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

Transition States in Protein Folding Kinetics: The Structural Interpretation of Phi-values

Phi-values are experimental measures of the effects of mutations on the folding kinetics of a protein. A central question is which structural information Phi-values contain about the transition state of folding. Traditionally, a Phi-value is interpreted as the 'nativeness' of a mutated residue in the transition state. However, this interpretation is often problematic because it assumes a linear relation between the nativeness of the residue and its free-energy contribution. We present here a better structural interpretation of Phi-values for mutations within a given helix. Our interpretation is based on a simple physical model that distinguishes between secondary and tertiary free-energy contributions of helical residues. From a linear fit of our model to the experimental data, we obtain two structural parameters: the extent of helix formation in the transition state, and the nativeness of tertiary interactions in the transition state. We apply our model to all proteins with well-characterized helices for which more than 10 Phi-values are available: protein A, CI2, and protein L. The model captures nonclassical Phi-values 1 in these helices, and explains how different mutations at a given site can lead to different Phi-values.Comment: 26 pages, 7 figures, 5 table

A mixed model approach for structured hazard regression

The classical Cox proportional hazards model is a benchmark approach to analyze continuous survival times in the presence of covariate information. In a number of applications, there is a need to relax one or more of its inherent assumptions, such as linearity of the predictor or the proportional hazards property. Also, one is often interested in jointly estimating the baseline hazard together with covariate effects or one may wish to add a spatial component for spatially correlated survival data. We propose an extended Cox model, where the (log-)baseline hazard is weakly parameterized using penalized splines and the usual linear predictor is replaced by a structured additive predictor incorporating nonlinear effects of continuous covariates and further time scales, spatial effects, frailty components, and more complex interactions. Inclusion of time-varying coefficients leads to models that relax the proportional hazards assumption. Nonlinear and time-varying effects are modelled through penalized splines, and spatial components are treated as correlated random effects following either a Markov random field or a stationary Gaussian random field. All model components, including smoothing parameters, are specified within a unified framework and are estimated simultaneously based on mixed model methodology. The estimation procedure for such general mixed hazard regression models is derived using penalized likelihood for regression coefficients and (approximate) marginal likelihood for smoothing parameters. Performance of the proposed method is studied through simulation and an application to leukemia survival data in Northwest England