CORRECTING FOR SPATIAL EFFECTS IN LIMITED DEPENDENT VARIABLE REGRESSION: ASSESSING THE VALUE OF "AD-HOC" TECHNIQUES

A common test for spatial dependence in regression analysis with continuous dependent variables is the Moran's I. For limited dependent variable models, the standard definition of a residual breaks down because yi is qualitative. Efforts to correct for potential spatial effects in limited dependent variable models have relied on ad-hoc methods such as including a spatial lag variable or using a regular sample that omits neighboring observations. Kelejian and Prucha have recently developed a version of Moran's I for limited dependent variable models. We present the statistic in a more accessible way and use it to test the value of previously-used ad-hoc techniques with a specific data set. Keywords: Morans I, Spatial Autocorrelation, Limited Dependent Variable Models, Land-Use Change, Geographical Information Systems (GIS),Moran's I, Spatial Autocorrelation, Limited Dependent Variable Models, Land-Use Change, Geographical Information Systems (GIS), Research Methods/ Statistical Methods,

Using Moran's I and GIS to study the spatial pattern of forest litter carbon density in a subtropical region of southeastern China

Spatial pattern information of carbon density in forest ecosystem including forest litter carbon (FLC) plays an important role in evaluating carbon sequestration potentials. The spatial variation of FLC density in the typical subtropical forests in southeastern China was investigated using Moran's I, geostatistics and a geographical information system (GIS). A total of 839 forest litter samples were collected based on a 12 km (south–north) × 6 km (east–west) grid system in Zhejiang province. Forest litter carbon density values were very variable, ranging from 10.2 kg ha⁻¹ to 8841.3 kg ha⁻¹, with an average of 1786.7 kg ha⁻¹. The aboveground biomass had the strongest positive correlation with FLC density, followed by forest age and elevation. Global Moran's I revealed that FLC density had significant positive spatial autocorrelation. Clear spatial patterns were observed using local Moran's I. A spherical model was chosen to fit the experimental semivariogram. The moderate "nugget-to-sill" (0.536) value revealed that both natural and anthropogenic factors played a key role in spatial heterogeneity of FLC density. High FLC density values were mainly distributed in northwestern and western part of Zhejiang province, which were related to adopting long-term policy of forest conservation in these areas, while Hang-Jia-Hu (HJH) Plain, Jin-Qu (JQ) Basin and coastal areas had low FLC density due to low forest coverage and intensive management of economic forests. These spatial patterns were in line with the spatial-cluster map described by local Moran's I. Therefore, Moran's I, combined with geostatistics and GIS, could be used to study spatial patterns of environmental variables related to forest ecosystem

Statistical inference and spatial patterns in correlates of IQ

Cross-national comparisons of IQ have become common since the release of a large dataset of international IQ scores. However, these studies have consistently failed to consider the potential lack of independence of these scores based on spatial proximity. To demonstrate the importance of this omission, we present a re-evaluation of several hypotheses put forward to explain variation in mean IQ among nations namely: (i) distance from central Africa, (ii) temperature, (iii) parasites, (iv) nutrition, (v) education, and (vi) GDP. We quantify the strength of spatial autocorrelation (SAC) in the predictors, response variables and the residuals of multiple regression models explaining national mean IQ. We outline a procedure for the control of SAC in such analyses and highlight the differences in the results before and after control for SAC. We find that incorporating additional terms to control for spatial interdependence increases the fit of models with no loss of parsimony. Support is provided for the finding that a national index of parasite burden and national IQ are strongly linked and temperature also features strongly in the models. However, we tentatively recommend a physiological – via impacts on host–parasite interactions – rather than evolutionary explanation for the effect of temperature. We present this study primarily to highlight the danger of ignoring autocorrelation in spatially extended data, and outline an appropriate approach should a spatially explicit analysis be considered necessary

Regional income convergence in Portugal (1991-2012)

Our research aims to address the problem of inequality in income distribution from a different perspective than the usual. We intend to verify if geography influences the pattern of inequality, that is, if the standard of living varies from region to region and if, in the process of growth, spatial units in Portugal have been converging in terms of most relevant variables, such as income. We search the answers to these questions by introducing the treatment of convergence between smaller territorial units, the municipalities as individuals. We intend to evaluate convergence or divergence in income growth and test empirically the theoretical hypothesis that β-convergence, although necessary, is not a sufficient condition for σ-convergence. To study convergence, we use information about GDP and wages for NUTS III regions, and wages for municipalities. We observe spatial dependence between municipalities, so we estimate spatial econometric models to test convergence. With regard to conditional convergence between municipalities, the model most appropriate is the one which includes in the explanatory variables the weight of primary sector employment, leading us to conclude that this variable distinguishes the "steady state" of the small economies. Variables like the activity rate and percentage of active population with higher education also reveal highly significant on the growth of wages, reflecting the different contexts of the labor market at regional level

Dynamics of Change in Spatial Dependencies in Blood Donation System in Poland

Blood donation allows to obtain blood and its components from healthy people in a bid to help treatment of anonymous individuals, relying on timely and sufficient supplies of matching blood. Being a social initiative, it depends on multiple factors. Those factors are possible to be shaped and are subject to research. This paper aims to present the dynamics of change in spatial dependencies determining development of blood donation in Poland from 2005 to 2010. Spatial analysis of data enables identification of similarities and differences between voivodeships in a given period. Testing of hypothesis concerning spatial autocorrelation was carried out using tools of spatial statistics. This paper's subject matter concentrates on pointing towards the direction and extent of changes illustrated with an example of analysis investigating the number of blood donations per hospital bed in wards with high demand on blood and its components. The number of blood donors per 1000 residents in 18 - 65 age was also analysed.Krwiodawstwo jest sposobem pozyskiwania krwi i jej składników od osób zdrowych na rzecz anonimowych osób, których leczenie jest uwarunkowane podaniem właściwej krwi w odpowiednim czasie oraz ilości. Jako akcja społeczna uwarunkowana jest od wielu czynników, będących przedmiotem kształtowania oraz badania. Celem niniejszego opracowania jest przedstawienie dynamiki zmian zależności przestrzennej w zakresie poziomu rozwoju krwiodawstwa w Polsce w latach 2005 - 2010. Analiza przestrzenna danych umożliwia określenie podobieństw i różnic między województwami w badanym okresie. Za pomocą narzędzi statystyki przestrzennej została zweryfikowana hipoteza o występowaniu autokorelacji przestrzennej. Przedmiotem opracowania jest wskazanie kierunku oraz zakresu zmian na przykładzie analizy zróżnicowania liczby donacji krwi przypadającej na łóżko szpitalne w oddziałach o wysokim zapotrzebowaniu na krew i jej składniki oraz liczby dawców przypadających na 1000 mieszkańców w wieku 18 -65

Finite Sample Properties of Moran's I Test for Spatial Autocorrelation in Probit and Tobit Models - Empirical Evidence

In this paper, we investigate the finite sample properties of Moran’s I test statistic for spatial autocorrelation in limited dependent variable models suggested by Kelejian and Prucha (2001). We analyze the socio- economic determinants of the availability of dialysis equipment in 5,507 Brazilian municipalities in 2009 by means of a probit and tobit specifica- tion. We assess the extent to which evidence of spatial autocorrelation can be remedied by the inclusion of spatial fixed effects. We find spa- tial autocorrelation in both model specifications. For the probit model, a spatial fixed effects approach removes evidence of spatial autocorrelation. However, this is not the case for the tobit specification. We further fill a void in the theoretical literature by investigating the finite sample prop- erties of these test statistics in a series of Monte Carlo simulations, using data sets ranging from 49 to 15,625 observations. We find that the tests are unbiased and have considerable power for even medium-sized sample sizes. Under the null hypothesis of no spatial autocorrelation, their em- pirical distribution cannot be distinguished from the asymptotic normal distribution, empirically confirming the theoretical results of Kelejian and Prucha (2001), although the sample size required to achieve this result is larger in the tobit case than in the probit case.

Regional growth patterns in Sweden - a search for hot spots

This paper gives an exploratory description of the regional growth pattern in Sweden during the period 1981-1999. The main issue is to test the hypothesis that municipalities with higher average income growth and net migration rates are more clustered that could be caused by pure chance. The paper is purely descriptive and we make use of statistical tests for spatial clustering as well as maps to identify what we reefer to as ''regional hot spots''. Our results are however very sensitive for the specification of the weights matrix.

Nonparametric regression with spatially dependent data

In this paper we present a new procedure for nonparametric regression in case of spatially dependent data. In particular, we extend usual local linear regression (along the lines of Martins-Filho and Yao, 2009) and propose a two-step method where information on spatial dependence is incorporated in the error covariance matrix, estimated nonparametrically. The finite sample performance of our proposed procedure is then shown via Monte Carlo simulations for various data generating processes.nonparametric smoothing, spatial dependence

Geospatial Variation in Caesarean Delivery

Aim: The purpose of this study was to evaluate the variation in caesarean delivery rates across counties in Georgia and to determine whether county-level characteristics were associated with clusters. Design: This was a retrospective, observational study. Methods: Rates of primary and repeat caesarean by maternal county of residence were calculated for 2008 through 2012. Global Moran\u27s I (Spatial Autocorrelation) was used to identify geographic clustering. Characteristics of high and low-rate counties were compared using student\u27s t test and chi squared test. Results: Spatial analysis of both primary and repeat caesarean rate identified the presence of clusters (Moran\u27s I = 0.375; p \u3c .001). Counties in high-rate clusters had significantly lower access to midwives, more deliveries paid by Medicaid, higher proportion of births for women belonging to racial/ethnic minority groups and were more likely to be rural