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# general linear model

The collective term for the body of statistical procedures (such as analysis of variance, correlation, factor analysis, principal components analysis and regression) based on the analysis of covariation among variables. Many statistical packages for computer applications of these procedures are available, including GLIM (General Linear Model).

The techniques incorporated within the general linear model are the most widely used of all parametric statistical methods. Their application assumes that the data meet a number of criteria, however, of which the most important are that:

{img src=show_image.php?name=2022.gif }Â the relationship between any pair of variables should be linear (or can be transformed into a linear relationship: see transformation of variables); {img src=show_image.php?name=2022.gif }Â the residuals from the estimated value of the dependent variable for each value of an independent variable in a regression should have a mean of zero; {img src=show_image.php?name=2022.gif }Â those residuals should be normally distributed and with equal variances (i.e. they should be homoscedastic not heteroscedastic); {img src=show_image.php?name=2022.gif }Â values on each independent variable should not be autocorrelated (i.e. the value at one observation should not determine the value of an adjacent observation â€” see spatial autocorrelation); and {img src=show_image.php?name=2022.gif }Â all variables should be measured without error.In addition, in multiple regression there should be no collinearity among the independent variables (i.e. they should be uncorrelated).

Where these criteria are not met, use of the methods is inappropriate and potentially misleading: the estimated regression coefficients may be either or both of biased and inefficient, for example, so that forecasts and predictions based on them are unreliable (see ecological fallacy). A range of other models allows investigators to avoid some of these problems (cf. categorical data analysis; logistic regression).Â (RJJ)

Suggested Reading Bailey, T.C. and Gatrell, A.C. 1995: Interactive spatial data analysis. London: Longman.Â Johnston, R.J. 1978: Multivariate statistical analysis in geography: a primer on the general linear model. London and New York: Longman.Â O\'Brien, L. 1992: Introducing quantitative geography: measurement, methods and generalised linear models. London and New York: Routledge.

##### general systems theory

Other Terms : residual | pricing policies | positive discrimination
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