On proximity and hierarchy : exploring and modelling space using multilevel modelling and spatial econometrics

Spatial econometrics and also multilevel modelling techniques are increasingly part of the regional scientists‟ toolbox. Both approaches are used to model spatial autocorrelation in a wide variety of applications. However, it is not always clear on which basis researchers make a choice between spatial econometrics and spatial multilevel modelling. Therefore it is useful to compare both techniques. Spatial econometrics incorporates neighbouring areas into the model design; and thus interprets spatial proximity as defined in Tobler‟s first law of geography. On the other hand, multilevel modelling using geographical units takes a more hierarchical approach. In this case the first law of geography can be rephrased as „everything is related to everything else, but things in the same region are more related than things in different regions‟. The hierarchy (multilevel) and the proximity (spatial econometrics) approach are illustrated using Belgian mobility data and productivity data of European regions. One of the advantages of a multilevel model is that it can incorporate more than two levels (spatial scales). Another advantage is that a multilevel structure can easily reflect an administrative structure with different government levels. Spatial econometrics on the other hand works with a unique set of neighbours which has the advantage that there still is a relation between neighbouring municipalities separated by a regional boundary. The concept of distance can also more easily be incorporated in a spatial econometrics setting. Both spatial econometrics and spatial multilevel modelling proved to be valuable techniques in spatial research but more attention should go to the rationale why one of the two approaches is chosen. We conclude with some comments on models which make a combination of both techniques

Multilevel Coupled Model Transformations for Precise and Reusable Definition of Model Behaviour

The use of Domain-Specific Languages (DSLs) is a promising field for the development of tools tailored to specific problem spaces, effectively diminishing the complexity of hand-made software. With the goal of making models as precise, simple and reusable as possible, we augment DSLs with concepts from multilevel modelling, where the number of abstraction levels are not limited. This is particularly useful for DSL definitions with behaviour, whose concepts inherently belong to different levels of abstraction. Here, models can represent the state of the modelled system and evolve using model transformations. These transformations can benefit from a multilevel setting, becoming a precise and reusable definition of the semantics for behavioural modelling languages. We present in this paper the concept of Multilevel Coupled Model Transformations, together with examples, formal definitions and tools to assess their conceptual soundness and practical value.Comment: Journal of Logical and Algebraic Methods in Programming. Available online 11 January 2019. In Press, Accepted Manuscrip

Carpooling and employers: a multilevel modelling approach

Both public policy-makers and private companies promote carpooling as a commuting alternative in order to reduce the number of Single Occupant Vehicle (SOV) users. The Belgian questionnaire Home-To-Work-Travel (HTWT) is used to examine the factors which explain the share of carpooling employees at a worksite. The modal split between carpooling and rail use was also subject of the analysis. The number of observations in the HTWT database (n=7460) makes it possible to use more advanced statistical models: such as multilevel regression models which incorporate, next to the worksite level, also the company and economic sector levels. As a consequence, a more employer-oriented approach replaces the traditional focus of commuting research on the individual. Significant differences in modal split between economic sectors appeared. The most carpool-oriented sectors are construction and manufacturing, while rail transport is more popular in the financial and public sector. Carpooling also tend to be an alternative at locations where rail is no real alternative. Next to this, regular work schedules and smaller sites are positively correlated with a higher share of carpooling employees. Finally, no real evidence could be found for the effectiveness of mobility management measures which promote carpooling. However, most of these measures are classified in the literature as less effective and a case study approach should complete the research on mobility management initiatives

Power loss investigation in HVDC for cascaded H-bridge multilevel inverters (CHB-MLI)

In the last decade, the use of voltage-source multilevel inverters in industrial and utility power applications has been increased significantly mainly due to the many advantages of multilevel inverters, compared to conventional two level inverters. These advantages include: 1) higher output voltage at low switching frequency, 2) low voltage stress (dv/dt), 3) lower total harmonic distortion (THD), 4) less electro-magnetic interference (EMI), 5) smaller output filter, and 6) higher fundamental output. However, the computation of multilevel inverter power losses is much more complicated compared to conventional two level inverters. This paper presents a detailed investigation of CHB-MLI losses for HVDC. Different levels, and IGBT switching devices have been considered in the study. The inverter has been controlled using selective harmonic elimination in which the switching angles were determined using the Genetic Algorithm (GA). MATLAB-SIMULINK is used for the modelling and simulation. This investigation should result in a deeper knowledge and understanding of the performance of CHB-MLI using different IGBT switching devices

Fitting multilevel multivariate models with missing data in responses and covariates that may include interactions and non-linear terms

The paper extends existing models for multilevel multivariate data with mixed response types to handle quite general types and patterns of missing data values in a wide range of multilevel generalized linear models. It proposes an efficient Bayesian modelling approach that allows missing values in covariates, including models where there are interactions or other functions of covariates such as polynomials. The procedure can also be used to produce multiply imputed complete data sets. A simulation study is presented as well as the analysis of a longitudinal data set. The paper also shows how existing multiprocess models for handling endogeneity can be extended by the framework proposed

Precise modelling of switching and conduction losses in cascaded h-bridge multilevel inverters

Nowadays, voltage source multilevel inverters are being used extensively in industry due to its many advantages, compared to conventional two level inverters, such as higher output voltage at low switching frequency, low voltage stress(dv/dt), lower total harmonic distortion (THD), less electro-magnetic interference (EMI), smaller output filter and higher fundamental output. However, the evaluation of multilevel inverter losses is much more complicated compared to two level inverters. This paper proposes an on-line model for precise calculation of conduction and switching losses for cascaded h-bridge multilevel inverter. The model is simple and efficient and gives clear process of loss calculation. A singlephase 7-level cascaded h-bridge with IGBT's as switching devices has been used as a case study of the proposed model. The inverter has been controlled using selective harmonic elimination in which the switching angles were determined using the Genetic Algorithm (GA). MATLAB-SIMULINK is used for the modelling and simulation

Marker effects and examination reliability: a comparative exploration from the perspectives of generalizability theory, Rasch modelling and multilevel modelling

This study looked at how three different analysis methods could help us to understand rater effects on exam reliability. The techniques we looked at were: generalizability theory (G-theory) item response theory (IRT): in particular the Many-Facets Partial Credit Rasch Model (MFRM) multilevel modelling (MLM) We used data from AS component papers in geography and psychology for 2009, 2010 and 2011 from Edexcel.</p

Multilevel Modelling with Spatial Effects

In multilevel modelling, interest in modeling the nested structure of hierarchical data has been accompanied by increasing attention to di¤erent forms of spatial interactions across different levels of the hierarchy. Neglecting such interactions is likely to create problems of inference, which typically assumes independence. In this paper we review approaches to multilevel modelling with spatial e¤ects, and attempt to connect the two literatures, discussing the advantages and limitations of various approaches.Multilevel Modelling, Spatial E¤ects, Fixed E¤ects, Random E¤ects, IGLS, FGS2SLS.

Multilevel Models with Stochastic Volatility for Repeated Cross-Sections: an Application to tribal Art Prices

In this paper we introduce a multilevel specification with stochastic volatility for repeated cross-sectional data. Modelling the time dynamics in repeated cross sections requires a suitable adaptation of the multilevel framework where the individuals/items are modelled at the first level whereas the time component appears at the second level. We perform maximum likelihood estimation by means of a nonlinear state space approach combined with Gauss-Legendre quadrature methods to approximate the likelihood function. We apply the model to the first database of tribal art items sold in the most important auction houses worldwide. The model allows to account properly for the heteroscedastic and autocorrelated volatility observed and has superior forecasting performance. Also, it provides valuable information on market trends and on predictability of prices that can be used by art markets stakeholders

A Model for the Analysis of Caries Occurrence in Primary Molar Tooth Surfaces

Recently methods of caries quantification in the primary dentition have moved away from summary ‘whole mouth’ measures at the individual level to methods based on generalised linear modelling (GLM) approaches or survival analysis approaches. However, GLM approaches based on logistic transformation fail to take into account the time-dependent process of tooth/surface survival to caries. There may also be practical difficulties associated with casting parametric survival-based approaches in a complex multilevel hierarchy and the selection of an optimal survival distribution, while non-parametric survival methods are not generally suitable for the assessment of supplementary information recorded on study participants. In the current investigation, a hybrid semi-parametric approach comprising elements of survival-based and GLM methodologies suitable for modelling of caries occurrence within fixed time periods is assessed, using an illustrative multilevel data set of caries occurrence in primary molars from a cohort study, with clustering of data assumed to occur at surface and tooth levels. Inferences of parameter significance were found to be consistent with previous parametric survival-based analyses of the same data set, with gender, socio-economic status, fluoridation status, tooth location, surface type and fluoridation status-surface type interaction significantly associated with caries occurrence. The appropriateness of the hierarchical structure facilitated by the hybrid approach was also confirmed. Hence the hybrid approach is proposed as a more appropriate alternative to primary caries modelling than non-parametric survival methods or other GLM-based models, and as a practical alternative to more rigorous survival-based methods unlikely to be fully accessible to most researchers