Factor regression model

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The factor regression model,[1] or hybrid factor model,[2] is a special multivariate model with the following form.


is the -th (known) observation.
is the -th sample (unknown) hidden factors.
is the (unknown) loading matrix of the hidden factors.
is the -th sample (known) design factors.
is the (unknown) regression coefficients of the design factors.
is a vector of (unknown) constant term or intercept.
is a vector of (unknown) errors, often white Gaussian noise.

Relationship between factor regression model, factor model and regression model[edit]

The factor regression model can be viewed as a combination of factor analysis model () and regression model ().

Alternatively, the model can be viewed as a special kind of factor model, the hybrid factor model [2]

where, is the loading matrix of the hybrid factor model and are the factors, including the known factors and unknown factors.


Factor regression software is available from here.[3]


  1. ^ Carvalho, Carlos M. (1 December 2008). "High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics". Journal of the American Statistical Association. 103 (484): 1438–1456. doi:10.1198/016214508000000869. 
  2. ^ a b Meng, J. (2011). "Uncover cooperative gene regulations by microRNAs and transcription factors in glioblastoma using a nonnegative hybrid factor model". International Conference on Acoustics, Speech and Signal Processing. Archived from the original on 2011-11-23. 
  3. ^ Wang, Quanli. "BFRM". BFRM. Archived from the original on 2011-10-03.