Autologistic Model Research Articles

Tsetse fly (G. f. fuscipes) distribution in the Lake Victoria basin of Uganda.

Tsetse flies transmit trypanosomes, the causative agent of human and animal African trypanosomiasis. The tsetse vector is extensively distributed across sub-Saharan Africa. Trypanosomiasis maintenance is determined by the interrelationship of three elements: vertebrate host, parasite and the vector responsible for transmission. Mapping the distribution and abundance of tsetse flies assists in predicting trypanosomiasis distributions and developing rational strategies for disease and vector control. Given scarce resources to carry out regular full scale field tsetse surveys to up-date existing tsetse maps, there is a need to devise inexpensive means for regularly obtaining dependable area-wide tsetse data to guide control activities. In this study we used spatial epidemiological modelling techniques (logistic regression) involving 5000 field-based tsetse-data (G. f. fuscipes) points over an area of 40,000 km2, with satellite-derived environmental surrogates composed of precipitation, temperature, land cover, normalised difference vegetation index (NDVI) and elevation at the sub-national level. We used these extensive tsetse data to analyse the relationships between presence of tsetse (G. f. fuscipes) and environmental variables. The strength of the results was enhanced through the application of a spatial autologistic regression model (SARM). Using the SARM we showed that the probability of tsetse presence increased with proportion of forest cover and riverine vegetation. The key outputs are a predictive tsetse distribution map for the Lake Victoria basin of Uganda and an improved understanding of the association between tsetse presence and environmental variables. The predicted spatial distribution of tsetse in the Lake Victoria basin of Uganda will provide significant new information to assist with the spatial targeting of tsetse and trypanosomiasis control.

Modeling spatiotemporal dynamics of outbreaking species: influence of environment and migration in a locust.

Many pest species exhibit huge fluctuations in population abundance. Understanding their large-scale and long-term dynamics is necessary to develop effective control and management strategies. Occupancy models represent a promising approach to unravel interactions between environmental factors and spatiotemporal dynamics of outbreaking populations. Here, we investigated population dynamics of the Australian plague locust, Chortoicetes terminifera, using density data collected between 1988 and 2010 by the Australian Plague Locust Commission over more than 3 million km2 in eastern Australia. We applied multistate and autologistic multi-season occupancy models to test competing hypotheses about environmental and demographic processes affecting the large-scale dynamics of the Australian plague locust. We found that rainfall and land cover predictors best explained the spatial variability in outbreak probability across eastern Australia. Outbreaks are more likely to occur in temperate than tropical regions, with a faster and more continuous response to rainfall in desert than in agricultural areas. Our results also support the hypothesis that migration tends to propagate outbreaks only locally (over distances lower than 400 km) rather than across climatic regions. Our study suggests that locust outbreak forecasting and management systems could be improved by implementing key environmental factors and migration in hierarchical spatial models. Finally, our modeling framework can be seen as a step towards bridging the gap between mechanistic and more phenomenological models in the spatial analysis of fluctuating populations.

Bayesian Inference of Spatially Correlated Binary Data Using Skew-Normal Latent Variables with Application in Tooth Caries Analysis

The analysis of spatially correlated binary data observed on lattices is an interesting topic that catches the attention of many scholars of different scientific fields like epidemiology, medicine, agriculture, biology, geology and geography. To overcome the encountered difficulties upon fitting the autologistic regression model to analyze such data via Bayesian and/or Markov chain Monte Carlo (MCMC) techniques, the Gaussian latent variable model has been enrolled in the methodology. Assuming a normal distribution for the latent random variable may not be realistic and wrong, normal assumptions might cause bias in parameter estimates and affect the accuracy of results and inferences. Thus, it entails more flexible prior distributions for the latent variable in the spatial models. A review of the recent literature in spatial statistics shows that there is an increasing tendency in presenting models that are involving skew distributions, especially skew-normal ones. In this study, a skew-normal latent variable modeling was developed in Bayesian analysis of the spatially correlated binary data that were acquired on uncorrelated lattices. The proposed methodology was applied in inspecting spatial dependency and related factors of tooth caries occurrences in a sample of students of Yasuj University of Medical Sciences, Yasuj, Iran. The results indicated that the skew-normal latent variable model had validity and it made a decent criterion that fitted caries data.

Nature reserve requirements for landscape-dependent ungulates: The case of endangered takin (Budorcas taxicolor) in Southwestern China

Large ungulates commonly perform seasonal or annual movements that encompass considerable land area and various habitat types. Effective conservation of these species relies not only on insights on their basic ecology, but also an understanding on their requirements to move across landscapes. To determine the key landscape characteristics of the endangered takin (Budorcas taxicolor), we systematically surveyed for their occurrence in the Northern MinShan Mountains, China, during 2010–2011. We then modeled takin distribution at a regional scale using autologistic regression models, and produced a predictive map for their distribution. The results showed that occurrence probabilities for takin were higher in areas with a larger range of elevation, closer to protected areas, farther from townships, and with more forest coverage. There was a considerable overlap between highly suitable takin habitat and the network of protected forest formed by nature reserves originally established to conserve giant panda (Ailuropoda melanoleuca). A broad elevation gradient and the protected area network were essential landscape characteristics in predicting takin distributions and our results suggested that takin should be considered landscape- and conservation-dependent species. The results of this study are applicable to the conservation of large ungulates throughout the mountains bordering the Tibetan Plateau and to a broader suite of mammals that conduct seasonal migrations.

A Centered Bivariate Spatial Regression Model for Binary Data with an Application to Presettlement Vegetation Data in the Midwestern United States

Spatially structured discrete data arise in diverse areas of application, such as forestry, epidemiology, or soil sciences. Data from several binary variables are often collected at each location. Variation in distributional properties across the spatial domain is of interest. The specific application that motivates our work involves characterizing historical distributions of two species of Oak in the Driftless Area in the Midwestern United States. Scientists are interested in understanding the patterns of interaction between species, as well as their relationships to spatial covariates. Accounting for spatial dependence is not only of inherent interest but also reduces prediction mean squared error, and is necessary for obtaining appropriate measures of uncertainty (i.e., standard errors and confidence intervals). To address the needs of the application, we introduce a centered bivariate autologistic model, which accounts for the statistical dependence in two response variables simultaneously, for the association between them and for the effect of spatial covariates. The model proposed here offers a relatively stable large-scale model structure, with model parameters which can be interpreted in the usual sense across levels of dependence. Since the model allows for separate dependence parameters for each variable, it offers, in essence, the equivalent of a model with a non-separable covariance function. The flexible model framework permits straightforward generalizations to structures with more than two variables, a temporal component, or an irregular lattice domain. Supplementary materials accompanying this paper appear on-line.

Approximate maximum likelihood estimation of the autologistic model

Approximate Maximum Likelihood Estimation (AMLE) is a simple and general method recently proposed for approximating MLEs without evaluating the likelihood function. The only requirement is the ability to simulate the model to be estimated. Thus, the method is quite appealing for spatial models because it does not require evaluation of the normalizing constant, which is often computationally intractable. An AMLE-based algorithm for parameter estimation of the autologistic model is proposed. The impact of the numerical choice of the input parameters of the algorithm is studied by means of extensive simulation experiments, and the outcomes are compared to existing approaches. AMLE is much more precise, in terms of Mean-Square-Error, with respect to Maximum pseudo-likelihood, and comparable to ML-type methods. Although the computing time is non-negligible, the implementation is straightforward and the convergence conditions are weak in most practically relevant cases.

Prediction of the spatial distribution of high-rise residential buildings by the use of a geographic field based autologistic regression model

As an indicator of urbanization, high-rise residential buildings, can meet the space requirements of an increasing population and improve land use efficiency. Such buildings are continuously built in the central areas of cities worldwide despite residential suburbanization. To predict high-rise residential building location, this study employs a geographic field model-based autologistic regression model (GFM-autologistic model). In line with this goal, a model is determined using both the value of the area under the receiver operating characteristic curve (ROC) and the Akaike information criterion (AIC) for GFM-autologistic, Euclidean distance (ED)-logistic and ED-autologistic models. The minimum AIC and the maximum ROC values of the GFM-autologistic model indicate that this model has the best fit. The GFM defines the external effect of ecological elements and locational factors, and it also quantifies distance decay through a linear intensity function with an influence threshold, thereby avoiding the bias caused by ED. Moreover, land prices are positive related to building height. High-rise residential development also considers open public spaces, such as rivers and city plazas. In summary, the spatial distribution of high-rise residential buildings displays a distance decay in the effect of ecological elements such as open spaces. Thus, this manuscript provides a theoretical basis for modern-city development planning and modern high-rise residential development.

Spatiotemporal variability of urban growth factors: A global and local perspective on the megacity of Mumbai

The rapid growth of megacities requires special attention among urban planners worldwide, and particularly in Mumbai, India, where growth is very pronounced. To cope with the planning challenges this will bring, developing a retrospective understanding of urban land-use dynamics and the underlying driving-forces behind urban growth is a key prerequisite. This research uses regression-based land-use change models – and in particular non-spatial logistic regression models (LR) and auto-logistic regression models (ALR) – for the Mumbai region over the period 1973–2010, in order to determine the drivers behind spatiotemporal urban expansion. Both global models are complemented by a local, spatial model, the so-called geographically weighted logistic regression (GWLR) model, one that explicitly permits variations in driving-forces across space. The study comes to two main conclusions. First, both global models suggest similar driving-forces behind urban growth over time, revealing that LRs and ALRs result in estimated coefficients with comparable magnitudes. Second, all the local coefficients show distinctive temporal and spatial variations. It is therefore concluded that GWLR aids our understanding of urban growth processes, and so can assist context-related planning and policymaking activities when seeking to secure a sustainable urban future.

Spatial epidemiology of porcine reproductive and respiratory syndrome in Thailand.

BackgroundPorcine reproductive and respiratory syndrome (PRRS) has become a worldwide endemic disease of pigs. In 2006, an atypical and more virulent PRRS (HP-PRRS) emerged in China and spread to many countries, including Thailand. This study aimed to provide a first description of the spatio-temporal pattern of PRRS in Thailand and to quantify the statistical relationship between the presence of PRRS at the sub-district level and a set of risk factors. This should provide a basis for improving disease surveillance and control of PRRS in Thailand.ResultsSpatial scan statistics were used to detect clusters of outbreaks and allowed the identification of six spatial clusters covering 15 provinces of Thailand. Two modeling approaches were used to relate the presence or absence of PRRS outbreaks at the sub-district level to demographic characteristics of pig farming and other epidemiological spatial variables: autologistic multiple regressions and boosted regression trees (BRT). The variables showing a statistically significant association with PRRS presence in the autologistic multiple regression model were the sub-district human population and number of farms with breeding sows. The predictive power of the model, as measured by the area under the curve (AUC) of the receiver operating characteristics (ROC) plots was moderate. BRT models had higher goodness of fit the metrics and identified the sub-district human population and density of farms with breeding sows as important predictor variables.ConclusionsThe results indicated that farms with breeding sows may be an important group for targeted surveillance and control. However, these findings obtained at the sub-district level should be complemented by farm-level epidemiological investigations in order to obtain a more comprehensive view of the factors affecting PRRS presence. In this study, the outbreaks of PRRS could not be differentiated from the potential novel HP-PPRS form, which was recently discovered in the country.

Incorporating spatial autocorrelation into species distribution models alters forecasts of climate-mediated range shifts.

Species distribution models (SDMs) are widely used to forecast changes in the spatial distributions of species and communities in response to climate change. However, spatial autocorrelation (SA) is rarely accounted for in these models, despite its ubiquity in broad-scale ecological data. While spatial autocorrelation in model residuals is known to result in biased parameter estimates and the inflation of type I errors, the influence of unmodeled SA on species' range forecasts is poorly understood. Here we quantify how accounting for SA in SDMs influences the magnitude of range shift forecasts produced by SDMs for multiple climate change scenarios. SDMs were fitted to simulated data with a known autocorrelation structure, and to field observations of three mangrove communities from northern Australia displaying strong spatial autocorrelation. Three modeling approaches were implemented: environment-only models (most frequently applied in species' range forecasts), and two approaches that incorporate SA; autologistic models and residuals autocovariate (RAC) models. Differences in forecasts among modeling approaches and climate scenarios were quantified. While all model predictions at the current time closely matched that of the actual current distribution of the mangrove communities, under the climate change scenarios environment-only models forecast substantially greater range shifts than models incorporating SA. Furthermore, the magnitude of these differences intensified with increasing increments of climate change across the scenarios. When models do not account for SA, forecasts of species' range shifts indicate more extreme impacts of climate change, compared to models that explicitly account for SA. Therefore, where biological or population processes induce substantial autocorrelation in the distribution of organisms, and this is not modeled, model predictions will be inaccurate. These results have global importance for conservation efforts as inaccurate forecasts lead to ineffective prioritization of conservation activities and potentially to avoidable species extinctions.

Using an autologistic regression model to identify spatial risk factors and spatial risk patterns of hand, foot and mouth disease (HFMD) in Mainland China.

BackgroundThere have been large-scale outbreaks of hand, foot and mouth disease (HFMD) in Mainland China over the last decade. These events varied greatly across the country. It is necessary to identify the spatial risk factors and spatial distribution patterns of HFMD for public health control and prevention. Climate risk factors associated with HFMD occurrence have been recognized. However, few studies discussed the socio-economic determinants of HFMD risk at a space scale.MethodsHFMD records in Mainland China in May 2008 were collected. Both climate and socio-economic factors were selected as potential risk exposures of HFMD. Odds ratio (OR) was used to identify the spatial risk factors. A spatial autologistic regression model was employed to get OR values of each exposures and model the spatial distribution patterns of HFMD risk.ResultsResults showed that both climate and socio-economic variables were spatial risk factors for HFMD transmission in Mainland China. The statistically significant risk factors are monthly average precipitation (OR = 1.4354), monthly average temperature (OR = 1.379), monthly average wind speed (OR = 1.186), the number of industrial enterprises above designated size (OR = 17.699), the population density (OR = 1.953), and the proportion of student population (OR = 1.286). The spatial autologistic regression model has a good goodness of fit (ROC = 0.817) and prediction accuracy (Correct ratio = 78.45%) of HFMD occurrence. The autologistic regression model also reduces the contribution of the residual term in the ordinary logistic regression model significantly, from 17.25 to 1.25 for the odds ratio. Based on the prediction results of the spatial model, we obtained a map of the probability of HFMD occurrence that shows the spatial distribution pattern and local epidemic risk over Mainland China.ConclusionsThe autologistic regression model was used to identify spatial risk factors and model spatial risk patterns of HFMD. HFMD occurrences were found to be spatially heterogeneous over the Mainland China, which is related to both the climate and socio-economic variables. The combination of socio-economic and climate exposures can explain the HFMD occurrences more comprehensively and objectively than those with only climate exposures. The modeled probability of HFMD occurrence at the county level reveals not only the spatial trends, but also the local details of epidemic risk, even in the regions where there were no HFMD case records.

Uniqueness condition for an auto-logistic model

Abstract Auto-logistic models are widely used to describe binary images texture and spatial presence–absence data. There exist some techniques, like Gibbs sampler algorithm among others, that allow simulating the process, but its performance depends on the model global properties at Z 2 . Under general conditions there will be at least a global distribution which conditionals are Gibbs specifications. The present work establishes sufficient conditions on the parameters of an auto-logistic model, in order to ensure the distribution’s uniqueness.

Ngspatial: A Package for Fitting the Centered Autologistic and Sparse Spatial Generalized Linear Mixed Models for Areal Data

Two important recent advances in areal modeling are the centered autologistic model and the sparse spatial generalized linear mixed model (SGLMM), both of which are reparameterizations of traditional models. The reparameterizations improve regression inference by alleviating spatial confounding, and the sparse SGLMM also greatly speeds computing by reducing the dimension of the spatial random effects. Package ngspatial ('ng' = non-Gaussian) provides routines for fitting these new models. The package supports composite likelihood and Bayesian inference for the centered autologistic model, and Bayesian inference for the sparse SGLMM.

Analyzing land-use change in farming-pastoral transitional region using autologistic model and household survey approach

Land change science (LCS) strives to understand and model land-use change, which will further advance the understanding of multiple issues in the socio-ecological systems. Based on GIS/RS techniques, autologistic model, and household survey method, this study investigated major land use changes and their causes from 1978 to 2008 in Uxin Banner (county-level), Inner Mongolia in China and then developed an understanding of the relationships between household livelihood and land-use pattern. Results showed that cultivated land increased from 1988 to 2000, and leveled off after 2000. Built-up land increased stably for the period 1978–2008. The change of grassland and bare land differed among the three periods. From 1978 to 1988, grassland increased by 23.3%, and bare land decreased by 20.48%. From 1988 to 2000, bare land expanded by 1.7%, but grassland declined by 1.3%. From 2000 to 2008, an increase in grassland area by 1.8% was observed, but a decrease in bare land area by 9.0% was witnessed. The autologistic models performed better than logistic models as indicated by lower Akaike Information Criterion (AIC) values. Factors associated with human activities significantly correlated with the change of cultivated land, forest land, grassland, and built-up land. The produce prices and extensive cultivated land use are major issues in the farming area. This study suggests that completing land circulation systems and maintaining the stability of price are effective solutions. By contrast, reclamation and overgrazing are major concerns in the pastoral areas. Implementing environmental policies effectively, transferring population out of rural pastoral areas, and developing modern animal husbandry are effective ways to address these issues.

Dynamic occupancy models for analyzing species' range dynamics across large geographic scales

Large-scale biodiversity data are needed to predict species' responses to global change and to address basic questions in macroecology. While such data are increasingly becoming available, their analysis is challenging because of the typically large heterogeneity in spatial sampling intensity and the need to account for observation processes. Two further challenges are accounting for spatial effects that are not explained by covariates, and drawing inference on dynamics at these large spatial scales. We developed dynamic occupancy models to analyze large-scale atlas data. In addition to occupancy, these models estimate local colonization and persistence probabilities. We accounted for spatial autocorrelation using conditional autoregressive models and autologistic models. We fitted the models to detection/nondetection data collected on a quarter-degree grid across southern Africa during two atlas projects, using the hadeda ibis (Bostrychia hagedash) as an example. The model accurately reproduced the range expansion between the first (SABAP1: 1987–1992) and second (SABAP2: 2007–2012) Southern African Bird Atlas Project into the drier parts of interior South Africa. Grid cells occupied during SABAP1 generally remained occupied, but colonization of unoccupied grid cells was strongly dependent on the number of occupied grid cells in the neighborhood. The detection probability strongly varied across space due to variation in effort, observer identity, seasonality, and unexplained spatial effects. We present a flexible hierarchical approach for analyzing grid-based atlas data using dynamical occupancy models. Our model is similar to a species' distribution model obtained using generalized additive models but has a number of advantages. Our model accounts for the heterogeneous sampling process, spatial correlation, and perhaps most importantly, allows us to examine dynamic aspects of species ranges.

Rivers and flooded areas identified by medium-resolution remote sensing improve risk prediction of the highly pathogenic avian influenza H5N1 in Thailand

Thailand experienced several epidemic waves of the highly pathogenic avian influenza (HPAI) H5N1 between 2004 and 2005. This study investigated the role of water in the landscape, which has not been previously assessed because of a lack of high-resolution information on the distribution of flooded land at the time of the epidemic. Nine Landsat 7 - Enhanced Thematic Mapper Plus scenes covering 174,610 km(2) were processed using k-means unsupervised classification to map the distribution of flooded areas as well as permanent lakes and reservoirs at the time of the main epidemic HPAI H5N1 wave of October 2004. These variables, together with other factors previously identified as significantly associated with risk, were entered into an autologistic regression model in order to quantify the gain in risk explanation over previously published models. We found that, in addition to other factors previously identified as associated with risk, the proportion of land covered by flooding along with expansion of rivers and streams, derived from an existing, sub-district level (administrative level no. 3) geographical information system database, was a highly significant risk factor in this 2004 HPAI epidemic. These results suggest that water-borne transmission could have partly contributed to the spread of HPAI H5N1 during the epidemic. Future work stemming from these results should involve studies where the actual distribution of small canals, rivers, ponds, rice paddy fields and farms are mapped and tested against farm-level data with respect to HPAI H5N1.

Spatiotemporal characterization of citrus postbloom fruit drop inBrazil and its relationship to pathogen dispersal

Citrus postbloom fruit drop (PFD) is caused byColletotrichum acutatumandC. gloeosporioides. These pathogens attack the flowers and cause premature fruit drop and the retention of fruit calyces. This study was designed to characterize the spatial and temporal dynamics ofPFDin commercial citrus‐growing areas to better understand the disease spread. Experiments were carried out in three young orchards (500 trees each) in two municipalities in Sao Paulo State,Brazil. Symptoms ofPFDon the flowers and presence of persistent calyces were assessed in each of three orchards for three years. Logistic, Gompertz and monomolecular models were fitted to the incidence data over time from the trees with symptoms. The spatial pattern of diseased trees was characterized by a dispersion index and by Taylor′s power law. An autologistic model was used for the spatiotemporal analysis. The logistic model provided the best fit to the disease incidence data, which had a fast progress rate of 0·53 per day. During the early epidemic ofPFD, the spatial pattern of diseased trees was random, which suggested that inoculum spread was due to mechanisms other than rain splash. As the disease incidence increased (up to 12·6%), the spatial pattern of diseased trees became aggregated. The rapid rate of disease progress and the distribution ofPFDsuggest that dispersal of the pathogen is possibly related to a mechanism other than splash dispersal, which is more typical of other fruit diseases caused byColletotrichumspp.

A multilevel model for spatially correlated binary data in the presence of misclassification: an application in oral health research

Dental caries is a highly prevalent disease affecting the tooth's hard tissues by acid-forming bacteria. The past and present caries status of a tooth is characterized by a response called caries experience (CE). Several epidemiological studies have explored risk factors for CE. However, the detection of CE is prone to misclassification because some cases are neither clearly carious nor noncarious, and this needs to be incorporated into the epidemiological models for CE data. From a dentist's point of view, it is most appealing to analyze CE on the tooth's surface, implying that the multilevel structure of the data (surface-tooth-mouth) needs to be taken into account. In addition, CE data are spatially referenced, that is, an active lesion on one surface may impact the decay process of the neighboring surfaces, and that might also influence the process of scoring CE. In this paper, we investigate two hypotheses: that is, (i) CE outcomes recorded at surface level are spatially associated; and (ii) the dental examiners exhibit some spatial behavior while scoring CE at surface level, by using a spatially referenced multilevel autologistic model, corrected for misclassification. These hypotheses were tested on the well-known Signal Tandmobiel® study on dental caries, and simulation studies were conducted to assess the effect of misclassification and strength of spatial dependence on the autologistic model parameters. Our results indicate a substantial spatial dependency in the examiners' scoring behavior and also in the prevalence of CE at surface level.

On Estimation and Selection of Autologistic Regression Models via Penalized Pseudolikelihood

Autologistic regression models are suitable for relating spatial binary responses in ecology to covariates such as environmental factors. For big ecological data, pseudolikelihood estimation is appealing due to its ease of computation, but at least two challenges remain. Although an important issue, it is unclear how model selection may be carried out under pseudolikelihood. In addition, for assessing the variation of pseudolikelihood estimates, parametric bootstrap using Monte Carlo simulation is often used but may be infeasible for very large data sizes. Here both these issues are addressed by developing a penalized pseudolikelihood estimation method and an approximation of the variance of the parameter estimates. A simulation study is conducted to evaluate the performance of the proposed method, followed by a data example in a study of land cover in relation to land ownership characteristics. Extension of these models and methods to spatial-temporal binary data is further discussed. This article has supplementary material online.

Forest harvesting impacts on mortality of an endangered lichen at the landscape and stand scales

Industrial forestry can negatively affect biodiversity, and rare or endangered species are particularly vulnerable. Boreal felt lichen (Erioderma pedicellatum (Hue) P.M.Jørg.) is a globally critically endangered species, and its population in Nova Scotia has been reduced through harvesting of its host tree balsam fir (Abies balsamea (L.) Mill.). We hypothesized that forest harvesting adjacent to and within the landscape of boreal felt lichen could increase the risk of mortality by negatively affecting microclimate of its habitat. Autologistic regression models were used to measure probability of mortality (death or disappearance) with harvesting history at the stand and landscape scales. Erioderma pedicellatum mortality and 17-year tree harvesting history derived from satellite data were used in the model. Modeling at the stand scale suggested that the probability of E. pedicellatum mortality increased as the area of tree harvesting increased. At the landscape scale, the model suggested that probability of E. pedicellatum mortality increased as the area of harvest within 500 m increased. Adjacent tree harvesting may increase solar radiation, wind, and temperature, which could have a negative effect on E. pedicellatum survival. We recommend maintaining uncut buffer zones around E. pedicellatum and limiting the size of harvest blocks and amount of harvesting in the landscape over a given time period to help conserve this endangered species.