The exact distribution of Moran's I

In analogy to the exact distribution of the Durbin—Watson d statistic for serial autocorrelation of regression residuals, the exact small sample distribution of Moran's I statistic (or alternatively Geary's c) can be derived. Use of algebraic results by Koerts and Abrahamse and theoretical results by Imhof, allows the authors to determine by numerical integration the exact distribution function of Moran's I for normally distributed variables. For the case in which the explanatory variables have been neglected, an upper and a lower bound can be given within which the exact distribution of Moran's I for regression residuals will lie. Furthermore, the proposed methodology is flexible enough to investigate related topics such as the characteristics of the exact distribution for distinct spatial structures as well as their different specifications, the exact power function under different spatial autocorrelation levels, and the distribution of Moran's I for nonnormal random variables.

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Analisis Perubahan Tata Guna Lahan di Kabupaten Bantul Menggunakan Metode Global Moran’s I

Jurnal Buana Informatika ◽

10.24002/jbi.v8i4.1446 ◽

2017 ◽

Vol 8 (4) ◽

Cited By ~ 1

Author(s):

Matheus Supriyanto Rumetna ◽

Eko Sediyono ◽

Kristoko Dwi Hartomo

Keyword(s):

Land Use ◽

Land Use Change ◽

Spatial Autocorrelation ◽

Land Use Changes ◽

Geographical Information ◽

Moran’S I ◽

Complete Spatial Randomness ◽

Moran's I ◽

Global Moran’S I ◽

Spatial Randomness

Abstract. Bantul Regency is a part of Yogyakarta Special Province Province which experienced land use changes. This research aims to assess the changes of shape and level of land use, to analyze the pattern of land use changes, and to find the appropriateness of RTRW land use in Bantul District in 2011-2015. Analytical methods are employed including Geoprocessing techniques and analysis of patterns of distribution of land use changes with Spatial Autocorrelation (Global Moran's I). The results of this study of land use in 2011, there are thirty one classifications, while in 2015 there are thirty four classifications. The pattern of distribution of land use change shows that land use change in 2011-2015 has a Complete Spatial Randomness pattern. Land use suitability with the direction of area function at RTRW is 24030,406 Ha (46,995406%) and incompatibility of 27103,115 Ha or equal to 53,004593% of the total area of Bantul Regency.Keywords: Geographical Information System, Land Use, Geoprocessing, Global Moran's I, Bantul Regency. Abstrak. Analisis Perubahan Tata Guna Lahan di Kabupaten Bantul Menggunakan Metode Global Moran’s I. Kabupaten Bantul merupakan bagian dari Provinsi Daerah Istimewa Yogyakarta yang mengalami perubahan tata guna lahan. Penelitian ini bertujuan untuk mengkaji perubahan bentuk dan luas penggunaan lahan, menganalisis pola sebaran perubahan tata guna lahan, serta kesesuaian tata guna lahan terhadap RTRW yang terjadi di Kabupaten Bantul pada tahun 2011-2015. Metode analisis yang digunakan antara lain teknik Geoprocessing serta analisis pola sebaran perubahan tata guna lahan dengan Spatial Autocorrelation (Global Moran’s I). Hasil dari penelitian ini adalah penggunaan tanah pada tahun 2011, terdapat tiga puluh satu klasifikasi, sedangkan pada tahun 2015 terdapat tiga puluh empat klasifikasi. Pola sebaran perubahan tata guna lahan menunjukkan bahwa perubahan tata guna lahan tahun 2011-2015 memiliki pola Complete Spatial Randomness. Kesesuaian tata guna lahan dengan arahan fungsi kawasan pada RTRW adalah seluas 24030,406 Ha atau mencapai 46,995406 % dan ketidaksesuaian seluas 27103,115 Ha atau sebesar 53,004593 % dari total luas wilayah Kabupaten Bantul. Kata Kunci: Sistem Informasi Georafis, tata guna lahan, Geoprocessing, Global Moran’s I, Kabupaten Bantul.

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Spatial Autocorrelation in the Study of Neighbourhoods towards Smart Cities: Empirical Evidence from Kerman, Iran

Scientific Research Journal ◽

10.24191/srj.v9i2.9405 ◽

2012 ◽

Vol 9 (2) ◽

pp. 1

Author(s):

Asra Hosseini

Keyword(s):

Spatial Autocorrelation ◽

Urban Areas ◽

Smart Cities ◽

Moran’S I ◽

Moran's I ◽

Urban Planner ◽

Universal Feature ◽

Autocorrelation Method ◽

Selection Of

From earliest cities to the present, spatial division into residential zones and neighbourhoods is the universal feature of urban areas. This study explored issue of measuring neighbourhoods through spatial autocorrelation method based on Moran's I index in respect of achieving to best neighbourhoods' model for forming cities smarter. The research carried out by selection of 35 neighbourhoods only within central part of traditional city of Kerman in Iran. The results illustrate, 75% of neighbourhoods' area in the inner city of Kerman had clustered pattern, and it shows reduction in Moran's index is associated with disproportional distribution of density and increasing in Moran's I and Z-score have monotonic relation with more dense areas and clustered pattern. It may be more efficient for urban planner to focus on spatial autocorrelation to foster neighbourhood cohesion rather than emphasis on suburban area. It is recommended characteristics of historic neighbourhoods can be successfully linked to redevelopment plans toward making city smarter, and also people's quality of life can be related to the way that neighbourhoods' patterns are defined.

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Spatial Autocorrelation in the Study of Neighbourhoods towards Smart Cities: Empirical Evidence from Kerman, Iran

Scientific Research Journal ◽

10.24191/srj.v9i2.5389 ◽

2012 ◽

Vol 9 (2) ◽

pp. 1

Author(s):

Asra Hosseini

Keyword(s):

Spatial Autocorrelation ◽

Smart Cities ◽

Moran’S I ◽

Moran's I ◽

Urban Planner ◽

Universal Feature ◽

Autocorrelation Method ◽

Selection Of ◽

Monotonic Relation

From earliest cities to the present, spatial division into residential zones and neighbourhoods is the universal feature ofurban areas. This study explored issue ofmeasuring neighbourhoods through spatial autocorrelation method based on Moran's I index in respect of achieving to best neighbourhoods' model for forming cities smarter. The research carried out by selection of 35 neighbourhoods only within central part of traditional city of Kerman in Iran. The results illustrate, 75% ofneighbourhoods, area in the inner city of Kerman had clustered pattern, and it shows reduction in Moran's index is associated with disproportional distribution of density and increasing in Moran's I and Z-score have monotonic relation with more dense areas and clustered pattern. It may be more efficient for urban planner to focus on spatial autocorrelation to foster neighbourhood cohesion rather than emphasis on suburban area. It is recommended characteristics of historic neighbourhoods can be successfully linked to redevelopment plans toward making city smarter, and also people's quality of life can be related to the way that neighbourhoods' patterns are defined.

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Geographical variations and associated factors of defaulting from immunization among children aged 12 to 23 months in Ethiopia: using spatial and multilevel analysis of 2016 Ethiopian Demographic and Health Survey

Environmental Health and Preventive Medicine ◽

10.1186/s12199-021-00984-8 ◽

2021 ◽

Vol 26 (1) ◽

Author(s):

Mukemil Awol ◽

Zewdie Aderaw Alemu ◽

Nurilign Abebe Moges ◽

Kemal Jemal

Keyword(s):

Multilevel Analysis ◽

Health Survey ◽

Associated Factors ◽

Demographic And Health Survey ◽

Community Level ◽

Scan Statistics ◽

Moran’S I ◽

Moran's I ◽

Depth Analysis ◽

Global Moran’S I

Abstract Background In Ethiopia, despite the considerable improvement in immunization coverage, the burden of defaulting from immunization among children is still high with marked variation among regions. However, the geographical variation and contextual factors of defaulting from immunization were poorly understood. Hence, this study aimed to identify the spatial pattern and associated factors of defaulting from immunization. Methods An in-depth analysis of the 2016 Ethiopian Demographic and Health Survey (EDHS 2016) data was used. A total of 1638 children nested in 552 enumeration areas (EAs) were included in the analysis. Global Moran’s I statistic and Bernoulli purely spatial scan statistics were employed to identify geographical patterns and detect spatial clusters of defaulting immunization, respectively. Multilevel logistic regression models were fitted to identify factors associated with defaulting immunization. A p value < 0.05 was used to identify significantly associated factors with defaulting of child immunization. Results A spatial heterogeneity of defaulting from immunization was observed (Global Moran’s I = 0.386379, p value < 0.001), and four significant SaTScan clusters of areas with high defaulting from immunization were detected. The most likely primary SaTScan cluster was seen in the Somali region, and secondary clusters were detected in (Afar, South Nation Nationality of people (SNNP), Oromiya, Amhara, and Gambella) regions. In the final model of the multilevel analysis, individual and community level factors accounted for 56.4% of the variance in the odds of defaulting immunization. Children from mothers who had no formal education (AOR = 4.23; 95% CI: 117, 15.78), and children living in Afar, Oromiya, Somali, SNNP, Gambella, and Harari regions had higher odds of having defaulted immunization from community level. Conclusions A clustered pattern of areas with high default of immunization was observed in Ethiopia. Both the individual and community-level characteristics were statistically significant factors of defaulting immunization. Therefore, the Federal Ethiopian Ministry of Health should prioritize the areas with defaulting of immunization and consider the identified factors for immunization interventions.

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Spatial distribution and determinant factors of anemia among adults aged 15–59 in Ethiopia; using mixed-effects ordinal logistic regression model

BMC Nutrition ◽

10.1186/s40795-021-00424-4 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Biruk Shalmeno Tusa ◽

Sewnet Adem Kebede ◽

Adisu Birhanu Weldesenbet

Keyword(s):

Public Health ◽

Spatial Distribution ◽

Scan Statistics ◽

Moran’S I ◽

Demographic And Health Surveys ◽

Targeted Prevention ◽

Hotspot Analysis ◽

Mixed Effect ◽

Moran's I ◽

Determinant Factors

Abstract Background Anemia is a global public health problem, particularly in developing countries. Assessing the geographic distributions and determinant factors is a key and crucial step in designing targeted prevention and intervention programmes to address anemia. Thus, the current study is aimed to assess the spatial distribution and determinant factors of anemia in Ethiopia among adults aged 15–59. Methods A secondary data analysis was done based on 2016 Ethiopian Demographic and Health Surveys (EDHS). Total weighted samples of 29,140 adults were included. Data processing and analysis were performed using STATA 14; ArcGIS 10.1 and SaTScan 9.6 software. Spatial autocorrelation was checked using Global Moran’s index (Moran’s I). Hotspot analysis was made using Gettis-OrdGi*statistics. Additionally, spatial scan statistics were applied to identify significant primary and secondary cluster of anemia. Mixed effect ordinal logistics were fitted to determine factors associated with the level of anemia. Result The spatial distribution of anemia in Ethiopia among adults age 15–59 was found to be clustered (Global Moran’s I = 0.81, p value < 0.0001). In the multivariable mixed-effectordinal regression analysis; Females [AOR = 1.53; 95% CI: 1.42, 1.66], Never married [AOR = 0.86; 95% CI: 0.77, 0.96], highly educated [AOR = 0.71; 95% CI: 0.60, 0.84], rural residents [AOR = 1.53; 95% CI: 1.23, 1.81], rich wealth status [AOR = 0.77; 95% CI: 0.69, 0.86] and underweight [AOR = 1.15; 1.06, 1.24] were significant predictors of anemia among adults. Conclusions A significant clustering of anemia among adults aged 15–59 were found in Ethiopia and the significant hotspot areas with high cluster anemia were identified in Somalia, Afar, Gambella, Dire Dewa and Harari regions. Besides, sex, marital status, educational level, place of residence, region, wealth index and BMI were significant predictors of anemia. Therefore, effective public health intervention and nutritional education should be designed for the identified hotspot areas and risk groups in order to decrease the incidence of anemia.

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The geographies of corruption in Nigeria: understanding the patterns and correlates

Journal of Financial Crime ◽

10.1108/jfc-10-2020-0213 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Richard Adeleke ◽

Opeyemi Alabede ◽

Tolulope Osayomi ◽

Ayodeji Iyanda

Keyword(s):

Positive Impact ◽

Market Competition ◽

State Level ◽

Well Being ◽

Moran’S I ◽

Market Size ◽

National Bureau ◽

Moran's I ◽

Content Type ◽

Domestic Debt

Purpose Globally, corruption has been identified as a major problem. Even though corruption is widespread, it varies in magnitude, types and consequences. In Nigeria, corruption is endemic, and it is responsible for the many socioeconomic problems in the country. Hence, the study aims to determine the patterns and state level correlations of corruption in Nigeria. Design/methodology/approach Data for this study were sourced from the National Bureau of Statistics and other official sources and were analyzed with Global Moran’s I, Local Moran’s I and multivariate step-wise regression. Findings This study’s findings revealed significant clustering of corruption in the country with Rivers States as the only hotspot (I = 0.068; z = 2.524; p < 0.05), while domestic debt and market size were the state level significant predictors. Research limitations/implications Only bribery as a form of corruption was examined in this study, more studies are needed on the predictors of other forms of corruption. Practical implications This study recommends increased market competition through investment grants, subsidies and tax incentives to facilitate trade interactions among Nigerians, which can lead to exchange of cultural norms that discourage corruption. It is also advocated that domestic debt must be effectively and efficiently channelled towards economic development which in the long run will have a positive impact on the socio-economic well-being of the citizens as well as drive down corrupt practices. Originality/value Although the causes of corruption have received considerable attention in the literature, little is known on the geographical distribution and the effect of market size and domestic debt on corruption in Nigeria.

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