# Adjusting shrinkage in PC scores Adjusts the shrinkage bias in the predicted PC scores based on the estimated shrinkage factors. ```r pc_adjust(train.eval, p, n, test.scores, method = c("d.gsp", "l.gsp", "osp"), n.spikes, n.spikes.max, smooth = TRUE) ``` ## Arguments - `train.eval`: Numeric vector containing the sample eigenvalues. The vector must have dimension `n` or `n-1`, it may be unordered. - `p`: The number of features. - `n`: The number of training samples. - `test.scores`: An $m\times k$ matrix or data frame containing the first $k$ predicted PC scores of $m$ many test samples. - `method`: String specifying the estimation method. Possible values are "`d.gsp`" (default),"`l.gsp`" and "`osp`". - `n.spikes`: Number of distant spikes in the population (Optional). - `n.spikes.max`: Upper bound of the number of distant spikes in the population. Optional, but needed if `n.spikes` is not specified. Ignored if `n.spikes` is specified. - `smooth`: Logical. If `TRUE` and `method="l.gsp"`, kernel smoothing will be performed on the estimated population eigenvalue spectrum. Default is `TRUE`. ## Details The different choices for `method` are: * "`d.gsp`": $d$-estimation method based on the Generalized Spiked Population (GSP) model. * "`l.gsp`": $\lambda$-estimation method based on the GSP model. * "`osp`": Estimation method based on the Ordinary Spiked Population (OSP) model. The $(i,j)^{th}$ element of `test.scores` should denote the $j^{th}$ predicted PC score for the $i^{th}$ subject in the test sample. At least one of `n.spikes` and `n.spikes.max` must be provided. If `n.spikes` is provided then `n.spikes.max` is ignored, else `n.spikes.max` is used to find out the number of distant spikes using `select.nspike`. The argument `nonspikes.out` is ignored if `method="d.gsp"` or "`osp`". The argument `smooth` is useful when the user assumes the population spectral distribution to be continuous. ## Returns A matrix containing the bias-adjusted PC scores. The dimension of the matrix is the same as the dimension of `test.scores`. A printed message shows the number of top PCs that were adjusted for shrinkage bias. ## References Dey, R. and Lee, S. (2019). **Asymptotic properties of principal component analysis and shrinkage-bias adjustment under the generalized spiked population model.** Journal of Multivariate Analysis, Vol 173, 145-164. ## Author(s) Rounak Dey, deyrnk@umich.edu ## See Also `hdpc_est,select.nspike` ## Examples ```r data(hapmap) #n = 198, p = 75435 for this data #################################################### ## Not run: #First estimate the number of spikes and then adjust test scores based on that train.eval<-hapmap$train.eval n<-hapmap$nSamp p<-hapmap$nSNP trainscore<-hapmap$trainscore testscore<-hapmap$testscore m<-select.nspike(train.eval,p,n,n.spikes.max=10,evals.out=FALSE)$n.spikes score.adj.o1<-pc_adjust(train.eval,p,n,testscore,method="osp",n.spikes=m) score.adj.d1<-pc_adjust(train.eval,p,n,testscore,method="d.gsp",n.spikes=m) score.adj.l1<-pc_adjust(train.eval,p,n,testscore,method="l.gsp",n.spikes=m) #Or you can provide an upper bound n.spikes.max score.adj.o2<-pc_adjust(train.eval,p,n,testscore,method="osp",n.spikes.max=10) score.adj.d2<-pc_adjust(train.eval,p,n,testscore,method="d.gsp",n.spikes.max=10) score.adj.l2<-pc_adjust(train.eval,p,n,testscore,method="l.gsp",n.spikes.max=10) #Plot the training score, test score, and adjusted scores plot(trainscore,pch=19) points(testscore,col='blue',pch=19) points(score.adj.o1,col='red',pch=19) points(score.adj.d2,col='green',pch=19) ## End(Not run) ```

pc_adjust function