Moran Statistic Research Articles

Confounded Local Inference: Extending Local Moran Statistics to Handle Confounding

Local statistical analysis has long been of interest to social and environmental scientists who analyze geographic data. Research into local spatial statistics experienced a step-change in the mid-1990s, which provided a large class of local statistical methods and models. The local Moran statistic is one commonly used local indicator of spatial association, able to detect both areas of similarity and observations that are very dissimilar from their surroundings. From this, many further local statistics have been developed to characterize spatial clusters and outliers. These statistics have seen limited adoption because they do not sufficiently model the relationships involved in confounded spatial data, where the analyst seeks to understand the local spatial structure of a given outcome variable that is influenced by one or more additional factors. Recent innovations used to do joint multivariate local analysis also do not model this kind of conditional local structure in data. This article provides tools to rigorously characterize confounded local inference and a new and different class of multivariate conditional local Moran statistics that can account for confounding. To do this, we return to the Moran scatterplot as the critical tool for local Moran-style covariance statistics. Extending this concept, a new method is available directly from a “Moran-form” multiple regression. We show the empirical and theoretical properties of this statistic, show how some existing heuristic approaches arise naturally from this framework, and show how the use of conditional inference can change interpretations in an empirical analysis of rent and housing stock in a rapidly changing neighborhood.

Length of Maternity Leave Impact on Mental and Physical Health of Mothers and Infants, a Systematic Review and Meta-analysis.

Recent legislative decisions in the United States have encouraged discussion about national parental leave programs. Currently, over 47% of the United States workforce is female. However, the United States is the only nation of the 37 member countries in the Organization for Economic Co-Operation and Development (OECD) to have no national requirement for maternity leave. The first few months of a child's life are vital to their physical and mental development. Likewise, a gradual return to pre-partum functioning is important for a newly postpartum woman. While it has been shown that maternity leave positively impacts various measures of maternal and infant mental and physical health, we lack consensus on the optimal length of paid or unpaid maternity leave. Accordingly, we conducted a systematic review and meta-analysis to evaluate the optimal length of paid or unpaid maternity leave to encourage maternal and infant mental and physical health in the United States. A systematic review and meta-analysis were conducted to synthesize and critically evaluate the current research investigating the association between maternity leave and maternal and infant mental and physical health using the Preferred Reporting in Systematic Reviews and Meta-Analyses guidelines. Databases EMBASE, PsycInfo, and PubMed were searched using specific inclusion and exclusion criteria. Methodological Index for Non-Randomized Studies scale assessed the methodological quality of the included eligible studies. The magnitude of heterogeneity between-study was tested using The Cochrane χ2 test and the Moran's I2 statistic. Possible publication bias was assessed through the funnel plot and the Egger regression test. A p-value of < 0.10 will be considered as an indication for the existence of potential publication bias. All statistical analyses were carried out with Stata software version 15. A total of 21 studies were analyzed. It was found that longer maternity leave may decrease rates of maternal mental and physical health complaints. It was also found that longer maternity leave leads to more positive mother-child interactions, decreased infant mortality, and longer periods of breastfeeding. Maternity leave of 12weeks or more confers the greatest benefit for mothers and their infants.

Investments in small retention as a factor influencing land-use changes. A case study of Poland

Building permit decisions are one of the most important elements of the investment process in Poland. It should be noted that water reservoirs influence the diversification of landscapes by increasing their attractiveness in both urban and rural areas. The article aimed to verify the relationship between the changes in land-use development and investments related to small retention. Another goal was classifying objects for which building permits have been obtained and registered. Changes in land-use development associated with the introduction of ponds, which blend in with the landscape, are desirable from the perspective of retaining water resources in urban and rural ecosystems. The research methodology was based on spatial data and included statistical analyses in three regions: Mazowieckie, Lodzkie and Swietokrzyskie. Studies carried out in these regions showed a spatial correlation associated with investments in small retention. The research used methods of the global I Moran statistic and local Moran statistics. The data used in the study came from the Register of Applications, Decisions and Notifications, made available by the Main Office of Construction Site. The research indicates clusters of investments in small retention in analysed regions. The majority of investors are residents who invest in earth ponds. The study shows that investment in small retention is connected with ecosystem services.

The use of spatial statistics in the analysis of salaries at poviat level in Poland

The spatial differentiation of salaries is the subject of many scientific studies, both theoretical and empirical. One of the factors determining remuneration in Poland is the structure and type of business activity, specific for a given region and depending on its poviats (counties) in terms of the level of the average gross monthly salary by means of spatial autocorrelation statistical methods. The analysed statistical data for 2010–2019 come from the Local Data Bank (Bank Danych Lokalnych – BDL) of Statistics Poland. Global and local measures were used in the analysis. The calculation of the global parameters of spatial autocorrelation was based on the I Moran and C Geary statistics, while the Ii Moran statistic, which belongs to local spatial indicators from the LISA group (Local Indicators of Spatial Association), was used to identify the local autocorrelation. The statistical significance of the global statistics was verified by means of a randomisation approach based on theoretical moments. The I Moran and C Geary global statistics indicated a significant (very weak or weak) and positive spatial autocorrelation between poviats in terms of the level of average gross monthly salaries in 2010–2019, which shows the existence of spatial poviat structures of similar values, i.e. clusters with high or low values of average salaries. The increase in I Moran’s statistics and the growth of the C Geary in the analysed period indicate a decrease in the differentiation of average monthly salaries between poviats, thus signifying an increase in the dependence of spatial autocorrelation. The analysis of the results of the obtained local statistics allowed the determination of clusters of similar poviats in Poland, e.g. Mazowiecki, Pomorski and Śląski. Furthermore, the results of the analysis indicated the presence of outlier poviats.

COVID-GAN+: Estimating Human Mobility Responses to COVID-19 through Spatio-temporal Generative Adversarial Networks with Enhanced Features

Estimating human mobility responses to the large-scale spreading of the COVID-19 pandemic is crucial, since its significance guides policymakers to give Non-pharmaceutical Interventions, such as closure or reopening of businesses. It is challenging to model due to complex social contexts and limited training data. Recently, we proposed a conditional generative adversarial network (COVID-GAN) to estimate human mobility response under a set of social and policy conditions integrated from multiple data sources. Although COVID-GAN achieves a good average estimation accuracy under real-world conditions, it produces higher errors in certain regions due to the presence of spatial heterogeneity and outliers. To address these issues, in this article, we extend our prior work by introducing a new spatio-temporal deep generative model, namely, COVID-GAN+. COVID-GAN+ deals with the spatial heterogeneity issue by introducing a new spatial feature layer that utilizes the local Moran statistic to model the spatial heterogeneity strength in the data. In addition, we redesign the training objective to learn the estimated mobility changes from historical average levels to mitigate the effects of spatial outliers. We perform comprehensive evaluations using urban mobility data derived from cell phone records and census data. Results show that COVID-GAN+ can better approximate real-world human mobility responses than prior methods, including COVID-GAN.

COVID-19 and internal migration in Serbia-geographical perspective

Internal migration is an essential part of regional population change. Driven by various determinants, internal migration has been unequal across time and space. Migration responses to the changes in societal circumstances make it relevant to investigate the spatial and temporal dimension of internal migration in Serbia before and in the aftermath of the COVID-19 pandemic outbreak. The research aims to identify to what extent and in what way the pandemic has changed the magnitude and geographical patterns of internal migration in Serbia. The study is based on additionally processed official statistics on internal migration for the period 2018-2020, from March to December for each year, at the municipal, district (oblast, plural-oblasti), and regional levels. These are aggregate administrative data on usual residence registration by month. The derived data on the net migration rate is cartographically presented using the classification method natural Breaks (Jenks). Spatial dependence was assessed applying the spatial autocorrelation method, based on the Local Moran statistic. The results revealed that the pandemic affected not only the volume of internal migration but also its spatial patterns. The findings present new insights on the role of internal migration in reallocation of population across Serbia before and during the COVID-19 pandemic while underlying the importance of further research to deepen the understanding of internal migration trends upon the COVID-19 outbreak.

GeoDa, From the Desktop to an Ecosystem for Exploring Spatial Data

Since its introduction more than 15 years ago, the GeoDa software for the exploration of spatial data has transitioned from a closed source Windows‐only solution to an open source and cross‐platform product that takes on the look and feel of the native operating system. This article reports on the evolution in the functionality and architecture of the software and pays particular attention to its new implementation as a library, libgeoda. This library, through a clearly structured API, can be integrated into other software environments, such as R (rgeoda) and Python (pygeoda). This integration is illustrated with two small empirical examples, investigating local clusters in a historical London cholera data set and among socioeconomic determinants of health in Chicago. A timing experiment demonstrates the competitive performance of GeoDa desktop, libgeoda (C++), rgeoda and pygeoda compared to established solutions in R spdep and Python PySAL, evaluating conditional permutation inference for the Local Moran statistic.

The Importance of Null Hypotheses: Understanding Differences in Local Moran’s under Heteroskedasticity

A recent review noted important differences in the results of the local Moran's statistic depending on the inference method. These differences had significant practical implications. In closing, the authors speculated the differences may be due to local spatial heterogeneity. In this article, we propose that different null hypotheses, not heteroskedasticity, generate these differences. To test this, we examine the null hypotheses implicit in common statistical significance tests of local Moran’s . We design an experiment to assess the impact of local heterogeneity on tests conducted under the two most common null hypotheses. In this experiment, we analyze the relationship between measures of local variance, such as the local spatial heteroskedasticity (LOSH) statistic, and components of the local Moran’s statistic. We run this experiment with controlled synthetic heteroskedastic data and with uncontrolled real‐world data with varying degrees and patterns of local heteroskedasticity. We show that, in both situations, estimates that use the same null are extremely similar, regardless of estimation method. In contrast, all estimates (regardless of the null) are moderately affected by spatial heteroskedasticity. Ultimately, this article demonstrates that there are important conceptual and computational differences about null hypothesis in local testing frameworks, and these differences can have significant practical implications. Therefore, researchers must be aware as to how their choices may shape the observed spatial patterns.

The geography of femicide in Sergipe, Brazil: matriarchy, human development, and income distribution.

This research analyzed a joint spatial distribution and explored the possible associations between epidemiological aspects and feminicide rates, in towns of the Sergipe State in Northeastern Brazil. An exploratory ecological study investigated the global spatial autocorrelation of epidemiological aspects with femicide rates from towns in Sergipe State, Brazil, (n = 75), in the 2013-2017 period, using the "global" and "local" Moran statistic method and a multiple spatial regression. The exposure variables included socioeconomic and demographic conditions, services and health condition, and femicide rates. We used the software Stata 11.0, SPSS 18.0 and GeoDa 0.95-i. The spatial distribution of femicide rates was not random and showed high spatial autocorrelation and predominance of significant spatial groupings of towns with the highest mortality rates due to femicide in the central region of Sergipe State. In the multiple regression analysis, the percentage of women in charge of families and the Municipal Human Development Index were positively associated with the femicide rates in towns in Sergipe's municipalities in the studied period (p < 0.05). The opposite situation occurred between the Income Concentration Index (GINI) and the femicide rates. This is the first study that has analyzed the factors associated with the spatial clusters of femicide rates in a geographical space where there is a predominance of patriarchal culture. There was a femicide increase in locations with the lowest social inequality, the highest human development and authority exercised by women in the family environment.

Caracterização e análise espacial da violência sexual contra crianças e adolescentes na Bahia

O estudo teve como objetivo analisar o fenômeno da violência sexual contra crianças e adolescentes no estado da Bahia, entre 2014 e 2016, desde a sua caracterização às relações espaciais. Trata-se de um estudo ecológico dos casos notificados de violência sexual em crianças e adolescentes, ocorridos na Bahia, com caracterização sociodemográfica dos casos, das ocorrências e dos agressores; tendência temporal das taxas e estatística I de Moran para análise espacial. Foram notificados 2.443 casos, as vítimas foram majoritariamente do sexo feminino (85,2%), média de idade 12 anos e pardas (69,3%); os agressores eram conhecidos (44,2%) e do sexo masculino (95,0%). Em relação a distribuição das taxas se observou variação de 1,7/100 mil hab. em janeiro de 2014, para 1,0/100 mil hab. em dezembro de 2016. Na espacialização observou-se incidência do fenômeno em quase totalidade dos municípios baianos (96%) com formação de clusters alto-alto em aproximadamente 6%. Assim, conclui-se que as crianças e adolescentes estão potencialmente expostos a violência sexual. A espacialização dos casos abre um leque de possibilidades para planejamento de estratégias de vigilância à saúde, visando intervenções mais assertivas.

Economic Activity of the Population by Age in the European Union Countries

The employment level research is an important element of economic analyses supporting the conduct of efficient regional or country policy. Many factors influence the level of this phenomenon, these are demographic, social and economic factors. The employment level can be considered in various categories and the demographic changes encourage to carry out employment analyses by age. Therefore, the subject of the analysis was employment (employment rate) of the European Union countries broken down by age. The main purpose of the article was to show similarities and differences in the level and structure of employment occurring in the European Union countries, and besides, examining the existence of spatial patterns in the period under investigation. To achieve this goal, selected quantitative tools were used, including classic and positional measures of central tendency, indicators of dynamics (average change rate) and measures of interdependence between variables (Pearson's correlation coefficient). In addition, selected spatial autocorrelation measures (global and local Moran's statistic) were used to identify spatial dependences. Data for analyses were taken from the Eurostat database. The results of the research showed the changing employment structure (by age) in the European Union countries and showed the existence of certain spatial dependences, especially in the oldest group of employed persons.

Mortality in motorcycle accidents in Alagoas (2001-2015): temporal and spatial modeling before and after the "lei seca".

To analyze the epidemiological profile and the Spatio-temporal distribution of mortality in motorcycle accidents in Alagoas before (2001-2007) and after the "Lei seca" (2008-2015). This is a mixed ecologic study. All deaths in the state with the codes V20-V29 (ICD-10) as the basic cause were included in the study. Sociodemographic variables and mortality rates per sex were analyzed. For the temporal analysis, the inflection point regression model was used. For spatial analysis, the rates were smoothed by the Local Empirical Bayesian Model and, subsequently, the Global and Local Moran statistic was used to identify the spatial clusters of risk. There were 1458 deaths caused by motorcycle accidents in the period studied; the following characteristics about the victims stand out: male (91.29%), economically active age (82.93%), and brown race (78.12%). In the male population, there was a growth trend between 2001 and 2007 (19.0%, p<0.001), and a decline from 2008 (-11.2%, p<0.001). Spatial modeling showed that the areas with the highest risk of mortality are located in the agreste and sertão of the state (p = 0.01). Mortality in motorcycle accidents is an important public health problem in Alagoas, with an emphasis on male mortality and geographic concentration within the state.

The Standard Errors of Persistence

A large literature on persistence finds that many modern outcomes strongly reflect characteristics of the same places in the distant past. However, alongside unusually high t statistics, these regressions display severe spatial autocorrelation in residuals, and the purpose of this paper is to examine whether these two properties might be connected. We start by running artificial regressions where both variables are spatial noise and find that, even for modest ranges of spatial correlation between points, t statistics become severely inflated leading to significance levels that are in error by several orders of magnitude. We analyse 27 persistence studies in leading journals and find that in most cases if we replace the main explanatory variable with spatial noise the fit of the regression commonly improves; and if we replace the dependent variable with spatial noise, the persistence variable can still explain it at high significance levels. We can predict in advance which persistence results might be the outcome of fitting spatial noise from the degree of spatial autocorrelation in their residuals measured by a standard Moran statistic. Our findings suggest that the results of persistence studies, and of spatial regressions more generally, might be treated with some caution in the absence of reported Moran statistics and noise simulations.

Pseudo eliminação da hanseníase em estado no nordeste brasileiro: análise a partir de regressão por pontos de inflexão e modelo bayesiano empírico local

Justificativa e Objetivos: Alagoas configura-se como um estado brasileiro no qual a hanseníase encontra-se eliminada, todavia há evidências de que se trata de uma pseudo eliminação. Neste sentido o objetivo do estudo foi analisar a dinâmica temporal e espacial da Hanseníase no estado de Alagoas-Brasil, entre 2010-2015. Métodos: Foi realizado estudo ecológico incluindo seis indicadores de monitoramento da hanseníase obtidos a partir de dados secundários do Sistema Nacional de Agravos de Notificação Para a análise temporal, adotou-se joinpoint regression model. A tendência foi classificada em crescente, decrescente ou estacionária. Para a análise espacial, utilizou-se o Modelo Bayesiano Empírico Local e a Estatística de Moran Global e Local. Resultados: A análise por joinpoint mostrou tendência de redução do coeficiente de prevalência (APC=-11,2; p=0,008) e de aumento da proporção de contatos examinados (APC=7,0; p=0,015). O coeficiente de detecção geral e de indivíduos com grau II de incapacidade física, bem como a proporção de cura apresentaram padrão estacionário. O coeficiente de detecção em menores de 15 anos mostrou inversão da tendência a partir de 2013 (APC=7,8; p=0,011). A estatística de Moran mostrou autocorrelação espacial, com municípios mais prioritários no sertão do estado. Conclusão: Apesar de a hanseníase ser considerada eliminada em Alagoas, a elevada carga na população geral, a presença em menores de 15 anos e de indivíduos incapacitados, a frágil proporção de cura, a qualidade duvidosa do exame de contatos e a localização geográfica do estado constituem elementos que sustentam que a eliminação trata-se de um processo operacional e não real. Descritores: Hanseníase. Análise espacial. Informática médica.

Spatial statistics of hydrography and water chemistry in a eutrophic boreal lake based on sounding and water samples.

Spatial variability, an essential characteristic of lake ecosystems, has often been neglected in field research and monitoring. In this study, we apply spatial statistical methods for the key physics and chemistry variables and chlorophyll a over eight sampling dates in two consecutive years in a large (area 103km2) eutrophic boreal lake in southern Finland. In the four summer sampling dates, the water body was vertically and horizontally heterogenic except with color and DOC, in the two winter ice-covered dates DO was vertically stratified, while in the two autumn dates, no significant spatial differences in any of the measured variables were found. Chlorophyll a concentration was one order of magnitude lower under the ice cover than in open water. The Moran statistic for spatial correlation was significant for chlorophyll a and NO2+NO3-N in all summer situations and for dissolved oxygen and pH in three cases. In summer, the mass centers of the chemicals were within 1.5km from the geometric center of the lake, and the 2nd moment radius ranged in 3.7-4.1km respective to 3.9km for the homogeneous situation. The lateral length scales of the studied variables were 1.5-2.5km, about 1km longer in the surface layer. The detected spatial "noise" strongly suggests that besides vertical variation also the horizontal variation in eutrophic lakes, in particular, should be considered when the ecosystems are monitored.

Density Estimation of Spatio-temporal Point Patterns Using Moran's Statistic

Moran's Index is a statistic that measures spatial autocorrelation, quantifying the degree of dispersion (or spread) of objects in space. When investigating data in an area, a single Moran statistic may not give a sufficient summary of the autocorrelation spread. However, by partitioning the area and taking the Moran statistic of each subarea, we discover patterns of the local neighbors not otherwise apparent. In this paper, we consider the model of the spread of an infectious disease, incorporate time factor, and simulate a multilevel Poisson process where the dependence among the levels is captured by the rate of increase of the disease spread over time, steered by a common factor in the scale. The main consequence of our results is that our Moran statistic is calculated from an explicit algorithm in a Monte Carlo simulation setting. Results are compared to Geary's statistic and estimates of parameters under Poisson process are given.

New Methods For Analyzing Spatio-Temporal Simulation Results Of Moran’s Index

Moran’s index is a statistic that measures spatial autocorrelation; it quantifies the degree of dispersion (or clustering) of objects in space. In data analysis across two dimensions over a general area, a single Moran statistic proves insufficient for identifying the spread, behavior, features, or latent surfaces shared by neighboring areas. An alternative method divides the general area and uses the Moran statistic of each resulting sub-area to identify features of neighboring areas. In this paper, we add a time variable to a spatial Poisson point process. On the basis of the results of this simulation, we investigate variations in Moran statistics of neighboring areas and put forward approaches for the related analysis. Results of this work emphasize the importance of observing caution in handling spatiotemporal data when using methods involving implicit normality assumptions.

Detecting Dependence Between Spatial Processes

Testing the assumption of independence between variables is a crucial aspect of spatial data analysis. However, the literature is limited and somewhat confusing. To our knowledge, we can mention only the bivariate generalization of Moran's statistic. This test suffers from several restrictions: it is applicable only to pairs of variables, a weighting matrix and the assumption of linearity are needed; the null hypothesis of the test is not totally clear. Given these limitations, we develop a new non-parametric test, Υ(m), based on symbolic dynamics with better properties. We show that the Υ(m) test can be extended to a multivariate framework, it is robust to departures from linearity, it does not need a weighting matrix and can be adapted to different specifications of the null. The test is consistent, computationally simple and with good size and power, as shown by a Monte Carlo experiment. An application to the case of the productivity of the manufacturing sector in the Ebro Valley illustrates our approach.

How to interpret and choose a Bayesian spatial model and a Poisson regression model in the context of describing small area cancer risks variations

BackgroundThe statistical Bayesian approach is widely used in disease mapping and Poisson regression. Results differ depending on the underlying hypothesis. Our objective is to give a comprehensive presentation of the tools that can be used to interpret results and choose between the different hypotheses. Data from the Isere cancer registry (France) illustrate this presentation. MethodWe consider, first, Bayesian models for disease mapping. Classic heterogeneity (Potthoff-Whithinghill statistic) and spatial autocorrelation tests (Moran statistic) of the SIRs, the DIC criteria of the different Bayesian models and finally the comparison of the empirical variance of the unstructured and structured heterogeneity components of the BYM model are considered. The last two criteria are considered for Bayesian Poisson regression including a covariate. Mapping the components of the BYM model with a covariate is also considered. ResultsFour cancer sites (prostate, lung, colon-rectum and bladder) in men diagnosed during the 1998–2007 period are used to illustrate our presentation. We show that the different criteria used to interpret and to choose a model give coherent results. ConclusionA relevant interpretation of results is a necessary step in choosing the best-adapted Bayesian model. This choice is easy to make with criteria such as the DIC. The comparison of the empirical variance of the unstructured and structured heterogeneity components of the BYM model is also informative.

Global and Local: Measuring Geographical Concentration of China's Manufacturing Industries

Based on a county-level Chinese industry survey data set, this article aims to extend the agglomeration literature by applying and comparing selected combination indexes of geographical concentration that incorporate both traditional indexes of inequality and measures of spatial autocorrelation at the global level and by applying and comparing a new measure, the focal location quotient (FLQ), to the local Moran's I, a commonly used local indicator of spatial association, at the county level. At the global level, the results show that the combination indexes used are generally effective for comparing the extent of geographical concentration across industries, and they could serve as useful dependent variables in modeling agglomeration effects across industries. At the local level, specific spatial patterns of production concentrations are identified for textiles, machinery, food manufacturing, and the electronics and telecommunication industries. FLQ tends to generate more generalized patterns than does the local Moran statistic. Mapping the local statistics is useful in supplementing the global measures, and those maps tend to support the results of the global combination indexes.