Within statistical factor analysis, the factor regression model,[1] or hybrid factor model,[2] is a special multivariate model with the following form:

where,

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

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.

Software

Open source software to perform factor regression is available.

References

  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. PMC 3017385. PMID 21218139.
  2. 1 2 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.
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