= Generalized Linear Model = A '''generalized linear model''' ('''GLM''') is a generalized modeling method. <> ---- == Design == A GLM has three components. 1. A '''distribution''' to characterize outcomes. 2. A '''linear model''' to relate an outcome with one or more independent variable(s). 3. A '''link function''' to relate the linear model with expected outcomes. The distribution can be any [[Statistics/ProbabilityNotation#Probability_density_functions|PDF]]. The link function generally is a non-linear transformation, such as a logarithm. It is also typically stated and notated as a function ''g'', as in ''g(E[y|'''X''']) = '''Xb'''''. It could equivalently be stated like ''E[y|'''X'''] = g^-1^('''Xb''')'', which can be a more straightforward approach, but the other orientation is simpler for interpretation. As an example, [[Statistics/OrdinaryLeastSquares|OLS]] is a particular form of a GLM where: * outcomes are assumed to be [[Statistics/NormalDistribution|normally distributed]] * outcomes are linearly modeled like '''''y''' = '''Xb''''' * a link function of ''1'' is implicitly used ---- CategoryRicottone