A Closed‐Form Consistent Estimator for Linear Models with Spatial Dependence

2020 ◽  
Author(s):  
Oleg A. Smirnov
Keyword(s):  
Closed Form ◽  
Spatial Dependence ◽  
Linear Models ◽  
Consistent Estimator

Car Ownership and the Built Environment: A Spatial Modeling Approach

2021 ◽  
pp. 036119812110494
Author(s):  
Jerome Laviolette ◽  
Catherine Morency ◽  
Owen D. Waygood ◽  
Konstadinos G. Goulias
Keyword(s):  
Built Environment ◽  
Spatial Dependence ◽  
Linear Models ◽  
Census Data ◽  
Model Specification ◽  
Car Ownership ◽  
Grocery Stores ◽  
Modeling Framework ◽  
Explanatory Variables ◽  
Environment Variables

Car ownership is linked to higher car use, which leads to important environmental, social and health consequences. As car ownership keeps increasing in most countries, it remains relevant to examine what factors and policies can help contain this growth. This paper uses an advanced spatial econometric modeling framework to investigate spatial dependences in household car ownership rates measured at fine geographical scales using administrative data of registered vehicles and census data of household counts for the Island of Montreal, Canada. The use of a finer level of spatial resolution allows for the use of more explanatory variables than previous aggregate models of car ownership. Theoretical considerations and formal testing suggested the choice of the Spatial Durbin Error Model (SDEM) as an appropriate modeling option. The final model specification includes sociodemographic and built environment variables supported by theory and achieves a Nagelkerke pseudo-R2 of 0.93. Despite the inclusion of those variables the spatial linear models with and without lagged explanatory variables still exhibit residual spatial dependence. This indicates the presence of unobserved autocorrelated factors influencing car ownership rates. Model results indicate that sociodemographic variables explain much of the variance, but that built environment characteristics, including transit level of service and local commercial accessibility (e.g., to grocery stores) are strongly and negatively associated with neighborhood car ownership rates. Comparison of estimates between the SDEM and a non-spatial model indicates that failing to control for spatial dependence leads to an overestimation of the strength of the direct influence of built environment variables.

Estimators of Random Effects Variance Components in Meta-Analysis

2000 ◽  
Vol 25 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Lynn Friedman
Keyword(s):  
Closed Form ◽  
Random Effects ◽  
Quadratic Forms ◽  
Relative Efficiency ◽  
Variance Component ◽  
Linear Models ◽  
Random Effect ◽  
Linear Functions ◽  
Effect Sizes ◽  
Random Effects Model

In meta-analyses, groups of study effect sizes often do not fit the model of a single population with only sampling, or estimation, variance differentiating the estimates. If the effect sizes in a group of studies are not homogeneous, a random effects model should be calculated, and a variance component for the random effect estimated. This estimate can be made in several ways, but two closed form estimators are in common use. The comparative efficiency of the two is the focus of this report. We show here that these estimators vary in relative efficiency with the actual size of the random effects model variance component. The latter depends on the study effect sizes. The closed form estimators are linear functions of quadratic forms whose moments can be calculated according to a well-known theorem in linear models. We use this theorem to derive the variances of the estimators, and show that one of them is smaller when the random effects model variance is near zero; however, the variance of the other is smaller when the model variance is larger. This leads to conclusions about their relative efficiency.

scholarly journals Generalized Linear Spatial Models to Predict Slate Exploitability

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Angeles Saavedra ◽  
Javier Taboada ◽  
María Araújo ◽  
Eduardo Giráldez
Keyword(s):  
Spatial Distribution ◽  
Generalized Linear Models ◽  
Spatial Dependence ◽  
Spatial Model ◽  
Linear Models ◽  
Spatial Models ◽  
Response Variable ◽  
Explanatory Variables ◽  
Model Residuals

The aim of this research was to determine the variables that characterize slate exploitability and to model spatial distribution. A generalized linear spatial model (GLSMs) was fitted in order to explore relationship between exploitability and different explanatory variables that characterize slate quality. Modelling the influence of these variables and analysing the spatial distribution of the model residuals yielded a GLSM that allows slate exploitability to be predicted more effectively than when using generalized linear models (GLM), which do not take spatial dependence into account. Studying the residuals and comparing the prediction capacities of the two models lead us to conclude that the GLSM is more appropriate when the response variable presents spatial distribution.

Closed Form Solutions to Nonlinear Heat Conduction Problems

2012 ◽  
Vol 326-328 ◽  
pp. 115-119
Author(s):  
J. Zabadal ◽  
R. Garcia ◽  
V. Ribeiro ◽  
F. Van Der Laan
Keyword(s):  
Heat Conduction ◽  
Partial Differential Equations ◽  
Closed Form ◽  
Control Systems ◽  
Analytical Method ◽  
Linear Models ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Heat Conduction ◽  
Closed Form Solutions ◽  
Standard Techniques

This work presents a new analytical method for solving nonlinear heat conduction problems in arbitrary domains. The method is based on approximate mappings which transforms nonlinear partial differential equations into linear models which can be solved using standard techniques. In order to verify whether the proposed formulation can be employed to conceive new online control systems, numerical results are reported.

scholarly journals spind: an R Package to Account for Spatial Autocorrelation in the Analysis of Lattice Data

2018 ◽  
Vol 6 ◽  
pp. e20760 ◽  
Author(s):  
Gudrun Carl ◽  
Sam Levin ◽  
Ingolf Kühn
Keyword(s):  
Spatial Autocorrelation ◽  
Spatial Dependence ◽  
Linear Models ◽  
Spatial Scales ◽  
Spatial Arrangement ◽  
R Package ◽  
Spatial Modelling ◽  
Species Distribution Modelling ◽  
Lattice Data ◽  
Dimensional Dependence

spind is an R package aiming to provide a useful toolkit to account for spatial dependence in the analysis of lattice data. Grid-based data sets in spatial modelling often exhibit spatial dependence, i.e. values sampled at nearby locations are more similar than those sampled further apart. spind methods, described here, take this kind of two-dimensional dependence into account and are sensitive to its variation across different spatial scales. Methods presented to account for spatial autocorrelation are based on the two fundamentally different approaches of generalised estimating equations as well as wavelet-revised methods. Both methods are extensions to generalised linear models. spind also provides functions for multi-model inference and scaling by wavelet multiresolution regression. Since model evaluation is essential for assessing prediction accuracy in species distribution modelling, spind additionally supplies users with spatial accuracy measures, i.e. measures that are sensitive to the spatial arrangement of the predictions.

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