Lecture

Spatial regression or spatial lag model

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In course

ENV-444: Exploratory data analysis in environmental health

This course teaches how to apply exploratory spatial data analysis to health information. Teaching focuses on the role of GIS and spatial statistics in spatial epidemiology. It proposes a context to investigate the relationship between health, quality of l ...

Description

This lecture discusses spatial regression models, focusing on spatial autocorrelation and the challenges it poses in traditional linear regression. It explores the concept of spatial lag models, which account for the systematic relationship between values in adjacent areas, leading to an overestimation of the relationship between variables. The instructor presents methods like Geographically Weighted Regression (GWR) and spatially weighted linear regression to address these issues, emphasizing the importance of considering local variations in attributes. The lecture also covers the calculation of spatial lag terms, the impact of autoregressive coefficients, and the correction of biases induced by spatial autocorrelation. Through examples and theoretical explanations, students learn how to apply these models to make more accurate inferences in spatial data analysis.

Instructors (2)

Stéphane Joost

Expertise Geographic Information Science and spatial statisticsMolecular ecology, Landscape genomics, Seascape genomicsSpatial epidemiology, Health geographics Publications Publications- List of publications Teaching & PhD PhD Students Marco André Vieira Ruas, Manon Laetitia Pribille, Martine Valérie Besse Past EPFL PhD Students Estelle Rochat, Solange Catherine Gaillard, Oliver Michele Selmoni, Anaïs Ladoy, Annie Sandrine Guillaume Past EPFL PhD Students as codirector Sylvie Stucki, Kevin Leempoel, Martí

Idris Guessous

Official source

Related concepts (32)

Boundary problem (spatial analysis)

A boundary problem in analysis is a phenomenon in which geographical patterns are differentiated by the shape and arrangement of boundaries that are drawn for administrative or measurement purposes. The boundary problem occurs because of the loss of neighbors in analyses that depend on the values of the neighbors. While geographic phenomena are measured and analyzed within a specific unit, identical spatial data can appear either dispersed or clustered depending on the boundary placed around the data.

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Autoregressive model

In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation which should not be confused with differential equation).

Nonlinear regression

In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations. In nonlinear regression, a statistical model of the form, relates a vector of independent variables, , and its associated observed dependent variables, . The function is nonlinear in the components of the vector of parameters , but otherwise arbitrary.

Autoregressive–moving-average model

In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the autoregression (AR) and the second for the moving average (MA). The general ARMA model was described in the 1951 thesis of Peter Whittle, Hypothesis testing in time series analysis, and it was popularized in the 1970 book by George E. P. Box and Gwilym Jenkins.

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Covers the probabilistic model for linear regression and the importance of regularization techniques.

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