General linear model

Definition: General linear model is a linear regression model that allows for analyzing data ( $\gamma$ ) according to a given set of regressors often also referred to as predictors in the context of experiment design, ( $\chi$ ) by estimating fit coefficients ( $\beta$ ). The general equation of the GLM is: $Y=X\beta + \varepsilon$ . For fNIRS, $\gamma$ is the time series of fNIRS measurements, $\chi$ is the design matrix including all regressors, $\beta$ is the coefficients to be estimated for each regressor, and $\varepsilon$ is the the error term which is assumed to be spherical Gaussian N(0, $\sigma$ ). The model is typically solved via generalized ordinary least squares: $\beta = (X^TX)^{-1}X^TY$ $cov(\beta) = (X^TX)^{-1}$ In order for this solution to be the best linear unbiased estimate of the coefficients, the Gauss-Markov assumptions have to be fulfilled, namely linearity, random sampling, non-collinearity, strict exogeneity and spherical errors.

Category: Analysis

Related terms: Linear regression, Generalized Linear Mixed Model, regression

Abbreviation or symbol: GLM

Synonym:

References: https://doi.org/10.1007/978-1-59745-530-5_10

Alternative definition:

Related terms (alternative definition): regression

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