The factor regression model can be viewed as a combination of
factor analysis model ( \mathbf{y}_n= \mathbf{A}\mathbf{x}_n+ \mathbf{c}+\mathbf{e}_n ) and
regression model ( \mathbf{y}_n= \mathbf{B}\mathbf{z}_n +\mathbf{c}+\mathbf{e}_n ). Alternatively, the model can be viewed as a special kind of factor model, the hybrid factor model : \begin{align} & \mathbf{y}_n = \mathbf{A}\mathbf{x}_n+ \mathbf{B}\mathbf{z}_n +\mathbf{c}+\mathbf{e}_n \\ = & \begin{bmatrix} \mathbf{A} & \mathbf{B} \end{bmatrix} \begin{bmatrix} \mathbf{x}_n \\ \mathbf{z}_n\end{bmatrix} +\mathbf{c}+\mathbf{e}_n \\ = & \mathbf{D}\mathbf{f}_n +\mathbf{c}+\mathbf{e}_n \end{align} where, \mathbf{D}=\begin{bmatrix} \mathbf{A} & \mathbf{B} \end{bmatrix} is the loading matrix of the hybrid factor model and \mathbf{f}_n=\begin{bmatrix} \mathbf{x}_n \\ \mathbf{z}_n\end{bmatrix} are the factors, including the known factors and unknown factors. == Software ==