Factor regression model: Difference between revisions

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TheWithin [[statistics|statistical]] [[factor analysis]], 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|pmc=3017385|pmid=21218139}}</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 |deadurlurl-status=yesdead |archiveurl=https://web.archive.org/web/20111123144133/http://www.cmsworldwide.com/ICASSP2011/Papers/ViewPapers.asp?PaperNum=4439 |archivedate=2011-11-23 |df= }}</ref> is a special [[Multivariate normal distribution|multivariate]] [[Mathematical model|model]] with the following form.:

{{multiple issues|

{{Underlinked|date=January 2013}}

{{context|date=July 2012}}

}}

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|pmc=3017385}}</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 |deadurl=yes |archiveurl=https://web.archive.org/web/20111123144133/http://www.cmsworldwide.com/ICASSP2011/Papers/ViewPapers.asp?PaperNum=4439 |archivedate=2011-11-23 |df= }}</ref> is a special [[Multivariate normal distribution|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>

where,

:<math> \mathbf{y}_n </math> is the <math>n</math>-th <math> G \times 1 </math> (known) [[observation]].

:<math> \mathbf{x}_n </math> is the <math>n</math>-th sample <math> L_x </math> (unknown) hidden factors.

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:<math> \mathbf{B} </math> is the (unknown) regression coefficients of the design factors.

:<math> \mathbf{c} </math> is a [[vector (mathematics and physics)|vector]] of (unknown) [[constant term]] or intercept.

:<math> \mathbf{e}_n </math> is a vector of (unknown) errors, often [[white Gaussian noise]].

== Relationship between factor regression model, factor model and regression model ==

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== Software ==

[https://www2.stat.duke.edu/~mw/mwsoftware/BFRM/index.html Open source software to perform factor regression is available].

Factor regression software is available from here.<ref>{{cite web|last=Wang |first=Quanli |title=BFRM |url=http://www.isds.duke.edu/research/software/west/bfrm/ |work=BFRM |deadurl=yes |archiveurl=https://web.archive.org/web/20111003195637/http://www.isds.duke.edu/research/software/west/bfrm/ |archivedate=2011-10-03 |df= }}</ref>

==References==