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 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.

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

An Approach to Flexible Multilevel Modelling

Multilevel modelling approaches tackle issues related to lack of flexibility and mixed levels of abstraction by providing features like deep modelling and linguistic extension. However, the lack of a clear consensus on fundamental concepts of the paradigm has in turn led to lack of common focus in current multilevel modelling tools and their adoption. In this paper, we propose a formal framework, together with its corresponding tools, to tackle these challenges. The approach facilitates definition of flexible multilevel modelling hierarchies by allowing addition and deletion of intermediate abstraction levels in the hierarchies. Moreover, it facilitates separation of concerns by allowing integration of different multilevel modelling hierarchies as different aspects of the system to be modelled. In addition, our approach facilitates reusability of concepts and their behaviour by allowing definition of flexible transformation rules which are applicable to different hierarchies with a variable number of levels. As a proof of concept, a prototype tool and a domain-specific language for the definition of these rules is provided.publishedVersio

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

Modelling football match scoring outcomes using multilevel models

Multilevel modelling technique recognizes the existence of hierarchal structures in the data by allowing for random effects at each level in the hierarchy, thus assessing the variation in the dependent variable at several hierarchical levels simultaneously. Multilevel modelling is becoming an increasingly popular technique for analysing nested data with such popularity accredited to the computational advances in the last two decades. In many sports, including football, the game fixtures are nested within seasons, which in turn are nested within country leagues invoking a multilevel structure in the data. Many gaming companies engage in sport data analysis in a bid to understand the dynamics and patterns of the game. This will assist the gaming company in developing fantasy sport games that will enhance gamer engagement and augment revenue to the company. This paper presents a comprehensive description of two and three level models, which are applied to a real football data set accessed from an online free football betting portal. The aim is to examine the relationship between the number of goals scored during a football match and several game-related predictors. These multilevel models, which assume a Poisson distribution and a logarithmic function, are implemented using the facilities of GLLAMM (Generalized Linear Latent and Mixed Models), which is a subroutine of STATA.peer-reviewe

Multilevel modelling of mechanical properties of textile composites: ITOOL Project

The paper presents an overview of the multi-level modelling of textile composites in the ITOOL project, focusing on the models of textile reinforcements, which serve as a basis for micromechanical models of textile composites on the unit cell level. The modelling is performed using finite element analysis (FEA) or approximate methods (method of inclusions), which provide local stiffness and damage information to FEA of composite part on the macro-level

Alternative approaches to multilevel modelling of survey noncontact and refusal

We review three alternative approaches to modelling survey noncontact and refusal: multinomial, sequential and sample selection (bivariate probit) models. We then propose a multilevel extension of the sample selection model to allow for both interviewer effects and dependency between noncontact and refusal rates at the household and interviewer level. All methods are applied and compared in an analysis of household nonresponse in the UK, using a dataset with unusually rich information on both respondents and nonrespondents from six major surveys. After controlling for household characteristics, there is little evidence of residual correlation between the unobserved characteristics affecting noncontact and refusal propensities at either the household or the interviewer level. We also find that the estimated coefficients of the multinomial and sequential models are surprisingly similar, which further investigation via a simulation study suggests is due to there being little overlap between the predictors of noncontact and refusal

Multilevel Modelling for Public Health and Health Services Research

This open access book is a practical introduction to multilevel modelling or multilevel analysis (MLA) – a statistical technique being increasingly used in public health and health services research. The authors begin with a compelling argument for the importance of researchers in these fields having an understanding of MLA to be able to judge not only the growing body of research that uses it, but also to recognise the limitations of research that did not use it. The volume also guides the analysis of real-life data sets by introducing and discussing the use of the multilevel modelling software MLwiN, the statistical package that is used with the example data sets. Importantly, the book also makes the training material accessible for download – not only the datasets analysed within the book, but also a freeware version of MLwiN to allow readers to work with these datasets. The book’s practical review of MLA comprises: Theoretical, conceptual, and methodological background Statistical background The modelling process and presentation of research Tutorials with example datasets Multilevel Modelling for Public Health and Health Services Research: Health in Context is a practical and timely resource for public health and health services researchers, statisticians interested in the relationships between contexts and behaviour, graduate students across these disciplines, and anyone interested in utilising multilevel modelling or multilevel analysis. “Leyland and Groenewegen’s wealth of teaching experience makes this book and its accompanying tutorials especially useful for a practical introduction to multilevel analysis.” ̶ Juan Merlo, Professor of Social Epidemiology, Lund University “Comprehensive and insightful. A must for anyone interested in the applications of multilevel modelling to population health”. ̶ S. (Subu) V. Subramanian, Professor of Population Health and Geography, Harvard University ; For researchers and students with a basic mastery of ordinary least squares and logistic regression Discusses multilevel analysis in context of public health, health services research, and epidemiology Includes an online component where users can download the datasets analyzed in the book, and also a freeware version of the multilevel modelling software MLwiN ​​​​​​​Can be used as part of a course on multilevel modelling, or as a self-training tex