deletions | additions       diff --git a/Correcting for unknown covariates using principal components.tex b/Correcting for unknown covariates using principal components.tex  index 2b4335a..0d54513 100644  --- a/Correcting for unknown covariates using principal components.tex  +++ b/Correcting for unknown covariates using principal components.tex 
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\subsection{Correcting for unknown covariates using principal components}  Both known and unknown covariates such as time of experiment, age of sample, etc. can affect molecular trait measurements and confound QTL studies. Principal component analysis (PCA) is sometimes used to capture and remove these effects from QTL studies \cite{Stephens_Gilad_Pritchard_2010,http://dx.oi.org/10.1038/nature10808}. \cite{Stephens_Gilad_Pritchard_2010, http://dx.oi.org/10.1038/nature10808}.  To leverage PCA while maintaining the discrete nature of the count data, the CHT directly models the covariate effects. To do this we include a user defined number of PCA loadings $u_{i\bullet}$ and fit coefficients $c_{h\bullet}$ when calculating $\lambda_{hi}$. \[  \lambda_{hi} = \left\{