scholarly journals Application of economic distance for the purposes of a spatial analysis of the unemployment rate for Poland

2010 ◽  
Vol 1 (1) ◽  
pp. 79-98 ◽  
Author(s):  
Michał Bernard Pietrzak
Keyword(s):  
Spatial Analysis ◽  
Physical Properties ◽  
Unemployment Rate ◽  
Spatial Econometrics ◽  
Weight Matrix ◽  
Spatial Weight Matrix ◽  
Economic Distance ◽  
Spatial Weight ◽  
The Matrix ◽  
The Impact

The article presents the problem of the application of the spatial weigh matrix based on economic distance in spatial analysis of the unemployment rate. The spatial weight matrix expresses potential spatial interactions between the researched areas and forms a basis for the instruments applied in spatial econometrics. While identifying the neighbourhood, the following criteria are used: a common border, distance, and the k number of the nearest neighbours. The potential force of impact is identified by means of the standardisation of the matrix by rows to unity, or by means of the distance based on the physical properties of the areas. The disadvantage of the matrix standardisation is the fact of accepting the same force of impact for all the areas. It seems natural is the differentiation of the force of the impact dependent on the selected areas which should result from the differences and similarities of the areas in the scope of the researched phenomenon and its determinants. The use of the distance based on physical properties of the areas allows considering the diverse force of impact of neighbouring areas, which, in turn, allows to obtain a more precise outcome of analyses. Unfortunately, physical properties do not constitute the determinants of economic phenomena covered by a spatial analysis which means that they are not related directly to the scrutinised phenomenon. The application of economic distance for building spatial weight matrix shown in the present paper constitutes a way of determining of the force of impact for the economic spatial processes that is alternative to the distance based on physical properties of the researched areas and to the proposal of the standardisation by rows to unity.

scholarly journals Two-stage procedure of building a spatial weight matrix with the consideration of economic distance

2010 ◽  
Vol 1 (1) ◽  
pp. 65-78
Author(s):  
Michał Bernard Pietrzak
Keyword(s):  
Physical Properties ◽  
Spatial Econometrics ◽  
Physical Distance ◽  
Weight Matrix ◽  
Two Stage ◽  
Spatial Weight Matrix ◽  
Economic Distance ◽  
Nearest Neighbours ◽  
Spatial Weight ◽  
Definition Of

The article discusses an essential problem of spatial econometrics which is the construction of a spatial weight matrix. This matrix expresses potential spatial interactions between the researched areas and forms the basis for spatial analyses. The objective of the paper was to consider various ways of defining the a spatial weight matrix. Consideration was given to the methods of identifying adjacency between areas in the form of neighbourhood in the sense of a common border, the adjacency identified on the basis of the physical distance and on the criterion of the k number of the nearest neighbours. Also, the issue of identifying the force of impact for the previously defined neighbourhood system was taken into account. The approaches that were considered include the standardisation of matrices by rows to unity, or the identification of the force of impact based on the physical properties of areas. The outcome of the considerations is the proposed two-stage procedure of building a spatial weight matrix. A definition of economic distance was proposed, the definition which constitutes an adequate instrument for measuring the force of interaction between neighbouring areas. The introduced economic distance is an important alternative to the identification of the force of impact of economic spatial processes in relation to the distance based on the physical properties of the researched areas and in relation to the proposal of the standardisation by rows to unity.

scholarly journals W: SPATIAL WEIGHT MATRIX DIVERSITY AND ITS IMPACT ON SPATIAL ANALYSIS RESULTS

2019 ◽  
Vol 2 (1) ◽  
pp. 209-213
Author(s):  
Simona Mackova
Keyword(s):  
Spatial Analysis ◽  
Spatial Econometrics ◽  
Stochastic Matrix ◽  
Spatial Regression ◽  
Regional Analysis ◽  
Geographical Location ◽  
Spillover Effects ◽  
Weight Matrix ◽  
Spatial Weight Matrix ◽  
Spatial Weight

Spatial econometrics presents irreplaceable tool for regional analysis. Omitting additional information about geographical location of observed units could neglect some important influences. The spatial weight matrix W determining neighbourhood relations and degree of influence between observed units belongs to the main components of spatial analysis. Various specification approaches of this non-stochastic matrix could be applied. There is a commonly held belief that spatial regression models are sensitive to spatial weight structure. Some analytics consider it as a myth and points out incorrect interpretation of the model coefficients or misspecified models. Does it really matter what kind of specification is used? This contribution brings an empirical example of several approaches to neighbourhood specification and compares obtained results. According to findings of this analysis, especially spillover effects are incomparable. That confirms unequal performance of spatial structures. The W matrix should be built carefully at the beginning of each spatial analysis task.   

scholarly journals Research on the Spatial Correlation and Spatial Lag of COVID-19 Infection Based on Spatial Analysis

2021 ◽  
Vol 13 (21) ◽  
pp. 12013
Author(s):  
Keqiang Dong ◽  
Liao Guo
Keyword(s):  
Spatial Analysis ◽  
Spatial Correlation ◽  
Lagrange Multiplier ◽  
Weight Matrix ◽  
Primary Data ◽  
Lagrange Multiplier Test ◽  
Spatial Lag ◽  
Spatial Weight Matrix ◽  
The World ◽  
Spatial Weight

COVID-19 has spread throughout the world since the virus was discovered in 2019. Thus, this study aimed to identify the global transmission trend of the COVID-19 from the perspective of the spatial correlation and spatial lag. The research used primary data collected of daily increases in the amount of COVID-19 in 14 countries, confirmed diagnosis, recovered numbers, and deaths. Findings of the Moran index showed that the propagation of infection was aggregated between 9 May and 21 May based on the composite spatial weight matrix. The results from the Lagrange multiplier test indicated the COVID-19 patients can infect others with a lag.

scholarly journals Spatial weight matrix impact on real estate hierarchical clustering in the process of mass valuation

2019 ◽  
Vol 10 (1) ◽  
pp. 131-151
Author(s):  
Sebastian Gnat
Keyword(s):  
Real Estate ◽  
Hierarchical Clustering ◽  
Information Entropy ◽  
Value Added ◽  
Weight Matrix ◽  
Spatial Constraints ◽  
Spatial Weight Matrix ◽  
Real Estate Valuation ◽  
Spatial Weight ◽  
The Impact

Research background: The value of the property can be determined on an individual or mass basis. There are a number of situations in which uniform and relatively fast results obtained by means of mass valuation undoubtedly outweigh the advantages of the individual approach. In literature and practice there are a number of different types of models of mass valuation of real estate. For some of them it is postulated or required to group the valued properties into homogeneous subset due to various criteria. One such model is Szczecin Algorithm of Real Estate Mass Appraisal (SAREMA). When using this algorithm, the area to be valued should be divided into the so-called location attractiveness areas (LAZ). Such division can be made in many ways. Regardless of the method of clustering, its result should be assessed, depending on the degree of implementation of the adopted criterion of division quality. A better division of real estate will translate into more accurate valuation results. Purpose of the article: The aim of the article is to present an application of hierarchical clustering with a spatial constraints algorithm for the creation of LAZ. This method requires the specification of spatial weight matrix to carry out the clustering process. Due to the fact that such a matrix can be specified in a number of ways, the impact of the proposed types of matrices on the clustering process will be described. A modified measure of information entropy will be used to assess the clustering results. Methods: The article utilises the algorithm of agglomerative clustering, which takes into account spatial constraints, which is particularly important in the context of real estate valuation. Homogeneity of clusters will be determined with the means of information entropy. Findings & Value added: The main achievements of the study will be to assess whether the type of the distance matrix has a significant impact on the clustering of properties under valuation.

scholarly journals Spatial weight matrix in dimensionality reduction reconstruction for micro-electromechanical system-based photoacoustic microscopy

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Yuanzheng Ma ◽  
Chang Lu ◽  
Kedi Xiong ◽  
Wuyu Zhang ◽  
Sihua Yang
Keyword(s):  
Image Reconstruction ◽  
Dimensionality Reduction ◽  
Optical Resolution ◽  
Distortion Correction ◽  
Electromechanical System ◽  
Weight Matrix ◽  
Photoacoustic Microscopy ◽  
Spatial Weight Matrix ◽  
Spatial Weight ◽  
Micro Electromechanical System

AbstractA micro-electromechanical system (MEMS) scanning mirror accelerates the raster scanning of optical-resolution photoacoustic microscopy (OR-PAM). However, the nonlinear tilt angular-voltage characteristic of a MEMS mirror introduces distortion into the maximum back-projection image. Moreover, the size of the airy disk, ultrasonic sensor properties, and thermal effects decrease the resolution. Thus, in this study, we proposed a spatial weight matrix (SWM) with a dimensionality reduction for image reconstruction. The three-layer SWM contains the invariable information of the system, which includes a spatial dependent distortion correction and 3D deconvolution. We employed an ordinal-valued Markov random field and the Harris Stephen algorithm, as well as a modified delay-and-sum method during a time reversal. The results from the experiments and a quantitative analysis demonstrate that images can be effectively reconstructed using an SWM; this is also true for severely distorted images. The index of the mutual information between the reference images and registered images was 70.33 times higher than the initial index, on average. Moreover, the peak signal-to-noise ratio was increased by 17.08% after 3D deconvolution. This accomplishment offers a practical approach to image reconstruction and a promising method to achieve a real-time distortion correction for MEMS-based OR-PAM.

scholarly journals On Misspecification of Spatial Weight Matrix for Small Area Estimation in Longitudinal Analysis

2013 ◽  
Vol 15 (4) ◽  
pp. 305-318
Author(s):  
Tomasz Żądło
Keyword(s):  
Sample Size ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Weight Matrix ◽  
Random Sample Size ◽  
Monte Carlo Simulation Study ◽  
Spatial Weight Matrix ◽  
First Case ◽  
Spatial Weight ◽  
Random Components

The problem of prediction of subpopulation (domain) total is studied as in Rao (2003). Considerations are based on spatially correlated longitudinal data. The domain of interest can be defined after sample selection what implies its random sample size. The special case of the General Linear Mixed Model is proposed where two random components obey assumptions of spatial and temporal moving average process respectively. Moreover, it is assumed that the population may change in time and elements’ affiliations to subpopulation may change in time as well. The proposed model is a generalization of longitudinal models studied by e.g. Verbeke, Molenberghs (2000) and Hedeker, Gibbons (2006). The best linear unbiased predictor (BLUP) is derived. It may be used even if the sample size in the subpopulation of interest in the period of interest is zero. In the Monte Carlo simulation study the accuracy of the empirical version of the BLUP will be studied in the case of correct and incorrect specification of the spatial weight matrix. Two cases of model misspecification are studied. In the first case the misspecified spatial weight is used. In the second case independence of random components is assumed but the variable which is used to compute elements of spatial weight matrix in the correct case will be used as auxiliary variable in the model.

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