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

Factors of convergence and divergence in union membership

This paper considers to what extent union decline in Britain has been characterised by convergence or divergence in union membership rates for people with different personal and job characteristics. It compares data on individual union membership in 1975, from a period when union membership was high and growing, to data in 2001 data when it is low and has been falling for over twenty years. Some factors of both convergence and divergence are identified. The clearest individual characteristic of convergence is gender. In 1975 there was a big male-female gap in union membership, whilst by 2001 one cannot reject the hypothesis that union membership rates were equal for men and women. The clearest case of divergence is age where the 1975-2001 period sees a widening of the age gap in union membership status. Other factors of convergence are the full- time/part-time status of jobs, ethnicity and workplace size. Other factors of divergence are industry and educational qualifications. Some other factors (like region) are neutral in that their relationship with union membership remains stable through time. Identification of these factors of convergence and divergence should be useful to many parties, including industrial relations scholars and union organisers. Finally, the fact that the magnitude of the relationships between union membership and a number of its determinants have shifted through time illustrates that one should be careful if one wishes to talk about empirical regularities in who is more or less likely to become a trade union member

Human Associations Help to Detect Conventionalized Multiword Expressions

In this paper we show that if we want to obtain human evidence about conventionalization of some phrases, we should ask native speakers about associations they have to a given phrase and its component words. We have shown that if component words of a phrase have each other as frequent associations, then this phrase can be considered as conventionalized. Another type of conventionalized phrases can be revealed using two factors: low entropy of phrase associations and low intersection of component word and phrase associations. The association experiments were performed for the Russian language

A probabilistic framework for analysing the compositionality of conceptual combinations

Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilised in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual combinations are compositional, and so can be considered as a function of the semantics of the constituent concepts, or not. While the systematicity and productivity of language provide a strong argument in favor of assuming compositionality, this very assumption is still regularly questioned in both cognitive science and philosophy. Additionally, the principle of semantic compositionality is underspecified, which means that notions of both "strong" and "weak" compositionality appear in the literature. Rather than adjudicating between different grades of compositionality, the framework presented here contributes formal methods for determining a clear dividing line between compositional and non-compositional semantics. In addition, we suggest that the distinction between these is contextually sensitive. Compositionality is equated with a joint probability distribution modeling how the constituent concepts in the combination are interpreted. Marginal selectivity is introduced as a pivotal probabilistic constraint for the application of the Bell/CH and CHSH systems of inequalities. Non-compositionality is equated with a failure of marginal selectivity, or violation of either system of inequalities in the presence of marginal selectivity. This means that the conceptual combination cannot be modeled in a joint probability distribution, the variables of which correspond to how the constituent concepts are being interpreted. The formal analysis methods are demonstrated by applying them to an empirical illustration of twenty-four non-lexicalised conceptual combinations