Factor regression model
- 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
Alternatively, the model can be viewed as a special kind of factor model, the hybrid factor model 
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.
- 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.
- 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.
- Wang, Quanli. "BFRM". BFRM.