Definition: Transformed general linear model
Index:
The Book of Statistical Proofs ▷
Statistical Models ▷
Multivariate normal data ▷
Transformed general linear model ▷
Definition
Sources:
Metadata: ID: D160 | shortcut: tglm | author: JoramSoch | date: 2021-10-21, 14:43.
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 \, Twhere 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.
- Soch J, Allefeld C, Haynes JD (2020): "Inverse transformed encoding models – a solution to the problem of correlated trial-by-trial parameter estimates in fMRI decoding"; in: NeuroImage, vol. 209, art. 116449, Appendix A; URL: https://www.sciencedirect.com/science/article/pii/S1053811919310407; DOI: 10.1016/j.neuroimage.2019.116449.
Metadata: ID: D160 | shortcut: tglm | author: JoramSoch | date: 2021-10-21, 14:43.