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| | I'm Elijah and I live with my husband and our three children in Tafers, in the south part. My hobbies are Bridge, College football and Auto audiophilia.<br><br>My website - [http://tinyurl.com/kg6kvbz http://tinyurl.com/kg6kvbz] |
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| 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.
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| :<math> \mathbf{y}_n= \mathbf{A}\mathbf{x}_n+ \mathbf{B}\mathbf{z}_n +\mathbf{c}+\mathbf{e}_n </math>
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| where,
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| :<math> \mathbf{y}_n </math> is the <math>n</math>-th <math> G \times 1 </math> (known) observation.
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| :<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{A} </math> is the (unknown) loading matrix of the hidden factors.
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| :<math> \mathbf{z}_n </math> is the <math>n</math>-th sample <math> L_z </math> (known) design factors.
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| :<math> \mathbf{B} </math> is the (unknown) regression coefficients of the design factors.
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| :<math> \mathbf{c} </math> is a vector of (unknown) constant term or intercept.
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| :<math> \mathbf{e}_n </math> is a vector of (unknown) errors, often white Gaussian noise.
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| == Relationship between factor regression model, factor model and regression model ==
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| 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>).
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| Alternatively, the model can be viewed as a special kind of factor model, the hybrid factor model <ref name="meng2011"/>
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| :<math>
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| \begin{align}
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| & \mathbf{y}_n = \mathbf{A}\mathbf{x}_n+ \mathbf{B}\mathbf{z}_n +\mathbf{c}+\mathbf{e}_n \\
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| = & \begin{bmatrix}
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| \mathbf{A} & \mathbf{B}
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| \end{bmatrix}
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| \begin{bmatrix}
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| \mathbf{x}_n \\
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| \mathbf{z}_n\end{bmatrix} +\mathbf{c}+\mathbf{e}_n \\
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| = & \mathbf{D}\mathbf{f}_n +\mathbf{c}+\mathbf{e}_n
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| \end{align}
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| </math>
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| where, <math> \mathbf{D}=\begin{bmatrix}
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| \mathbf{A} & \mathbf{B}
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| \end{bmatrix} </math> is the loading matrix of the hybrid factor model and <math> \mathbf{f}_n=\begin{bmatrix}
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| \mathbf{x}_n \\
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| \mathbf{z}_n\end{bmatrix} </math> are the factors, including the known factors and unknown factors.
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| == Software ==
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| 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}}</ref>
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| ==References==
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| {{Reflist}}
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| [[Category:Factor analysis]]
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| [[Category:Latent variable models]]
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| [[Category:Regression analysis]]
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I'm Elijah and I live with my husband and our three children in Tafers, in the south part. My hobbies are Bridge, College football and Auto audiophilia.
My website - http://tinyurl.com/kg6kvbz