A Bayesian spatial random effects model characterisation of tumour heterogeneity implemented using Markov chain Monte Carlo (MCMC) simulation

The focus of this study is the development of a statistical modelling procedure for characterising intra-tumour heterogeneity, motivated by recent clinical literature indicating that a variety of tumours exhibit a considerable degree of genetic spatial variability. A formal spatial statistical model has been developed and used to characterise the structural heterogeneity of a number of supratentorial primitive neuroecto-dermal tumours (PNETs), based on diffusionweighted magnetic resonance imaging. Particular attention is paid to the spatial dependence of diffusion close to the tumour boundary, in order to determine whether the data provide statistical evidence to support the proposition that water diffusivity in the boundary region of some tumours exhibits a deterministic dependence on distance from the boundary, in excess of an underlying random 2D spatial heterogeneity in diffusion. Tumour spatial heterogeneity measures were derived from the diffusion parameter estimates obtained using a Bayesian spatial random effects model. The analyses were implemented using Markov chain Monte Carlo (MCMC) simulation. Posterior predictive simulation was used to assess the adequacy of the statistical model. The main observations are that the previously reported relationship between diffusion and boundary proximity remains observable and achieves statistical significance after adjusting for an underlying random 2D spatial heterogeneity in the diffusion model parameters. A comparison of the magnitude of the boundary-distance effect with the underlying random 2D boundary heterogeneity suggests that both are important sources of variation in the vicinity of the boundary. No consistent pattern emerges from a comparison of the boundary and core spatial heterogeneity, with no indication of a consistently greater level of heterogeneity in one region compared with the other. The results raise the possibility that DWI might provide a surrogate marker of intra-tumour genetic regional heterogeneity, which would provide a powerful tool with applications in both patient management and in cancer research

Species richness-environment relationships of European arthropods at two spatial grains : habitats and countries

We study how species richness of arthropods relates to theories concerning net primary productivity, ambient energy, water-energy dynamics and spatial environmental heterogeneity. We use two datasets of arthropod richness with similar spatial extents (Scandinavia to Mediterranean), but contrasting spatial grain (local habitat and country). Samples of ground-dwelling spiders, beetles, bugs and ants were collected from 32 paired habitats at 16 locations across Europe. Species richness of these taxonomic groups was also determined for 25 European countries based on the Fauna Europaea database. We tested effects of net primary productivity (NPP), annual mean temperature (T), annual rainfall (R) and potential evapotranspiration of the coldest month (PETmin) on species richness and turnover. Spatial environmental heterogeneity within countries was considered by including the ranges of NPP, T, R and PETmin. At the local habitat grain, relationships between species richness and environmental variables differed strongly between taxa and trophic groups. However, species turnover across locations was strongly correlated with differences in T. At the country grain, species richness was significantly correlated with environmental variables from all four theories. In particular, species richness within countries increased strongly with spatial heterogeneity in T. The importance of spatial heterogeneity in T for both species turnover across locations and for species richness within countries suggests that the temperature niche is an important determinant of arthropod diversity. We suggest that, unless climatic heterogeneity is constant across sampling units, coarse-grained studies should always account for environmental heterogeneity as a predictor of arthropod species richness, just as studies with variable area of sampling units routinely consider area

Dundee Discussion Papers in Economics 253:Spatial Interactions in Hedonic Pricing Models: The Urban Housing Market of Aveiro, Portugal

Spatial heterogeneity, spatial dependence and spatial scale constitute key features of spatial analysis of housing markets. However, the common practice of modelling spatial dependence as being generated by spatial interactions through a known spatial weights matrix is often not satisfactory. While existing estimators of spatial weights matrices are based on repeat sales or panel data, this paper takes this approach to a cross-section setting. Specifically, based on an a priori definition of housing submarkets and the assumption of a multifactor model, we develop maximum likelihood methodology to estimate hedonic models that facilitate understanding of both spatial heterogeneity and spatial interactions. The methodology, based on statistical orthogonal factor analysis, is applied to the urban housing market of Aveiro, Portugal at two different spatial scales

Overlapping jurisdictions and demand for local public services: does spatial heterogeneity matter?

This paper aims to test the existence of vertical interactions in terms of public spending between overlapping local jurisdictions in France using a data set of 110 French municipalities and their corresponding departments in 2001 and 2005. To do so, we consider that demand for municipal services is conditioned by the services provided by departments. We then estimate two specifications which allow spatial heterogeneity to be modeled and which are compared with a simple spatial error specification (without spatial heterogeneity). The two estimated spatial regimes models are able to eradicate spatial autocorrelation in the error term. The estimation results show that an appropriate consideration of spatial heterogeneity can lead to new insights. The spatial error specification reveals a robust complementary demand relationship between services provided by departmental and municipal governments. However, these results are not in accord with the results produced by the spatial regime models, which provide evidence of heterogeneity with independence, complementarity or substitution between the services offered by the two overlapping jurisdictions.Local public expenditures; Overlapping jurisdictions; Spatial heterogeneity; Spatial econometrics

Local Geography of Row-Crop Quality Land and Cropland Cash Rental Rates

While farmland rental markets are likely to be spatially differentiated, the fine spatial structure of row-crop quality land should have a significant effect on cash rent determination. This study provides a rigorous empirical understanding of the effect of land spatial heterogeneity on cash rental rates. The lacunarity index is employed to measure spatial heterogeneity of land quality, which is built directly upon a soil quality measure, the land parcel’s corn suitability rating index (CSR). A panel data random effect model is applied on annual survey data of farmland cash rental rates of Iowa for 1987-2009. As expected, land spatial heterogeneity has a statistically significant and negative effect on local cash rent rates. The effect’s origin warrants further research.land spatial heterogeneity, rental market, Agricultural Finance, C5, G1, Q1,

Incorporating Spatial Complexity into Economic Models of Land Markets and Land Use Change

Recent work in regional science, geography, and urban economics has advanced spatial modeling of land markets and land use by incorporating greater spatial complexity, including multiple sources of spatial heterogeneity, multiple spatial scales, and spatial dynamics. Doing so has required a move away from relying solely on analytical models to partial or full reliance on computational methods that can account for these added features of spatial complexity. In the first part of the paper, we review economic models of urban land development that have incorporated greater spatial complexity, focusing on spatial simulation models with spatial endogenous feedbacks and multiple sources of spatial heterogeneity. The second part of the paper presents a spatial simulation model of exurban land development using an auction model to represent household bidding that extends the traditional Capozza and Helsley (1990) model of urban growth to account for spatial dynamics in the form of local land use spillovers and spatially heterogeneous land characteristics.urban growth, urbanization, land development, spatial dynamics, heterogeneity, agent-based models, spatial interactions, Land Economics/Use, Research Methods/ Statistical Methods,

Forecasting with Spatial Panel Data

This paper compares various forecasts using panel data with spatial error correlation. The true data generating process is assumed to be a simple error component regression model with spatial remainder disturbances of the autoregressive or moving average type. The best linear unbiased predictor is compared with other forecasts ignoring spatial correlation, or ignoring heterogeneity due to the individual effects, using Monte Carlo experiments. In addition, we check the performance of these forecasts under misspecification of the spatial error process, various spatial weight matrices, and heterogeneous rather than homogeneous panel data models.forecasting, BLUP, panel data, spatial dependence, heterogeneity

The European Regional Convergence Process, 1980-1995: Do Spatial Regimes and Spatial Dependence Matter?

We show in this paper that spatial dependence and spatial heterogeneity matter in the estimation of the b-convergence process among 138 European regions over the 1980-1995 period. Using spatial econometrics tools, we detect both spatial dependence and spatial heterogeneity in the form of structural instability across spatial convergence clubs. The estimation of the appropriate spatial regimes spatial error model shows that the convergence process is different across regimes. We also estimate a strongly significant spatial spillover effect: the average growth rate of per capita GDP of a given region is positively affected by the average growth rate of neighboring regions.convergence, club convergence, spatial econometrics, European regions, spatial regimes, spatial autocorrelation

Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production.We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations

Evaluating the Temporal and the Spatial Heterogeneity of the European Convergence Process, 1980-1999

In this paper, we suggest a general framework that allows testing simultaneously for temporal heterogeneity, spatial heterogeneity and spatial autocorrelation in b-convergence models. Based on a sample of 145 European regions over the 1980-1999 period, we estimate a Seemingly Unrelated Regression Model with spatial regimes and spatial autocorrelation for two sub-periods: 1980-1989 and 1989-1999. The assumption of temporal independence between the two-periods is rejected and the estimation results point to the presence of spatial error autocorrelation in both sub-periods and spatial instability in the second sub-period, indicating the formation of a convergence club between the peripheral regions of the European Union.b-convergence models, spatial autocorrelation, convergence clubs, temporal instability