Modeling Transport Mode Decisions Using Hierarchical Binary Spatial Regression Models with Cluster Effects

This work is motivated by a mobility study conducted in the city of Munich, Germany. The variable of interest is a binary response, which indicates whether public transport has been utilized or not. One of the central questions is to identify areas of low/high utilization of public transport after adjusting for explanatory factors such as trip, individual and household attributes. The goal is to develop flexible statistical models for a binary response with covariate, spatial and cluster effects. One approach for modeling spatial effects are Markov Random Fields (MRF). A modification of a class of MRF models with proper joint distributions introduced by Pettitt et al. (2002) is developed. This modification has the desirable property to contain the intrinsic MRF in the limit and still allows for efficient spatial parameter updates in Markov Chain Monte Carlo (MCMC) algorithms. In addition to spatial effects, cluster effects are taken into consideration. Group and individual approaches for modeling these effects are suggested. The first one models heterogeneity between clusters, while the second one models heterogeneity within clusters. A naive approach to include individual cluster effects results in an unidentifiable model. It is shown how an appropriate reparametrization gives identifiable parameters. This provides a new approach for modeling heterogeneity within clusters. For hierarchical spatial binary regression models with individual cluster effects two MCMC algorithms for parameter estimation are developed. The first one is based on a direct evaluation of the likelihood. The second one is based on the representation of binary responses with Gaussian latent variables through a threshold mechanism, which is particularly useful for probit models. Simulation results show a satisfactory behavior of the MCMC algorithms developed. Finally the proposed model classes are applied to the mobility study and results are interpreted

Modelling the Dairy Farm Size Distribution in Poland Using an Instrumental Variable Generalized Cross Entropy Markov Approach

The aim of this paper is to analyse the evolution of the dairy farm structure of Poland during the post-socialist period. First the paper focuses on how the farm structure has changed over time and what path it is likely to follow in the coming decade. Second, it is tested whether the evolution of farm size is explained by non-stationary effects. Finally, several statistical indicators are computed on farm mobility and on which farms are likely to survive. An instrumental variable generalised cross entropy Markov chain approach which incorporates prior information is applied for estimation. Prior information included general and plausible information on farm mobility and structural adjustments based on independent literature. The projections show that dairy farm numbers will continue to decline, although accompanied by an increase in the number of medium-sized and large farms. Subsistence dairy farms are expected to slowly leave the sector in the coming decade.dairy, farm size, Poland, Markov chain, generalised cross entropy., Livestock Production/Industries,

Modelling dairy farm size distribution in Poland using an instrumental variable generalized cross entropy markov chain approach

The aim of this paper is to analyse the evolution of the dairy farm structure of Poland during the post-socialist period. First the paper focuses on how the farm structure has changed over time and what path it is likely to follow in the coming decade. Second, it is tested whether the evolution of farm size is explained by non-stationary effects. Finally, several statistical indicators are computed on farm mobility and on which farms are likely to survive. An instrumental variable generalised cross entropy Markov chain approach which incorporates prior information is applied for estimation. Prior information included general and plausible information on farm mobility and structural adjustments based on independent literature. The projections show that dairy farm numbers will continue to decline, although accompanied by an increase in the number of medium-sized and large farms. Subsistence dairy farms are expected to slowly leave the sector in the coming decade

Quasichemical Models of Multicomponent Nonlinear Diffusion

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between components. We develop an approach to nonlinear multicomponent diffusion based on the idea of the reaction mechanism borrowed from chemical kinetics. Chemical kinetics gave rise to very seminal tools for the modeling of processes. This is the stoichiometric algebra supplemented by the simple kinetic law. The results of this invention are now applied in many areas of science, from particle physics to sociology. In our work we extend the area of applications onto nonlinear multicomponent diffusion. We demonstrate, how the mechanism based approach to multicomponent diffusion can be included into the general thermodynamic framework, and prove the corresponding dissipation inequalities. To satisfy thermodynamic restrictions, the kinetic law of an elementary process cannot have an arbitrary form. For the general kinetic law (the generalized Mass Action Law), additional conditions are proved. The cell--jump formalism gives an intuitively clear representation of the elementary transport processes and, at the same time, produces kinetic finite elements, a tool for numerical simulation.Comment: 81 pages, Bibliography 118 references, a review paper (v4: the final published version