Moran Spatial Filter Eigenvector Mapping and Field Verification of Latent Non-Zero Autocorrelation Georeferenced Clusters Stratified by Homeless Time Series Socioeconomic Causation Covariates in ampa-Hillsborough County, Florida

In the context of spatial regression analysis, several methods are employable to control for non-asymptotic approximation effects rendered from inconspicuous spatial dependencies amongst georeferenced, homeless-related, socioeconomic stratified, time series, observational prognosticators. Maximum likelihood or Bayesian approaches account for spatial dependencies in a parametric framework, whereas recent spatial filtering approaches focus on non-parametrically removing spatial autocorrelation. In this article we propose a semiparametric spatial filtering approach that allows homeless researchers to deal explicitly with (a) spatially lagged autoregressive models and (b) simultaneous autoregressive spatial models. Our primary assumption was temporally dependent, homeless stratified, socioeconomic, causation covariate, clustering propensities may be revealed employing orthogonal, synthetic, eigenfunction, spatial filters. We created a spatial weights matrix in PROC AUTOREG so that neighboring socioeconomic stratified, frequency samples received a weight that was proportional to the calculable inverse distance measurement between a geographic sub-county, time series, sampled geographic location and its neighbor. We spatially tabularized Euclidean distances in ArcGIS along the links in the eigenfunction eigen decomposition analysis. Our hypothesis was that multivariate autoregressively dependent, diagnostic, frequency model, spatial filter eigenvectors could cartographically and geo-statistically distinguish among the effects of non-parameterizable non-Gaussian non-normalities [e.g., spatial heteroscedasticity(i.e, uncommon variance)],in Euclidean distance measurements between dereferenceable homeless geographically stratified (henceforth geo-stratified), hot and cold spot, sub-county clusters employing a stochastic simulation of temporally regressable, socioeconomic indexed prognosticators. As in one nonparametric spatial filtering approach, a specific subset of eigenvectors from the transformed spatial link matrix in PROC AUTOREG captured dependencies among the disturbances in the empirically stratified datasets of the regressed, homeless, socioeconomic cluster model eigen-estimators. However, the optimal subset in the proposed orthogonal spatial filtering model was identified more intuitively by an objective function that minimized latent, non-zero autocorrelation, in the sampled eigenvectors rather than maximized a model fit. The proposed objective function had the advantage that it lead to a robust and smaller subset of parsimoniously selected eigenvectors. An application of the proposed eigenvector spatial filtering approach in Proc Autoreg employed an empirical parameter estimator dataset for optimally delineating the sub-county georeferenced hot/cold spot clusters in Tampa-Hillsborough County. The top causes of homelessness based on the eigenvector, spatial filter geo-stratified, high positively autocorrelated, georeferenceable, hot spot clusters were (1) unemployment and 2) drug usage/ transaction. In slightly positive autocorrelated clusters homelessness causation was identified as 1) previous incarceration, 2) medical care/ food shortage and 3) domestic violence especially for female victims. Mental health was the primary, diagnostic frequency covariate in the residually negatively autocorrelated clusters. The vast majority interviewed in the negatively autocorrelated cluster during field validation (“ground trothing”) exercises had severe psychological illnesses that remained largely untreated. An observational study found significant levels of mobility aid are required among the homeless in Tampa. A collection of time series, spatial autocorrelation socioeconomic, time sensitive, stratified, frequency, cluster indexed maps should be created and field validated. These maps may be employable by health and human service agencies in Tampa-Hillsborough County to predictively count the population, inventory resources, and increase awareness of targeted services especially for homeless pregnant women and children using ArcGIS and SAS predictive analytical tools. These time series autocorrelation maps may be constructed employing a selection of eigen decomposable eigen-orthogonalize, synthetic eigenvectors as rendered from an empirical geographically sampled, frequency dataset of geo-stratifiable, socioeconomic cluster, causation eigen-covariates quantitated within an autocorrelation connectivity matrix in PROC AUTOREG. New supportive facilities and shelters for the homeless should be located in areas with a high availability of employment, inexpensive or free medical care and food in Tampa-Hillsborough County. Furthermore, free mobile drug addiction programs and family domestic violence interventions should be implemented in the county. To diagnose residual autocorrelation, in empirically sampled, time series, homeless, socioeconomic, diagnostic covariates, Proc Autoreg procedure can perform a first order autocorrelation employing generalized Durbin-Watson (DW) statistics and their marginal probabilities. Exact p-values may be reported for generalized DW tests to any specified order in an homeless socioeconomic, time series, cluster model. Constructing a Bayesian Hierarchical Clustering (BHC) algorithm in Python may efficiently reveal clustering georeferenced stratified socioeconomic, time series covariates. This algorithm may define a probabilistic model of sub-county, homeless socioeconomic datasets which may be used to compute the predictive distribution of a sampled socioeconomic georeferenced, geo-stratified, sub-county, capture point and the probability of it belonging to any of existing clusters in the tree. The algorithm uses a model-based criterion to decide on merging clusters rather than an ad-hoc distance metric. Hence, Bayesian hypothesis testing may be used to decide which merges are advantageous and to output the recommended depth of the tree which may be interpreted as a novel fast bottom-up approximate inference method for a Dirichlet process (i.e., countably infinite) mixture, homeless socioeconomic, aggregation bias model. In so doing the BHS may allow a hierarchical representation of the sampled homeless socioeconomic data, incorporating both finer to coarser grained clusters, in such a way that a researcher can also make forecasts about new sub-county data points, compare different hierarchies in a principled manner, and automatically discover interesting levels of the hierarchy to examine.

Keywords: Autocorrelation; Eigenvector; Homeless; Semi-parametric; Spatial filters; Tamp-Hillsborough