Index: The Book of Statistical ProofsStatistical ModelsMultivariate normal dataTransformed general linear model ▷ Definition

Definition: Let there be two general linear models of measured data using design matrices X \in \mathbb{R}^{n \times p} and X_t \in \mathbb{R}^{n \times t}

\label{eq:glm1} Y = X B + E, \; E \sim \mathcal{MN}(0, V, \Sigma) \label{eq:glm2} Y = X_t \Gamma + E_t, \; E_t \sim \mathcal{MN}(0, V, \Sigma_t)

and assume that X_t can be transformed into X using a transformation matrix T \in \mathbb{R}^{t \times p}

\label{eq:X-Xt-T} X = X_t \, T

where p < t and X, X_t and T have full ranks \mathrm{rk}(X) = p, \mathrm{rk}(X_t) = t and \mathrm{rk}(T) = p.

Then, a linear model of the parameter estimates from \eqref{eq:glm2}, under the assumption of \eqref{eq:glm1}, is called a transformed general linear model.

 
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Metadata: ID: D160 | shortcut: tglm | author: JoramSoch | date: 2021-10-21, 14:43.