Factor regression model: Difference between revisions

Revision as of 03:30, 8 May 2011

Revision as of 20:31, 9 May 2011

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{{Wikify|date=May 2011}}

{{Orphan|date=May 2011}}

The factor regression model,<ref>{{cite journal|last=Carvalho|first=Carlos M.|title=High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics|journal=Journal of the American Statistical Association|date=1 December 2008|volume=103|issue=484|pages=1438–1456|doi=10.1198/016214508000000869}}</ref> or hybrid factor model,<ref name="meng2011">{{cite journal|last=Meng|first=J.|title=Uncover cooperative gene regulations by microRNAs and transcription factors in glioblastoma using a nonnegative hybrid factor model|journal=International Conference on Acoustics, Speech and Signal Processing|year=2011|url=http://www.cmsworldwide.com/ICASSP2011/Papers/ViewPapers.asp?PaperNum=4439}}</ref> is a special multivariate model with the following form.

:<math> \mathbf{y}_n= \mathbf{A}\mathbf{x}_n+ \mathbf{B}\mathbf{z}_n +\mathbf{c}+\mathbf{e}_n </math>

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<math> \mathbf{e}_n </math> is (unknown) error or white Gaussian noise.

== The Relationship between Factor Regression Model, Factor Analysis Model and Regression Model ==

The factor regression model can be viewed as a combination of [[factor analysis]] model (<math> \mathbf{y}_n= \mathbf{A}\mathbf{x}_n+ \mathbf{c}+\mathbf{e}_n </math>) and [[regression model]] (<math> \mathbf{y}_n= \mathbf{B}\mathbf{z}_n +\mathbf{c}+\mathbf{e}_n </math>).