Simultaneous Autoregressive Research Articles

Exploring and modeling the level of service of urban public transit: the case of the Greater Toronto and Hamilton Area, Canada

This study assesses the availability of public transit (i.e. supply) in the Greater Toronto and Hamilton Area (GTHA), Canada. We examine transit service intensity at the census tract level by assembling and analyzing a suitable GIS database for the study area. We make use of a version of the ‘Local Index of Transit Availability’ (LITA) to measure and explore service levels based on the coverage, capacity, and frequency of the transit system. Generated LITA measures are regressed against a number of locational covariates to establish a statistical relationship between the level of transit service and the characteristics of the site transit is servicing. We utilize a simultaneous auto-regressive (SAR) model to account for spatial effects and correct for the estimation bias that usually arises from the conventional Ordinary Least Squares (OLS) modeling approach. Results from exploring LITA indicate that the core areas of municipalities were not necessarily well serviced by public transit. Suburban peripheral tracts and those adjacent to the shoreline were characterized by average transit service at best, and areas adjacent to municipal borders indicated discontinuity in transit service. Furthermore, the multivariate analyses suggest that population density and income, as well as the presence of certain socio-economic groups in a tract (e.g. recent immigrants, young adults and elderly) can serve as key locational variables when examining transit availability.

Inter- and Intraspecific Geographic Variation of Body Size in South American Redbelly Toads of the Genus Melanophryniscus Gallardo, 1961 (Anura: Bufonidae)

Amphibians show strong dependence on environmental variables (water balance, temperature). However, interactions affecting geographic distribution of body size are poorly known. We present an analysis of body size within and between species of an anuran genus using a climatic approach. We studied geographic body size distribution in 23 species of South American redbelly toads (Melanophryniscus) spanning 16° latitude, 22° longitude, and 2,400 m altitude. Body size was analyzed in relation to climatic parameters including temperature, precipitation, seasonality, evapotranspiration, and water balance at interspecific, interpopulational (all populations regardless of species), and intraspecific (populations within species) levels. LogSVL was regressed against climatic principal components scores using simultaneous autoregression. Interspecifically and interpopulationally, temperature and precipitation are the main factors responsible for the observed size clines, larger body sizes being associated with decreasing maximum ambient temperature and water availability. Intraspecific results for two species suggested comparable body-size trends. That temperature affects these size clines is reinforced by the strong positive correlation of logSVL with altitude. Because anurans strongly depend on water for survival and reproduction, it is reasonable that ,besides temperature, larger body size is favored in drier environments, which is supported by the correlation between body size and coefficients of variation of annual rainfall: lower surface : volume ratios in larger species would help conserve water in unpredictable environments. Also, Melanophryniscus has reproductive peculiarities associated with ephemeral aquatic environments: explosive breeding synchronized with rainfall; eggs deposited in several clutches; and rapid tadpole development, which suggest a strong relationship between life history and water balance.

Predicting urban forest growth and its impact on residential landscape water demand in a semiarid urban environment

We present an innovative approach to estimating residential irrigation water demand for a large metropolitan area using GIS data, weather station data, and a water budget modeling approach commonly used by plant scientists and landscape management professionals. An important question addressed by our study is how a growing urban forest affects the overall irrigation water demand of a semiarid metropolitan area. To estimate the amount of water required by residential landscaping, we consider water demand to be a function of the areal extent of residential landscaping (i.e. tree/shrub or turf grass), the water-loss rate for different landscaping types, the efficiency with which the landscape is irrigated, and local climatic factors (i.e. reference evapotranspiration and precipitation). We estimated irrigation water demand for 542 residential neighborhoods in Salt Lake County, UT, USA for 2005. To investigate the effects of a maturing urban forest on water demand, we used simultaneous autoregression (SAR) models to predict the spatial extent of future forest canopy and future exposed turf grass in residential neighborhoods. For both the forest canopy model and the turf grass model we used the median age of housing stock as the dependent variable. Psuedo R 2 were 0.70 and 0.82 for the tree/shrub canopy and turf grass models, respectively. Based on projected areal extents of tree/shrub canopy, exposed turf grass, and turf grass under canopy, we estimated future water demands for the 542 residential neighborhoods. Our predictive model suggests that as urban tree canopy increases in residential urban areas, exposed turf grass decreases, with a net effect of a slight decrease in residential landscape water demand. This can be explained by the relative differences in water lost through evapotranspiration by different landscape types, namely; trees/shrub (i.e. woody plants), exposed turf grass, and turf grass under tree canopy.

A test of Allen’s rule in subterranean mammals: the genus Ctenomys (Caviomorpha, Ctenomyidae)

We tested the applicability of Allen's rule in 47 species and 32 unnamed forms (populations that are probably good species or undefined taxa within a superspecies or species group) of the South American subterranean Hystricomorph rodents of the genus Ctenomys (tuco-tucos) (Rodentia: Ctenomyidae) by analyzing tail length in relation with head and body length, and body mass. Tail length allometry was analyzed by Reduced Major Axis regression while the possible correlation of relative tail length with temperature, precipitation and evapotranspiration variables was explored through Simultaneous Autoregression to account for spatial autocorrelations. Our results indicate that tuco-tucos do not follow Allen's rule but its converse, tail proportion relative to body mass increasing with latitude while body size decreases in the same direction (the trend is similar for tail length relative to head and body length but not statistically significant). Regarding climatic variables, the main predictors of relative tail length were temperature and evapotranspiration variables with trends confirming the positive (non-Allenian) correlation of relative tail length with latitude. We conclude that tuco-tucos, being almost fully subterranean, thermoregulate behaviorally by maintaining constant temperatures within their burrows independent of geographic location. The former confirms previous results that indicated that Ctenomys follows the converse to Bergmann's rule. Relative tail length variation would be a result of simple allometric growth.

Environmental correlates of body size distributions of European springtails (Hexapoda: Collembola)

ABSTRACTAim Species–body size distributions (SBDs) are plots of species richness across body size classes. They have been linked to energetic constraints, speciation–extinction dynamics and to evolutionary trends. However, little is known about the spatial variation of size distributions. Here we study SBDs of European springtails (Collembola) at a continental scale and test whether minimum, average and maximum body size and the shapes of size distributions change across latitudinal and longitudinal gradients and whether SBDs of islands and mainlands differ. We also test whether the island rule and the positive body size–range size relationship of vertebrates also holds for Collembola.Location Europe.Methods We use a unique data set on the spatial distributions of 2102 species of European springtails across 52 countries and larger islands together with associated data on body size, area, climate variables, longitude and latitude. Differences in the central moments of SBDs are inferred from simultaneous spatial autoregression models.Results The SBD of the European Collembola and its largest suborder Entomobryomorpha is unimodal and symmetrical. Average, minimum and maximum body weight and the skewness of the mainland/island SBDs peaked at intermediate latitudes. We could not find simple latitudinal gradients in minimum and maximum body weight. Average and maximum body size increased with country/island area in accordance with the island rule in vertebrates, while minimum body size did not significantly differ between islands and mainlands. Finally, we found a weak but statistically significant positive correlation of range size and body size.Main conclusions We provide evidence for differences in body size distributions between islands and mainlands that are in part in line with the island rule in invertebrates. We also find evidence for an interspecific body size–range size relationship similar to that of vertebrates although the vertebrate pattern is much stronger than the springtail pattern. Our results on latitudinal gradients of maximum and average body size imply the need to account for species richness and area effects in the study of latitudinal gradients in body size. We recommend implementing sample size and area effects in the study of body size distributions on islands and mainlands.

Analysis of potential impacts of climate change on forests of the United States Pacific Northwest

As global climate changes over the next century, forest productivity is expected to change as well. Using PRISM climate and productivity data measured on a grid of 3356 plots, we developed a simultaneous autoregressive (SAR) model to estimate the impacts of climate change on potential productivity of Pacific Northwest (PNW) forests of the United States. Productivity, measured by projected potential mean annual increment (PMAI) at culmination, is explained by the interaction of annual temperature, precipitation, and precipitation in excess of evapotranspiration through the growing season. By utilizing information regarding spatial error in the SAR model, the resulting spatial bias is reduced thereby improving the accuracy of the resulting maps. The model, coupled with climate change output from four generalized circulation models, was used to predict the productivity impacts of four different scenarios derived from the fourth IPCC special report on emissions, representing different future economic and environmental states of the world, viz., scenario A1B, A2, B1 (low growth, high economic development and low energy usage), and COMMIT. In these scenarios, regional average temperature is expected to increase from 0.5 to 4.5 °C, while precipitation shows no clear trend over time. For the west and east side of the Cascade Mountains, respectively, PMAI increases: 7% and 20% under A1B scenario; 8% and 23% under scenario A2; 5% and 15% under scenario B1, and 2% and 5% under the COMMIT scenario. These projections should be viewed as potential changes in productivity, since they do not reflect the mitigating effects of any shifts in management or public policy. For managers and policy makers, the results suggest the relative magnitude of effects and the potential variability of impacts across a range of climate scenarios.

Macrophytes as indicators of stream condition in the wet tropics region, Northern Queensland, Australia

This study investigates the use of aquatic macrophytes as indicators of stream condition in catchments with varied land use and levels of riparian disturbance in the Wet Tropics region of North Queensland (Australia), a region of global significance in terms of faunal and floral diversity. In a paired catchment design spatial variations in macrophyte assemblage structure were characterised using multivariate and univariate techniques. Seven metrics were trialled: total macrophyte cover, species richness, % alien taxa, % native taxa, % submerged taxa, % emergent taxa and % Poaceae. Forty-four macrophyte taxa were recorded from the study area. Poaceae, Cyperaceae and mosses were the most frequently recorded taxa. Upper catchment areas in all tributaries surveyed were dominated by mosses and Cladopus queenslandicus (Domin) C.D.K. Cook (Podestemaceae). This assemblage occurred in areas with intact riparian canopy cover and good overall riparian condition. Macrophyte assemblages in lower catchment areas were distributed along gradients of riparian disturbance. Simultaneous autoregression model coefficients indicated that riparian condition had a negative influence on macrophyte cover, species richness and the proportions of alien taxa, emergent taxa and Poaceae present at sites in the Wet Tropics. Macrophyte metrics were not strongly influenced by the types of land use or water quality. These findings suggest that a riparian condition assessment would provide an adequate first assessment of the state of aquatic macrophyte assemblages in Wet Tropics streams.

Effects of habitat history and extinction selectivity on species-richness patterns of an island land snail fauna

Aim Local-scale diversity patterns are not necessarily regulated by contemporary processes, but may be the result of historical events such as habitat changes and selective extinctions that occurred in the past. We test this hypothesis by examining species-richness patterns of the land snail fauna on an oceanic island where forest was once destroyed but subsequently recovered. Location Hahajima Island of the Ogasawara Islands in the western Pacific. Methods Species richness of land snails was examined in 217 0.25 × 0.25 km squares during 1990–91 and 2005–07. Associations of species richness with elevation, current habitat quality (proportion of habitat composed of indigenous trees and uncultivated areas), number of alien snail species, and proportion of forest loss before 1945 in each area were examined using a randomization test and simultaneous autoregressive (SAR) models. Extinctions in each area and on the entire island were detected by comparing 2005–07 records with 1990–91 records and previously published records from surveys in 1987–91 and 1901–07. The association of species extinction with snail ecotype and the above environmental factors was examined using a spatial generalized linear mixed model (GLMM). Results The level of habitat loss before 1945 explained the greatest proportion of variation in the geographical patterns of species richness. Current species richness was positively correlated with elevation in the arboreal species, whereas it was negatively correlated with elevation in the ground-dwelling species. However, no or a positive correlation was found between elevation and richness of the ground-dwelling species in 1987–91. The change of the association with elevation in the ground-dwelling species was caused by greater recent extinction at higher elevation, possibly as a result of predation by malacophagous flatworms. In contrast, very minor extinction levels have occurred in arboreal species since 1987–91, and their original patterns have remained unaltered, mainly because flatworms do not climb trees. Main conclusions The species-richness patterns of the land snails on Hahajima Island are mosaics shaped by extinction resulting from habitat loss more than 60 years ago, recent selective extinction, and original faunal patterns. The effects of habitat destruction have remained long after habitat recovery. Different factors have operated during different periods and at different time-scales. These findings suggest that historical processes should be taken into account when considering local-scale diversity patterns.

Spatial autocorrelation and the selection of simultaneous autoregressive models

ABSTRACTAim Spatial autocorrelation is a frequent phenomenon in ecological data and can affect estimates of model coefficients and inference from statistical models. Here, we test the performance of three different simultaneous autoregressive (SAR) model types (spatial error = SARerr, lagged = SARlag and mixed = SARmix) and common ordinary least squares (OLS) regression when accounting for spatial autocorrelation in species distribution data using four artificial data sets with known (but different) spatial autocorrelation structures.Methods We evaluate the performance of SAR models by examining spatial patterns in model residuals (with correlograms and residual maps), by comparing model parameter estimates with true values, and by assessing their type I error control with calibration curves. We calculate a total of 3240 SAR models and illustrate how the best models [in terms of minimum residual spatial autocorrelation (minRSA), maximum model fit (R2), or Akaike information criterion (AIC)] can be identified using model selection procedures.Results Our study shows that the performance of SAR models depends on model specification (i.e. model type, neighbourhood distance, coding styles of spatial weights matrices) and on the kind of spatial autocorrelation present. SAR model parameter estimates might not be more precise than those from OLS regressions in all cases. SARerr models were the most reliable SAR models and performed well in all cases (independent of the kind of spatial autocorrelation induced and whether models were selected by minRSA, R2 or AIC), whereas OLS, SARlag and SARmix models showed weak type I error control and/or unpredictable biases in parameter estimates.Main conclusions SARerr models are recommended for use when dealing with spatially autocorrelated species distribution data. SARlag and SARmix might not always give better estimates of model coefficients than OLS, and can thus generate bias. Other spatial modelling techniques should be assessed comprehensively to test their predictive performance and accuracy for biogeographical and macroecological research.

Red herrings revisited: spatial autocorrelation and parameter estimation in geographical ecology

There have been numerous claims in the ecological literature that spatial autocorrelation in the residuals of ordinary least squares (OLS) regression models results in shifts in the partial coefficients, which bias the interpretation of factors influencing geographical patterns. We evaluate the validity of these claims using gridded species richness data for the birds of North America, South America, Europe, Africa, the ex‐USSR, and Australia. We used richness in 110×110 km cells and environmental predictor variables to generate OLS and simultaneous autoregressive (SAR) multiple regression models for each region. Spatial correlograms of the residuals from each OLS model were then used to identify the minimum distance between cells necessary to avoid short‐distance residual spatial autocorrelation in each data set. This distance was used to subsample cells to generate spatially independent data. The partial OLS coefficients estimated with the full dataset were then compared to the distributions of coefficients created with the subsamples. We found that OLS coefficients generated from data containing residual spatial autocorrelation were statistically indistinguishable from coefficients generated from the same data sets in which short‐distance spatial autocorrelation was not present in all 22 coefficients tested. Consistent with the statistical literature on this subject, we conclude that coefficients estimated from OLS regression are not seriously affected by the presence of spatial autocorrelation in gridded geographical data. Further, shifts in coefficients that occurred when using SAR tended to be correlated with levels of uncertainty in the OLS coefficients. Thus, shifts in the relative importance of the predictors between OLS and SAR models are expected when small‐scale patterns for these predictors create weaker and more unstable broad‐scale coefficients. Our results indicate both that OLS regression is unbiased and that differences between spatial and nonspatial regression models should be interpreted with an explicit awareness of spatial scale.

공간 시계열 모형을 이용한 소지역 추정

시계열 모형과 공간통계 모형이 결합된 공간 시계열 모형에 관한 많은 연구가 발표되고 있다. 최근 de Luna와 Genton(2003, 2005)은 공간 시계열 모형을 이용한 실업률의 소지역 추정을 발표하는 등 공간 시계열 기법을 이용한 소지역 추정방법의 연구도 빠르게 진행되고 있다. 본 논문에서는 공간 시계열 모형을 이용한 소지역 추정기법을 설명하고 이 기법과 신기 일과 이상은(2003)이 발표한 공간모형을 이용한 소지역 추정을 비교하였다. Small area estimation has been studied using various methods such as direct, indirect, synthetic and based on regression or time series model . In this paper we investigate a motel-based small area estimation which takes into account the spare time autoregressive model. The Economic Active Population Surveys in 2001 are used for analysis and the results from space-time autoregressive(STAR) and simultaneous autoregressive(SAR) model are compared with using MSE, MAE and MB.

A Learning-Based Method for Image Super-Resolution From Zoomed Observations

We propose a technique for super-resolution imaging of a scene from observations at different camera zooms. Given a sequence of images with different zoom factors of a static scene, we obtain a picture of the entire scene at a resolution corresponding to the most zoomed observation. The high-resolution image is modeled through appropriate parameterization, and the parameters are learned from the most zoomed observation. Assuming a homogeneity of the high-resolution field, the learned model is used as a prior while super-resolving the scene. We suggest the use of either a Markov random field (MRF) or an simultaneous autoregressive (SAR) model to parameterize the field based on the computation one can afford. We substantiate the suitability of the proposed method through a large number of experimentations on both simulated and real data.

Analysis of determinants of mammalian species richness in South America using spatial autoregressive models

Classically, hypotheses concerning the distribution of species have been explored by evaluating the relationship between species richness and environmental variables using ordinary least squares (OLS) regression. However, environmental and ecological data generally show spatial autocorrelation, thus violating the assumption of independently distributed errors. When spatial autocorrelation exists, an alternative is to use autoregressive models that assume spatially autocorrelated errors. We examined the relationship between mammalian species richness in South America and environmental variables, thereby evaluating the relative importance of four competing hypotheses to explain mammalian species richness. Additionally, we compared the results of ordinary least squares (OLS) regression and spatial autoregressive models using Conditional and Simultaneous Autoregressive (CAR and SAR, respectively) models. Variables associated with productivity were the most important at determining mammalian species richness at the scale analyzed. Whereas OLS residuals between species richness and environmental variables were strongly autocorrelated, those from autoregressive models showed less spatial autocorrelation, particularly the SAR model, indicating its suitability for these data. Autoregressive models also fit the data better than the OLS model (increasing R2by 5–14%), and the relative importance of the explanatory variables shifted under CAR and SAR models. These analyses underscore the importance of controlling for spatial autocorrelation in biogeographical studies.

Robust methods for the analysis of spatially autocorrelated data

In this paper we propose a new robust technique for the analysis of spatial data through simultaneous autoregressive (SAR) models, which extends the Forward Search approach of Cerioli and Riani (1999) and Atkinson and Riani (2000). Our algorithm starts from a subset of outlier-free observations and then selects additional observations according to their degree of agreement with the postulated model. A number of useful diagnostics which are monitored along the search help to identify masked spatial outliers and high leverage sites. In contrast to other robust techniques, our method is particularly suited for the analysis of complex multidimensional systems since each step is performed through statistically and computationally efficient procedures, such as maximum likelihood. The main contribution of this paper is the development of joint robust estimation of both trend and autocorrelation parameters in spatial linear models. For this purpose we suggest a novel definition of the elemental sets of the Forward Search, which relies on blocks of contiguous spatial locations.

A GIS–Environmental Justice Analysis of Particulate Air Pollution in Hamilton, Canada

The authors address two research questions: (1) Are populations with lower socioeconomic status, compared with people of higher socioeconomic status, more likely to be exposed to higher levels of particulate air pollution in Hamilton, Ontario, Canada? (2) How sensitive is the association between levels of particulate air pollution and socioeconomic status to specification of exposure estimates or statistical models? Total suspended particulate (TSP) data from the twenty-three monitoring stations in Hamilton (1985–94) were interpolated with a universal kriging procedure to develop an estimate of likely pollution values across the city based on annual geometric means and extreme events. Comparing the highest with the lowest exposure zones, the interpolated surfaces showed more than a twofold increase in TSP concentrations and more than a twentyfold difference in the probability of exposure to extreme events. Exposure estimates were related to socioeconomic and demographic data from census tract areas by using ordinary least squares and simultaneous autoregressive (SAR) models. Control for spatial autocorrelation in the SAR models allowed for tests of how robust specific socioeconomic variables were for predicting pollution exposure. Dwelling values were significantly and negatively associated with pollution exposure, a result robust to the method of statistical analysis. Low income and unemployment were also significant predictors of exposure, although results varied depending on the method of analysis. Relatively minor changes in the statistical models altered the significant variables. This result emphasizes the value of geographical information systems (GIS) and spatial statistical techniques in modelling exposure. The result also shows the importance of taking spatial autocorrelation into account in future justice – health studies.

Stationary and Non-stationary Simultaneous Switching Autoregressive Models with an Application to Financial Time Series

A common observation among economists on many economic time-series, including major financial time-series, is the asymmetrical movement between the downward phase and the upward phase of their sample paths. Since this feature of time irreversibility cannot be described by the Gaussian ARMA, ARIMA or ARCH time-series models, we propose stationary and non-stationary simultaneous switching autoregressive (SSAR) models, which are nonlinear switching time-series models. We discuss some properties of these time-series models and the estimation method for their unknown parameters. The asymmetrical conditional heteroscedasticity can be easily incorporated into the SSAR models. We also report a simple empirical result on Nikkei 225 Spot and Futures indices by using a non-stationary SSAR model. JEL Classification Numbers: C22, C32.

On the Dynamic Relations Among Housing Prices, Stock Prices and Interest Rate, Evidence in Taiwan - Simultaneous Equations Model and Vector Autoregression Model

In this study we apply Simultaneous Equations Model and Vector Autoregression Model to examine the dynamic relations among stock prices, interest rat e and housing prices in Taiwan from January 1985 to October 1997. In general, the results support the positive relations between stock prices and housing prices, the negative relations between interest rate and stock prices and the positive relations between interest rate and housing prices, when the interest rate go up, then the stock prices slow down, but the housing prices still maintain go up over one year, we split the period of time to three parts, reach the same conclusions through Forcast Error Pecomposition, the stock prices have high explanation of interest rate and housing price, but housing price canft explain the stock price, that is, if the housing prices go up and then stock prices go up, but stock prices go up canft induce the housing prices go up, the Last, interest rate and stock prices are leading time factors of housing prices. Key words: Housing price, stock price, Interest rate, simultaneous equations model vector Autoregression model

Multispectral random field models for synthesis and analysis of color images

Multispectral extensions to the traditional gray level simultaneous autoregressive (SAR) and Markov random field (MRF) models are considered. Furthermore, a new image model is proposed, the pseudo-Markov model, which retains the characteristics of the multispectral Markov model, yet admits to a simplified parameter estimation method. These models are well-suited to analysis and modeling of color images. For each model considered, procedures are developed for parameter estimation and image synthesis. Experimental results, based on known image models and natural texture samples, substantiate the validity of thee results.

Modeling textured images using generalized long correlation models

The long correlation (LC) models are a general class of random field (RF) models which are able to model correlations, extending over large image regions with few model parameters. The LC models have seen limited use, due to lack of an effective method for estimating the model parameters. In this work, we develop an estimation scheme for a very general form of this model and demonstrate its applicability to texture modeling applications. The relationship of the generalized LC models to other classes of RF models, namely the simultaneous autoregressive (SAR) and Markov random field (MRF) models, is shown. While it is known that the SAR model is a special case of the LC model, we show that the MRF model is also encompassed by this model. Consequently, the LC model may be considered as a generalization of the SAR and MRF models.

Sparse spatial autoregressions

Given local spatial error dependence, one can construct sparse spatial weight matrices. As an illustration of the power of such sparse structures, we computed a simultaneous autoregression using 20 640 observations in under 19 min despite needing to compute a 20 640 by 20 640 determinant 10 times.