Spatial Models
Virgilio Gómez-Rubio in Bayesian Inference with INLA, 2020
Spatial statistics is traditionally divided into three main areas depending on the type of problem and data: lattice data, geostatistics and point patterns (Cressie, 2015). Sometimes, spatial data is also measured over time and spatio-temporal models can be proposed (Cressie and Wikle, 2011). In the next sections models for the different types of spatial data will be considered. In Section 8.6 models for spatio-temporal data will be described. Blangiardo and Cameletti (2015) and Krainski et al. (2018) provide a thorough description of most of the models described in this section. Bivand et al. (2013) and Lovelace et al. (2019) provide general description on handling spatial data in R and are recommended reads.
Summary and Further Readings
Gueorguieva Ralitza in Statistical Methods in Psychiatry and Related Fields, 2017
Although we provided some examples with clustering, including an analysis of region of interest data from an fMRI study, we did not focus specifically on situations in which we model the spatial associations among the data points. Such data are encountered in structural and functional imaging studies, in disease mapping applications, and in geographic information systems. Data can be intensively collected (e.g., one might have data on thousands of voxels within individuals or hundreds of locations on a map). Both spatial and time components are present when one is interested in modeling how the response of the spatial network of points changes over time. In such applications, it is critically important to take into account the interrelationships among the observed responses in space and time. When modeling disease spread or brain connectivity, the strength of associations varies not only by proximity but also by the connections that exist among different observation units in space and time. Therefore, although some simple spatial applications can be handled with the methods described in this book by using the spatial power variance–covariance structure of the repeated measures (Chapter 3), specialized methods are needed for more complex data. The book by Diggle (2003) is an excellent reference for analyzing spatial point patterns. Geostatistical modeling is described at a fairly non-technical level by Diggle and Ribeiro (2007). Temporal trend modeling in geographic information systems is presented from an applied perspective by Ott and Swiaczny (2001). The book of Gelfand (2010) is a general reference on spatial statistics. An overview of brain imaging analysis and statistical methods is provided by Bowman (2014).
Statistical Software: R and SAS
Albert Vexler, Alan D. Hutson, Xiwei Chen in Statistical Testing Strategies in the Health Sciences, 2017
Crawley (2012) introduced the riches of the R environment, aimed at beginners and intermediate users in the fields ranging from science to economics and from medicine to engineering. The book covers data handling, graphics, mathematical functions, and a wide range of statistical techniques, for example, regression, analysis of variance, generalized linear modeling, Bayesian analysis, spatial statistics, and multivariate methods.
Forty years on: a new national study of hearing in England and implications for global hearing health policy
Published in International Journal of Audiology, 2023
Dialechti Tsimpida, Maria Panagioti, Evangelos Kontopantelis
We utilised the geographical information systems (GIS) approach in public health (Wang 2020) to estimate the accuracy of the existing hearing loss data and compare it with the ELSA dataset. Spatial statistics is a distinct area of research; it focuses on examining the distributions, attributes, and relationships of features in spatial data to help gain a better understanding of the data (Scott and Janikas 2010). Spatial statistics differentiate from the traditional statistical theory by rejecting the idea of assumed independence of observations. Instead, consider that space and location influence the observations, assuming that nearby units are somehow associated (Getis 1999; Fotheringham and Rogerson 2013; Griffith 2020). The above can be summarised in Tobler’s first law of geography, which argues that “Everything is related to everything else, but near things are more related than distant things” (Tobler 1970).
Geographical patterns and effects of human and mechanical factors on road traffic crashes in Nigeria
Published in International Journal of Injury Control and Safety Promotion, 2020
Richard Adeleke, Tolulope Osayomi, Ayodeji E Iyanda
The data were analysed with the aid of spatial statistical techniques such as Global Moran’s I and spatial regression model. Other statistical techniques used include Pearson correlation and OLS regression. Spatial statistics is based on the assumption of the non-independence of observations; that is, nearby features are closely associated (Tobler, 1970). Consequently, spatial statistics are used in the analysis of spatial patterns, modelling spatial relationships and detecting spatial clusters (Osayomi, 2019). The Global Moran’s I was used to determine the nature of the geographical distribution of road traffic crashes, fatality and injury. Global Moran’s I value varies from −1 through 0 to +1. If Moran’s I value is near +1, it is an indication of a high positive spatial autocorrelation which also means that states with similar values of RTCs, fatality and injury are clustered over space. In contrast, a Moran’s I value near −1 is an indication of a high negative spatial autocorrelation, which means that states with dissimilar values of RTCs, fatality and injury are adjacent. A random pattern is depicted when the z scores are between −1.96 and +1.96 with a p value greater than 0.05. On the other hand, the pattern is clustered when the p value is less than 0.05.
Editorial
Published in Journal of Applied Statistics, 2021
The paper titled ‘Spatially explicit survival modeling for small area cancer data’ [4] was awarded the 2018 best JAS paper. The committee recognized that the authors of this paper advanced the state-of-the-art applied statistics methodology by innovatively combining spatial statistics with survival analysis to model survival data that contain geographical information. The authors laid out the details of computational implementation of their approach, making it feasible for other researchers to adopt the method. The application of the approach to prostate cancer using SEER data was viewed as of great interest to people who desire to analyze similar data. There were also two highly commended papers recognized by the Committee, one is entitled ‘The relative performance of ensemble methods with deep convolutional neural networks for image classification’ [1] and the other one is entitled ‘A new algorithm for clustering based on kernel density estimation’ [2]. In [1], the authors compared various ensemble techniques for image classification in terms of classification accuracy and the authors noted that the behavior of ensemble with deep network is not well studied, therefore, their work would provide a comprehensive comparison for the researchers who work on Big data classification using similar methods. In [2], the paper introduced a clustering method based on kernel density estimation and compared the performance of the proposed method with k-means and hierarchical clustering.
Related Knowledge Centers
- Stereology
- Sampling
- Geostatistics
- Statistical Geography
- Spatial Epidemiology
- Spatial Network