Ecological Regression Research Articles

Discovering hidden statistical issues through individual-level models in ecological studies

ABSTRACTIn ecological studies, individual inference is made based on results from ecological models. Interpretation of the results requires caution since ecological analysis on group level may not hold in the individual level within the groups, leading to ecological fallacy. Using an ecological regression example for analyzing voting behaviors, we highlight that the explicit use of individual-level models is crucial in understanding the results of ecological studies. In particular, we clarify three relevant statistical issues for each individual-level models: assessment of the uncertainty of parameter estimates obtained from a wrong model, the use of shrinkage estimation method for simultaneous estimation of many parameters, and the necessity of sensitivity analysis rather than adhering to one seemingly most compelling assumption.

Ecological Assessment of Quality of Surface Water of Small and Medium Rivers of Poltava Region

Purpose. Environmental assessment of the quality of surface water of small and medium rivers of the Poltava region, in particular: medium rivers – Psel, Vorskla, Merla and five small rivers –Govtva, Grun, Kolomak, Poluzorie, Tashan. Methods. Field, atomic absorption spectrophotometry, cluster analysis. Results. In accordance with the quality standard for surface water of cultural and household purposes, all indicators for medium-sized rivers are within the normal range. There was an excess of zinc in the waters of small rivers - Grun, Tashyas and Poluzorie. The low content of soluble oxygen does not meet the norm. When comparing values ​​with the norm of quality of water for reservoirs of fishery management, excess BOD-5 for the Vorskla and Psel rivers is defined; the content of ammonia and nitrites significantly exceeded the normative value for the river Vorskla, Psel, Merla. The excess of surfactants for medium rivers is determined. The river Vorskla is mostly polluted with cupper; the Psel river – with zinc and iron, in water from the Gotvva, Tashan, Poluzorie and Grun rivers we have identified exceeding BOD-5. Regarding the water-soluble nitrogen compounds, only the nitrogen content corresponds to the normative value. The greatest pollution with ammonia is observed for the Govtva and Kolomak rivers. Excess of MAC on the content of nitrites was identified for the Kolomak river. As a result of the cluster analysis of the river, the degree and nature of pollution of surface water are grouped into three main groups: the first is the Kolomak river, the second one is the Merla, Psel, Grun, Vorskla rivers, the third one is the Tashan, Poluzorie and Govtva rivers. In the future, the results can serve as a tool for regulation, monitoring and solution of pollution problems. Conclusions. Small rivers of Poltava region are under considerable anthropogenic impact, their ecological status is estimated as ecological regression. Therefore, priority attention should be paid to improving the ecological status of small rivers in the Poltava region and implementation of the proposed nature conservation measures.

Does including violent crime rates in ecological regression models of sexually transmissible infection rates improve model quality? Insights from spatial regression analyses.

We obtained multiyear (2008-12) cross-sectional county-level data on violent crime and three STIs (chlamydia, gonorrhoea, and primary and secondary (P&S) syphilis) from counties in all the contiguous states in the US (except Illinois and Florida, due to lack of data). We used two measures of STI morbidity (one categorical and one continuous) and applied spatial regression with the spatial error model for each STI, with and without violent crime rate as an independent variable. We computed the associated Akaike's information criterion (AIC) and Bayesian information criterion (BIC) as our measure of the relative goodness of fit of the models. Including the violent crime rate as an independent variable improved the quality of the regression models after controlling for several sociodemographic factors. We found that the lower calculated AICs and BICs indicated more favourable goodness of fit in all the models that included violent crime rates, except for the categorical P&S syphilis model, in which the violent crime variable was not statistically significant. Because violent crime rates can account for the hard-to-measure social determinants of STIs, including violent crime rate as an independent variable can improve ecological regression models of STIs.

The impact of the economic recession on inequalities in induced abortion in the main cities of Spain.

The aim of this study was to analyse the trends in socioeconomic inequalities in induced abortion during the pre-crisis and crisis periods in the postcodes of two major cities of Spain. Ecological regression model showed that rates of induced abortion tended to increase between the two pre-crisis periods, but remained stable between the second pre-crisis period and the crisis period. In addition, we observed socioeconomic inequalities in induced abortion in both cities and in all age groups, and that these inequalities persisted across the three study periods.

Регулирование состояния насаждений на антропогенно преобразованных территориях: принцип дендрологического разнообразия

In low-forest areas with a poor natural of woody vegetation, the ecological capacity of the territory is increased by the introduction of the forest plantations for various purposes, which contribute to the regulation of phytosanitary conditions and the preservation a biodiversity of the regional. Among the ecological-adequate methods for the preservation of ecological optimum in the systems of multifunctional plantations of various purposes are importance of fundamentally: the inclusion of adapted entomophilic and fruit-bearing tree and shrub species, the creation of ecotonic zones of abundant flowering herbs and other landscape-ecological elements. Optimization of the phytocoenotic situation expands environmental preferendum beneficial insects, their attracted by the possibility of additional supply and new safe havens creation for the entomophages its expanded a food range and the use in foods not typical for them types of pests. Collection of material was carried out in the forest plantations of various a special purposes. The objects of the study were useful insects. A samples have been taken by the mowing trees of crowns by the nets of entomological , a visual inspection of the model branches and the manual collecting of predators and phyllophages with species of parasite with the subsequent by cultivation of adult insects in the laboratory conditions. Stabilization of the ratio of harmful and useful insects in the communities is facilitated by the introduction of forest plantations into the landscapes. In this regard, many atypical species of insects in the forest-equipped areas is expand their food spectrum, using non-specialized a species of pests. The number of individuals of parasitic insects here increases by an average of 4.0 times, the abundance of predators increases by three times, the density of economically dangerous pests is reduced by 1.5-4.0 times. Against field pests (harmful bugs and grain flea beetles) the biocenotic role of forests plantation is most pronounced. Their number on forest-protected crops is reduced by 4.0 and 3.5 times, respectively. The increase in dryness of the climate provokes an increase in the density of pests (by 41-96%) and a reduction in the number of their natural enemies (by 16-28%), with the total number of insects increasing by 11-31%. The diversity of dendroflora is determines the effectiveness of action the parasites and predators. Most of the entomophages (28.0% of the total number of useful arthropods) are concentrated in the plant crowns сем. Rosaceae. Attractiveness of plants Sambucus и Lonicera for the parasites and predators are less pronounced – their number here is on average 4.0-10.0 times lower. The complexity of the structure of phytocenosis with the inclusion in the composition of landings blooming profusely woody species increases a exchange the faunal by the facies and strengthening of the complex of the entomophages in the gradient of vertical. Optimization of phytosanitary conditions in the forest stands of different purpose is based on the selection of adapted tree species, positively changing fitered and contributing to the preservation and enhancement of biocenotic relations, biodiversity, restoration of natural mechanisms of self-regulation and, as a result, stabilety functioning of the forest reclamation complexes. Increasing dryness of the climate in the southern direction affects the diversity and abundance of faunal communities of forest reclamation complexes. Zonal of affiliation the communities of entomofaunal to the more arid areas leads to an increase in the total number of insects on 11-31%. Positive effect for a harmonious the entomofauna of community, with an adequate ratio of harmful and useful component, is fold to the areas adjacent to planting - the state of ecological stress. On remote site from the direct influence the forest plantation areas is manifested ecological regression.

The double burden of malnutrition among adolescents: analysis of data from the Global School-Based Student Health and Health Behavior in School-Aged Children surveys in 57 low- and middle-income countries

Adults and young children in countries experiencing the nutrition transition are known to be affected simultaneously by undernutrition and overnutrition. Adolescence is a critical period for growth and development. Yet, it is unknown to what extent this double burden of malnutrition affects adolescents in low- and middle-income countries (LMICs) and the macrolevel contextual factors associated with the double burden of malnutrition. The aim was to quantify the magnitude of the double burden of malnutrition among adolescents and to examine the potential sources of heterogeneity in prevalence estimates across LMICs. We used individual-participant data from the Global School-Based Student Health and Health Behavior in School-Aged Children surveys conducted in 57 LMICs between 2003 and 2013, comprising 129,276 adolescents aged 12-15 y. Pooled estimates of stunting, thinness, or both; overweight or obesity; and concurrent stunting and overweight or obesity were calculated overall, by regions, and stratified by sex, with random-effects meta-analysis. Guided by UNICEF's conceptual framework for child malnutrition, we used ecological linear regression models to examine the association between macrolevel contextual factors (internal conflict, lack of democracy, gross domestic product, food insecurity, urbanization, and survey year) and stunting, thinness, and overweight and obesity prevalence, respectively. The prevalence of stunting was 10.2% (95% CI: 8.3%, 12.2%) and of thinness was 5.5% (95% CI: 4.3%, 6.9%). The prevalence of overweight or obesity was 21.4% (95% CI: 18.6%, 24.2%). Between 38.4% and 58.7% of the variance in adolescent malnutrition was explained by macrolevel contextual factors. The prevalence of concurrent stunting and overweight or obesity was 2.0% (95% CI: 1.7%, 2.5%). The double burden of malnutrition among adolescents in LMICs is common. Context-sensitive implementation and scale-up of interventions and policies for the double burden of malnutrition are needed to achieve the Sustainable Development Goal to end malnutrition in all of its forms by 2030. This trial was registered at clinicaltrials.gov as NCT03346473.

More green space is related to less antidepressant prescription rates in the Netherlands: A Bayesian geoadditive quantile regression approach

BackgroundExposure to green space seems to be beneficial for self-reported mental health. In this study we used an objective health indicator, namely antidepressant prescription rates. Current studies rely exclusively upon mean regression models assuming linear associations. It is, however, plausible that the presence of green space is non-linearly related with different quantiles of the outcome antidepressant prescription rates. These restrictions may contribute to inconsistent findings. ObjectiveOur aim was: a) to assess antidepressant prescription rates in relation to green space, and b) to analyze how the relationship varies non-linearly across different quantiles of antidepressant prescription rates. MethodsWe used cross-sectional data for the year 2014 at a municipality level in the Netherlands. Ecological Bayesian geoadditive quantile regressions were fitted for the 15%, 50%, and 85% quantiles to estimate green space–prescription rate correlations, controlling for physical activity levels, socio-demographics, urbanicity, etc. ResultsThe results suggested that green space was overall inversely and non-linearly associated with antidepressant prescription rates. More important, the associations differed across the quantiles, although the variation was modest. Significant non-linearities were apparent: The associations were slightly positive in the lower quantile and strongly negative in the upper one. ConclusionOur findings imply that an increased availability of green space within a municipality may contribute to a reduction in the number of antidepressant prescriptions dispensed. Green space is thus a central health and community asset, whilst a minimum level of 28% needs to be established for health gains. The highest effectiveness occurred at a municipality surface percentage higher than 79%. This inverse dose-dependent relation has important implications for setting future community-level health and planning policies.

Sensitivity analysis on the ecological bias for Seoul tuberculosis data

In ecological studies, researchers often try to convey the analysis results to individual level based on aggregate data. In order to do this correctly, the possibility of ecological bias should be studied and addressed. One of the key ideas used to address the ecological bias issue is to derive the ecological model from the individual model and to check whether the parameter of interest in the individual model is identifiable in the ecological model. However, the procedure depends on unverifiable assumptions, and we recommend checking how sensitive the results are to these unverifiable assumptions. We analyzed the tuberculosis data that was collected in Seoul in 2005 using a spatial ecological regression model for the aggregate count data with spatial correlation, and found that the deprivation index is likely to have a small positive effect on the occurrence risk of tuberculosis in individual level in Seoul. We considered this finding in various aspects by performing in depth sensitivity analyses. In particular, our findings are shown to be robust to the distribution assumptions for the individual exposure and missing binary covariate across various scenarios.

A simple function for full-subsets multiple regression in ecology with R.

Full‐subsets information theoretic approaches are becoming an increasingly popular tool for exploring predictive power and variable importance where a wide range of candidate predictors are being considered. Here, we describe a simple function in the statistical programming language R that can be used to construct, fit, and compare a complete model set of possible ecological or environmental predictors, given a response variable of interest and a starting generalized additive (mixed) model fit. Main advantages include not requiring a complete model to be fit as the starting point for candidate model set construction (meaning that a greater number of predictors can potentially be explored than might be available through functions such as dredge); model sets that include interactions between factors and continuous nonlinear predictors; and automatic removal of models with correlated predictors (based on a user defined criterion for exclusion). The function takes continuous predictors, which are fitted using smoothers via either gam, gamm (mgcv) or gamm4, as well as factor variables which are included on their own or as two‐level interaction terms within the gam smooth (via use of the “by” argument), or with themselves. The function allows any model to be constructed and used as a null model, and takes a range of arguments that allow control over the model set being constructed, including specifying cyclic and linear continuous predictors, specification of the smoothing algorithm used, and the maximum complexity allowed for smooth terms. The use of the function is demonstrated via case studies that highlight how appropriate model sets can be easily constructed and the broader utility of the approach for exploratory ecology.

Ecological Fallacy and Covariates: New Insights based on Multilevel Modelling of Individual Data

SummaryThe paper provides a new and more explicit formulation of the assumptions needed by the ordinary ecological regression to provide unbiased estimates and clarifies why violations of these assumptions will affect any method of ecological inference. Empirical evidence is obtained by showing that estimates provided by three main ecological inference methods are heavily biased when compared with multilevel logistic regression applied to a unique set of individual data on voting behaviour. The main findings of our paper have two important implications that can be extended to all situations where the assumptions needed to apply ecological inference are violated in the data: (i) only ecological inference methods that allow one to model the effect of covariates have a chance to produce unbiased estimates, and (ii) there are certain data generating mechanisms producing a kind of bias in ecological estimates that cannot be corrected by modelling the effect of covariates.

Spatio-Temporal Poverty Analysis with INLA in Hierarchical Bayes Ecological Regression

Spatio-temporal analysis widely used to describe geo-referenced data that contain information about space and time, with many important response variables and predictors. The models are usually presented as maps to represent the spatial dependence and temporal correlation from time to time. Spatio-temporal models presented in this paper are designed with hierarchical fashion and estimated with INLA (Integrated Nested Laplace Approximation) as the current estimation method for Bayesian analysis. INLA based on latent Gaussian posterior distribution which provides great computational benefit and solve the convergence issue in MCMC (Markov Chain Monte Carlo) algorithm. We model the poverty data set using classical, dynamic and space-time interaction of spatio-temporal models, and investigate the poverty relationship with socio-economics predictors. Using R-INLA package and deviance information criteria for models best fit selection, we conclude dynamical non-parametric is the most proper model on its ecological regressions.

Using ecological propensity score to adjust for missing confounders in small area studies.

SummarySmall area ecological studies are commonly used in epidemiology to assess the impact of area level risk factors on health outcomes when data are only available in an aggregated form. However, the resulting estimates are often biased due to unmeasured confounders, which typically are not available from the standard administrative registries used for these studies. Extra information on confounders can be provided through external data sets such as surveys or cohorts, where the data are available at the individual level rather than at the area level; however, such data typically lack the geographical coverage of administrative registries. We develop a framework of analysis which combines ecological and individual level data from different sources to provide an adjusted estimate of area level risk factors which is less biased. Our method (i) summarizes all available individual level confounders into an area level scalar variable, which we call ecological propensity score (EPS), (ii) implements a hierarchical structured approach to impute the values of EPS whenever they are missing, and (iii) includes the estimated and imputed EPS into the ecological regression linking the risk factors to the health outcome. Through a simulation study, we show that integrating individual level data into small area analyses via EPS is a promising method to reduce the bias intrinsic in ecological studies due to unmeasured confounders; we also apply the method to a real case study to evaluate the effect of air pollution on coronary heart disease hospital admissions in Greater London.

Modelling spatial patterns of misaligned disease data: An application on measles incidence in Namibia

IntroductionQuite often disease data are available in aggregated formats mostly to maintain confidentiality. This leads to a misalignment problem when the goal is to analyze risk at a different level of spatial resolution different from the original administrative level where data were available. ObjectiveTo estimate and map the risk of measles at a sub-region level in Namibia using data obtained at a regional level. MethodsUsing measles data from Namibia for the period 2005–2014, both multi-step and direct approaches were applied to correct for misalignment. Subsequently, ecological Bayesian regression models were fitted and compared. ResultsResults show that the variables standardized birth rate, counts of measles cases for previous year, unemployment rate and proportion of vaccinated children against measles by age 12 months were significant determinants of measles risk. Constituencies having elevated measles risk were identified mostly in the northern corridor with Angola. ConclusionWe recommend that relevant authorities should make geographical target intervention and redesign prevention and control strategies based on these findings.

Evidence of social deprivation on the spatial patterns of excess winter mortality

ObjectivesThe aims of this study are to identify the patterns of excess winter mortality (due to diseases of the circulatory system) and to analyse the association between the excess winter deaths (EWD) and socio-economic deprivation in Portugal.MethodsThe number of EWD in 2002–2011 was estimated by comparing the number of deaths in winter months with the average number in non-winter months. The EWD ratio of each municipality was calculated by following the indirect standardization method and then compared with two deprivation indexes (socio-material and housing deprivation index) through ecological regression models.ResultsThis study found that: (1) the EWD ratio showed considerable asymmetry in its geography; (2) there are significant positive associations between the EWD ratio and both deprivation indexes; and (3) at the higher level of deprivation, housing conditions have a stronger association with EWD than socio-material conditions.ConclusionsThe significant association between two deprivation dimensions (socio-material and housing deprivation) and EWDs suggests that EWD geographical pattern is influenced by deprivation.

National sex work policy and HIV prevalence among sex workers: an ecological regression analysis of 27 European countries

Sex workers are disproportionately affected by HIV compared with the general population. Most studies of HIV risk among sex workers have focused on individual-level risk factors, with few studies assessing potential structural determinants of HIV risk. In this Article, we examine whether criminal laws around sex work are associated with HIV prevalence among female sex workers. We estimate cross-sectional, ecological regression models with data from 27 European countries on HIV prevalence among sex workers from the European Centre for Disease Control; sex-work legislation from the US State Department's Country Reports on Human Rights Practices and country-specific legal documents; the rule of law and gross-domestic product per capita, adjusted for purchasing power, from the World Bank; and the prevalence of injecting drug use among sex workers. Although data from two countries include male sex workers, the numbers are so small that the findings here essentially pertain to prevalence in female sex workers. Countries that have legalised some aspects of sex work (n=17) have significantly lower HIV prevalence among sex workers than countries that criminalise all aspects of sex work (n=10; β=-2·09, 95% CI -0·80 to -3·37; p=0·003), even after controlling for the level of economic development (β=-1·86; p=0·038) and the proportion of sex workers who are injecting drug users (-1·93; p=0·026). We found that the relation between sex work policy and HIV among sex workers might be partly moderated by the effectiveness and fairness of enforcement, suggesting legalisation of some aspects of sex work could reduce HIV among sex workers to the greatest extent in countries where enforcement is fair and effective. Our findings suggest that the legalisation of some aspects of sex work might help reduce HIV prevalence in this high-risk group, particularly in countries where the judiciary is effective and fair. European Centre for Disease Prevention and Control.

The Research of Sports Education Ecological Imbalance and Regression Research

With the progress of the society development, people gradually are to the ecological and harmonious sports activities is more and more attention. How the school sports teaching in the healthy development of the environment, will need to set up and improve the sports ecological education. However, in recent years, the school sports teaching are in a state of imbalance. Based on this, the ecological imbalance in physical education is discussed in this paper, regression and has important practical significance. Ecology as a discipline research, the main research direction is the relationship between biology and biological, as well as the relationship between the non-biological and biological .In the sports in the teaching process, with a variety of interconnected relations, this relationship is the relationship between teachers and students, the relationship between the students, and sports teaching environment and the relationship between the teachers and students each other. And sports teaching activity that ecosystem is the micro in ecological system, therefore, the research of ecological sports teaching is in line with the law of ecological system, and in such an environment, the ecological sports education system appeared a serious imbalance, the students’ physical quality gradually reduce, the teacher also does not carry on the innovation of the physical exploration research, sports as part of the ecological system, more and more lost its balance effect, these factors will be the health sports teaching have very big effect.

Predicting Subnational Ebola Virus Disease Epidemic Dynamics from Sociodemographic Indicators.

BackgroundThe recent Ebola virus disease (EVD) outbreak in West Africa has spread wider than any previous human EVD epidemic. While individual-level risk factors that contribute to the spread of EVD have been studied, the population-level attributes of subnational regions associated with outbreak severity have not yet been considered.MethodsTo investigate the area-level predictors of EVD dynamics, we integrated time series data on cumulative reported cases of EVD from the World Health Organization and covariate data from the Demographic and Health Surveys. We first estimated the early growth rates of epidemics in each second-level administrative district (ADM2) in Guinea, Sierra Leone and Liberia using exponential, logistic and polynomial growth models. We then evaluated how these growth rates, as well as epidemic size within ADM2s, were ecologically associated with several demographic and socio-economic characteristics of the ADM2, using bivariate correlations and multivariable regression models.ResultsThe polynomial growth model appeared to best fit the ADM2 epidemic curves, displaying the lowest residual standard error. Each outcome was associated with various regional characteristics in bivariate models, however in stepwise multivariable models only mean education levels were consistently associated with a worse local epidemic.DiscussionBy combining two common methods—estimation of epidemic parameters using mathematical models, and estimation of associations using ecological regression models—we identified some factors predicting rapid and severe EVD epidemics in West African subnational regions. While care should be taken interpreting such results as anything more than correlational, we suggest that our approach of using data sources that were publicly available in advance of the epidemic or in real-time provides an analytic framework that may assist countries in understanding the dynamics of future outbreaks as they occur.

Pollen exposure and hospital admissions for asthma in London, UK 2005-11

Introduction A high proportion of the UK population has been reported as allergic to pollen. These have increased in prevalence in the UK population quickly over the last 20 years. Pollen from trees in the UK is released in the March to May period and grass pollen and output mid-May to July most years. It is highly variable on a daily basis due to a number of factors including latitude, altitude, phenology and weather. Factors that could be important in influencing pollen-asthma associations include precipitation, thunderstorms, wind, periods of dry weather, and heat. Methods Estimation was made of the association between measured pollen (grains/m3 air) (Met Office, UK) and asthma hospital admissions (Hospital Episode Statistics data, Department of Health) in an ecological time series regression for the period 2005-11 in London. Regression models were specified to estimate percentage change in risk at the 95th percentile versus the 0th percentile associated with 0-7 day lags in unconstrained distributed lag models. Within season trend was accounted for using natural cubic splines of observation days in study seasons. Models were adjusted for air pollution (PM10, NO2, SO2 and O3) and weather variables (temperature, rain and humidity). Results Increases in hospital admissions of 17.2% (95% CI 8.9, 25.5) and 14.1% (95% CI 6.2, 22.0) were noted at 4- and 5-day lags post pollen exposure, respectively, with a 0-95th percentile increase in grass pollen exposure (no increase was found on same day). There was little observed effect from any of the tree pollens. Grass pollen count correlated with O3 levels but not other air pollutants measured. Conclusions Lag effects may be important when examining the relationship between grass pollen and hospital admissions. No synergistic relationship was found between air pollution and pollen and their effect on asthma admissions to hospitals.

A survey on ecological regression for health hazard associated with air pollution

In the last 30 years, a large number of studies have provided substantial statistical evidence of the adverse health effects associated with air pollution. Statistical literature is very rich and includes a plethora of models to manage different types of spatial data. This paper starts with a thorough discussion on the spatial nature of the available data on health and air pollution. Health data are usually provided by Health Authorities as mortality and morbidity counts at a small area level. Thus we mainly focus on reviewing and discussing the spatial and spatio-temporal regression models proposed for disease count data on irregular lattices. In general, measuring the effect of exposure on health outcomes is an extremely hard task, and to obtain reliable estimates of the exposure effect and associated uncertainty one needs to build models that account for the residual variability not captured by the exposure–response relationship. In this context, Bayesian hierarchical models including spatial random effects play a prominent role: we consider both univariate and multivariate models and discuss some extensions to the spatio-temporal setting. Since model estimation can be prohibitive, practitioners are provided with a list of available software for Bayesian inference that avoids the need for complicated coding.

Empirical Zoning Distributions for Small Area Data

It is well established that using data summaries for a set of geographic areas or zones to estimate the parameters of a statistical model, commonly called ecological inference, frequently leads to the modifiable area unit problem (MAUP). In this article, the zoning effect of the MAUP is investigated for a range of scales. A zoning distribution is defined, and then used to characterize the zoning effect for parameter estimates from ecological analyses. Zone‐independent parameter estimates are obtained using the mean of the zoning distribution, and assessed using the variance of the zoning distribution. Zoning distributions are illustrated for parameter estimates from two ecological regression models at multiple scales using Australian National Health Survey data. For both a continuous response variable and a binary response variable, the empirical zoning distributions are unimodal, relatively symmetrical with appreciable variation, even when based on a large number of zones. The “ecological mean,” or expected value of the empirical zoning distribution at each scale, displays systematic variation with scale and the zoning distribution variance also depends on scale. The results demonstrate that the zoning effect should not be ignored, and the sensitivity of ecological analysis results to the analysis zones should be assessed.