Lecture

Geographically Weighted Regression

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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 introduces Geographically Weighted Regression (GWR), a spatially explicit approach to measure the relationship between variables, locally considering the value of an explanatory factor. GWR employs a spatial weighting function assuming that nearby places are more similar. The residuals produced by GWR are generally lower than those of ordinary linear regression, and the outputs are location-specific, suitable for mapping and further 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

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Related concepts (32)

Spatial analysis

Spatial analysis is any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques using different analytic approaches, especially spatial statistics. It may be applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, or to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures.

Regression analysis

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features'). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion.

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.

Segmented regression

Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various independent variables. Segmented regression is useful when the independent variables, clustered into different groups, exhibit different relationships between the variables in these regions.

Bayesian linear regression

Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining the posterior probability of the regression coefficients (as well as other parameters describing the distribution of the regressand) and ultimately allowing the out-of-sample prediction of the regressand (often labelled ) conditional on observed values of the regressors (usually ).

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