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- Creators: Arizona State University
- Creators: Li, Ziqi
- Creators: Lu, Xuetao
- Creators: McCulloch, Robert
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.
Embedded within the regression framework, local models can estimate conditioned relationships between observed spatial phenomena and hypothesized explanatory variables and help infer the intangible spatial processes that contribute to the observed spatial patterns. Rather than investigating averaged characteristics corresponding to processes over space as global models do, these models estimate a surface of spatially varying parameters with a value for each location. Additionally, some models such as variants within the Geographically Weighted Regression (GWR) framework, also estimate a parameter to represent the spatial scale across which the processes vary representing the inherent heterogeneity of the estimated surfaces. Since different processes tend to operate at unique spatial scales, some extensions to local models such as Multiscale GWR (MGWR) estimate unique scales of association for each predictor in a model and generate significantly more information on the nature of geographic processes than their predecessors. However, developments within the realm of local models are fairly nascent and hence an understanding around their correct application as well as recognizing their true potential in exploring fundamental spatial science issues is under-developed. The techniques within these frameworks are also currently limited thus restricting the kinds of data that can be analyzed using these models. Therefore the goal of this dissertation is to advance techniques within local multiscale modeling specifically by coining new diagnostics, exploring their novel application in understanding long-standing issues concerning spatial scale and by expanding the tool base to allow their use in wider empirical applications. This goal is realized through three distinct research objectives over four chapters, followed by a discussion on the future of the developments within local multiscale modeling. A correct understanding of the capability and promise of local multiscale models and expanding the fields where they can be employed will not only enhance geographical research by strengthening the intuition of the nature of geographic processes, but will also exemplify the importance and need for using such tools bringing quantitative spatial science to the fore.
An understanding of the formation of spatial heterogeneity is important because spatial heterogeneity leads to functional consequences at the ecosystem scale; however, such an understanding is still limited. Particularly, research simultaneously considering both external variables and internal feedbacks (self-organization) is rare, partly because these two drivers are addressed under different methodological frameworks. In this dissertation, I show the prevalence of internal feedbacks and their interaction with heterogeneity in the preexisting template to form spatial pattern. I use a variety of techniques to account for both the top-down template effect and bottom-up self-organization. Spatial patterns of nutrients in stream surface water are influenced by the self-organized patch configuration originating from the internal feedbacks between nutrient concentration, biological patchiness, and the geomorphic template. Clumps of in-stream macrophyte are shaped by the spatial gradient of water permanence and local self-organization. Additionally, significant biological interactions among plant species also influence macrophyte distribution. The relative contributions of these drivers change in time, responding to the larger external environments or internal processes of ecosystem development. Hydrologic regime alters the effect of geomorphic template and self-organization on in-stream macrophyte distribution. The relative importance of niche vs. neutral processes in shaping biodiversity pattern is a function of hydrology: neutral processes are more important in either very high or very low discharge periods. For the spatial pattern of nutrients, as the ecosystem moves toward late succession and nitrogen becomes more limiting, the effect of self-organization intensifies. Changes in relative importance of different drivers directly affect ecosystem macroscopic properties, such as ecosystem resilience. Stronger internal feedbacks in average to wetter years are shown to increase ecosystem resistance to elevated external stress, and make the backward shifts (vegetation loss) much more gradual. But it causes increases in ecosystem hysteresis effect. Finally, I address the question whether functional consequences of spatial heterogeneity feed back to influence the processes from which spatial heterogeneity emerged through a conceptual review. Such feedbacks are not likely. Self-organized spatial patterning is a result of regular biological processes of organisms. Individual organisms do not benefit from such order. It is order for free, and for nothing.
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.
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.