Matching Items (3)
- All Subjects: spatial statistics
- All Subjects: Spatial linear mixed model
- Creators: Li, Ziqi
- Creators: Lu, Xuetao
- Creators: Rey, Sergio S.J.
- Creators: Zhou, Shuang
As urban populations become increasingly dense, massive amounts of new 'big' data that characterize human activity are being made available and may be characterized as having a large volume of observations, being produced in real-time or near real-time, and including a diverse variety of information. In particular, spatial interaction (SI) data - a collection of human interactions across a set of origins and destination locations - present unique challenges for distilling big data into insight. Therefore, this dissertation identifies some of the potential and pitfalls associated with new sources of big SI data. It also evaluates methods for modeling SI to investigate the relationships that drive SI processes in order to focus on human behavior rather than data description.
A critical review of the existing SI modeling paradigms is first presented, which also highlights features of big data that are particular to SI data. Next, a simulation experiment is carried out to evaluate three different statistical modeling frameworks for SI data that are supported by different underlying conceptual frameworks. Then, two approaches are taken to identify the potential and pitfalls associated with two newer sources of data from New York City - bike-share cycling trips and taxi trips. The first approach builds a model of commuting behavior using a traditional census data set and then compares the results for the same model when it is applied to these newer data sources. The second approach examines how the increased temporal resolution of big SI data may be incorporated into SI models.
Several important results are obtained through this research. First, it is demonstrated that different SI models account for different types of spatial effects and that the Competing Destination framework seems to be the most robust for capturing spatial structure effects. Second, newer sources of big SI data are shown to be very useful for complimenting traditional sources of data, though they are not sufficient substitutions. Finally, it is demonstrated that the increased temporal resolution of new data sources may usher in a new era of SI modeling that allows us to better understand the dynamics of human behavior.
Spatial regression is one of the central topics in spatial statistics. Based on the goals, interpretation or prediction, spatial regression models can be classified into two categories, linear mixed regression models and nonlinear regression models. This dissertation explored these models and their real world applications. New methods and models were proposed to overcome the challenges in practice. There are three major parts in the dissertation.
In the first part, nonlinear regression models were embedded into a multistage workflow to predict the spatial abundance of reef fish species in the Gulf of Mexico. There were two challenges, zero-inflated data and out of sample prediction. The methods and models in the workflow could effectively handle the zero-inflated sampling data without strong assumptions. Three strategies were proposed to solve the out of sample prediction problem. The results and discussions showed that the nonlinear prediction had the advantages of high accuracy, low bias and well-performed in multi-resolution.
In the second part, a two-stage spatial regression model was proposed for analyzing soil carbon stock (SOC) data. In the first stage, there was a spatial linear mixed model that captured the linear and stationary effects. In the second stage, a generalized additive model was used to explain the nonlinear and nonstationary effects. The results illustrated that the two-stage model had good interpretability in understanding the effect of covariates, meanwhile, it kept high prediction accuracy which is competitive to the popular machine learning models, like, random forest, xgboost and support vector machine.
A new nonlinear regression model, Gaussian process BART (Bayesian additive regression tree), was proposed in the third part. Combining advantages in both BART and Gaussian process, the model could capture the nonlinear effects of both observed and latent covariates. To develop the model, first, the traditional BART was generalized to accommodate correlated errors. Then, the failure of likelihood based Markov chain Monte Carlo (MCMC) in parameter estimating was discussed. Based on the idea of analysis of variation, back comparing and tuning range, were proposed to tackle this failure. Finally, effectiveness of the new model was examined by experiments on both simulation and real data.
Geographically Weighted Regression (GWR) has been broadly used in various fields to
model spatially non-stationary relationships. Classic GWR is considered as a single-scale model that is based on one bandwidth parameter which controls the amount of distance-decay in weighting neighboring data around each location. The single bandwidth in GWR assumes that processes (relationships between the response variable and the predictor variables) all operate at the same scale. However, this posits a limitation in modeling potentially multi-scale processes which are more often seen in the real world. For example, the measured ambient temperature of a location is affected by the built environment, regional weather and global warming, all of which operate at different scales. A recent advancement to GWR termed Multiscale GWR (MGWR) removes the single bandwidth assumption and allows the bandwidths for each covariate to vary. This results in each parameter surface being allowed to have a different degree of spatial variation, reflecting variation across covariate-specific processes. In this way, MGWR has the capability to differentiate local, regional and global processes by using varying bandwidths for covariates. Additionally, bandwidths in MGWR become explicit indicators of the scale at various processes operate. The proposed dissertation covers three perspectives centering on MGWR: Computation; Inference; and Application. The first component focuses on addressing computational issues in MGWR to allow MGWR models to be calibrated more efficiently and to be applied on large datasets. The second component aims to statistically differentiate the spatial scales at which different processes operate by quantifying the uncertainty associated with each bandwidth obtained from MGWR. In the third component, an empirical study will be conducted to model the changing relationships between county-level socio-economic factors and voter preferences in the 2008-2016 United States presidential elections using MGWR.