validity of the own-written R-code by means of a simulation study. Finally, we show that the new model improves considerably the fit of the Tribal art data with respect to both the hedonic regression model and the classic multilevel model.

Analysis and Implementation of Multiphase-Multilevel Inverter for Open-Winding Loads

Research work carried out in focusing a novel multiphase-multilevel ac motor drive system much suitable for low-voltage high-current power applications. In specific, six-phase asymmetrical induction motor with open-end stator winding configuration, fed from four standard two-level three-phase voltage source inverters (VSIs). Proposed synchronous reference frame control algorithm shares the total dc source power among the 4 VSIs in each switching cycle with three degree of freedom. Precisely, first degree of freedom concerns with the current sharing between two three-phase stator windings. Based on modified multilevel space vector pulse width modulation shares the voltage between each single VSIs of two three-phase stator windings with second and third degree of freedom, having proper multilevel output waveforms. Complete model of whole ac motor drive based on three-phase space vector decomposition approach was developed in PLECS - numerical simulation software working in MATLAB environment. Proposed synchronous reference control algorithm was framed in MATLAB with modified multilevel space vector pulse width modulator. The effectiveness of the entire ac motor drives system was tested. Simulation results are given in detail to show symmetrical and asymmetrical, power sharing conditions. Furthermore, the three degree of freedom are exploited to investigate fault tolerant capabilities in post-fault conditions. Complete set of simulation results are provided when one, two and three VSIs are faulty. Hardware prototype model of quad-inverter was implemented with two passive three-phase open-winding loads using two TMS320F2812 DSP controllers. Developed McBSP (multi-channel buffered serial port) communication algorithm able to control the four VSIs for PWM communication and synchronization. Open-loop control scheme based on inverse three-phase decomposition approach was developed to control entire quad-inverter configuration and tested with balanced and unbalanced operating conditions with simplified PWM techniques. Both simulation and experimental results are always in good agreement with theoretical developments.

Multilevel Analysis in Household Survey: An Application to Health Condition Data

The aim of this thesis is to apply multilevel regression model in context of household surveys. Hierarchical structure in this type of data is characterized by many small groups. In last years comparative and multilevel analysis in the field of perceived health have grown in size. The purpose of this thesis is to develop a multilevel analysis with three level of hierarchy for Physical Component Summary outcome to: evaluate magnitude of within and between variance at each level (individual, household and municipality); explore which covariates affect on perceived physical health at each level; compare model-based and design-based approach in order to establish informativeness of sampling design; estimate a quantile regression for hierarchical data. The target population are the Italian residents aged 18 years and older. Our study shows a high degree of homogeneity within level 1 units belonging from the same group, with an intraclass correlation of 27% in a level-2 null model. Almost all variance is explained by level 1 covariates. In fact, in our model the explanatory variables having more impact on the outcome are disability, unable to work, age and chronic diseases (18 pathologies). An additional analysis are performed by using novel procedure of analysis :"Linear Quantile Mixed Model", named "Multilevel Linear Quantile Regression", estimate. This give us the possibility to describe more generally the conditional distribution of the response through the estimation of its quantiles, while accounting for the dependence among the observations. This has represented a great advantage of our models with respect to classic multilevel regression. The median regression with random effects reveals to be more efficient than the mean regression in representation of the outcome central tendency. A more detailed analysis of the conditional distribution of the response on other quantiles highlighted a differential effect of some covariate along the distribution.

An Input-Process-Output Approach to Interorganizational Teams: The Influence of Work Group Diversity, Trust and Shared Leadership on Communication Network and Team Outputs.

The market’s challenges bring firms to collaborate with other organizations in order to create Joint Ventures, Alliances and Consortia that are defined as “Interorganizational Networks” (IONs) (Provan, Fish and Sydow; 2007). Some of these IONs are managed through a shared partecipant governance (Provan and Kenis, 2008): a team composed by entrepreneurs and/or directors of each firm of an ION. The research is focused on these kind of management teams and it is based on an input-process-output model: some input variables (work group’s diversity, intra-team's friendship network density) have a direct influence on the process (team identification, shared leadership, interorganizational trust, team trust and intra-team's communication network density), which influence some team outputs, individual innovation behaviors and team effectiveness (team performance, work group satisfaction and ION affective commitment). Data was collected on a sample of 101 entrepreneurs grouped in 28 ION’s government teams and the research hypotheses are tested trough the path analysis and the multilevel models. As expected trust in team and shared leadership are positively and directly related to team effectiveness while team identification and interorganizational trust are indirectly related to the team outputs. The friendship network density among the team’s members has got positive effects on the trust in team and on the communication network density, and also, through the communication network density it improves the level of the teammates ION affective commitment. The shared leadership and its effects on the team effectiveness are fostered from higher level of team identification and weakened from higher level of work group diversity, specifically gender diversity. Finally, the communication network density and shared leadership at the individual level are related to the frequency of individual innovative behaviors. The dissertation’s results give a wider and more precise indication about the management of interfirm network through “shared” form of governance.

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

A MULTILEVEL MODEL TO ADDRESS BATCH EFFECTS IN COPY NUMBER ESTIMATION USING SNP ARRAYS

Submicroscopic changes in chromosomal DNA copy number dosage are common and have been implicated in many heritable diseases and cancers. Recent high-throughput technologies have a resolution that permits the detection of segmental changes in DNA copy number that span thousands of basepairs across the genome. Genome-wide association studies (GWAS) may simultaneously screen for copy number-phenotype and SNP-phenotype associations as part of the analytic strategy. However, genome-wide array analyses are particularly susceptible to batch effects as the logistics of preparing DNA and processing thousands of arrays often involves multiple laboratories and technicians, or changes over calendar time to the reagents and laboratory equipment. Failure to adjust for batch effects can lead to incorrect inference and requires inefficient post-hoc quality control procedures that exclude regions that are associated with batch. Our work extends previous model-based approaches for copy number estimation by explicitly modeling batch effects and using shrinkage to improve locus-specific estimates of copy number uncertainty. Key features of this approach include the use of diallelic genotype calls from experimental data to estimate batch- and locus-specific parameters of background and signal without the requirement of training data. We illustrate these ideas using a study of bipolar disease and a study of chromosome 21 trisomy. The former has batch effects that dominate much of the observed variation in quantile-normalized intensities, while the latter illustrates the robustness of our approach to datasets where as many as 25% of the samples have altered copy number. Locus-specific estimates of copy number can be plotted on the copy-number scale to investigate mosaicism and guide the choice of appropriate downstream approaches for smoothing the copy number as a function of physical position. The software is open source and implemented in the R package CRLMM available at Bioconductor (http:www.bioconductor.org).

ON MARGINALIZED MULTILEVEL MODELS AND THEIR COMPUTATION

Clustered data analysis is characterized by the need to describe both systematic variation in a mean model and cluster-dependent random variation in an association model. Marginalized multilevel models embrace the robustness and interpretations of a marginal mean model, while retaining the likelihood inference capabilities and flexible dependence structures of a conditional association model. Although there has been increasing recognition of the attractiveness of marginalized multilevel models, there has been a gap in their practical application arising from a lack of readily available estimation procedures. We extend the marginalized multilevel model to allow for nonlinear functions in both the mean and association aspects. We then formulate marginal models through conditional specifications to facilitate estimation with mixed model computational solutions already in place. We illustrate this approach on a cerebrovascular deficiency crossover trial.

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we develop multilevel latent class model, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.