# P-Values to Classify New Observations (Penalized Multicategory Logistic Regression) Computes nonparametric p-values for the potential class memberships of new observations. The p-values are based on 'penalized logistic regression'. utf8 ```r pvs.logreg(NewX, X, Y, tau.o = 10, find.tau=FALSE, delta=2, tau.max=80, tau.min=1, a0 = NULL, b0 = NULL, pen.method = c('vectors', 'simple', 'none'), progress = FALSE) ``` ## Arguments - `NewX`: data matrix consisting of one or several new observations (row vectors) to be classified. - `X`: matrix containing training observations, where each observation is a row vector. - `Y`: vector indicating the classes which the training observations belong to. - `tau.o`: the penalty parameter (see section 'Details' below). - `find.tau`: logical. If TRUE the program searches for the best `tau`. For more information see section 'Details'. - `delta`: factor for the penalty parameter. Should be greater than 1. Only needed if `find.tau == TRUE`. - `tau.max`: maximal penalty parameter considered. Only needed if `find.tau == TRUE`. - `tau.min`: minimal penalty parameter considered. Only needed if `find.tau == TRUE`. - `a0, b0`: optional starting values for logistic regression. - `pen.method`: the method of penalization (see section 'Details' below). - `progress`: optional parameter for reporting the status of the computations. ## Details Computes nonparametric p-values for the potential class memberships of new observations. Precisely, for each new observation `NewX[i,]` and each class `b` the number `PV[i,b]` is a p-value for the null hypothesis that `Y[i]` equals `b`. This p-value is based on a permutation test applied to an estimated Bayesian likelihood ratio, using 'penalized logistic regression'. This means, the conditional probability of $Y = y$, given $X = x$, is assumed to be proportional to $exp(a_y + b_y^T x)$. The parameters $a_y$, $b_y$ are estimated via penalized maximum log-likelihood. The penalization is either a weighted sum of the euclidean norms of the vectors $(b_1[j],b_2[j],\ldots,b_L[j])$ (`pen.method=='vectors'`) or a weighted sum of all moduli $|b_{\theta}[j]|$ (`pen.method=='simple'`). The weights are given by `tau.o` times the sample standard deviation (within groups) of the $j$-th components of the feature vectors. In case of `pen.method=='none'`, no penalization is used, but this option may be unstable. If `find.tau == TRUE`, the program searches for the best penalty parameter. To determine the best parameter `tau` for the p-value `PV[i,b]`, the new observation `NewX[i,]` is added to the training data with class label `b` and then for all training observations with `Y[j] != b` the estimated probability of `X[j,]` belonging to class `b` is computed. Then the `tau` which minimizes the sum of these values is chosen. First, `tau.o` is compared with `tau.o*delta`. If `tau.o*delta` is better, it is compared with `tau.o*delta^2`, etc. The maximal parameter considered is `tau.max`. If `tau.o` is better than `tau.o*delta`, it is compared with `tau.o*delta^-1`, etc. The minimal parameter considered is `tau.min`. ## Returns `PV` is a matrix containing the p-values. Precisely, for each new observation `NewX[i,]` and each class `b` the number `PV[i,b]` is a p-value for the null hypothesis that $Y[i] = b$. If `find.tau == TRUE`, `PV` has an attribute `"tau.opt"`, which is a matrix and `tau.opt[i,b]` is the best `tau` for observation `NewX[i,]` and class `b` (see section 'Details'). `tau.opt[i,b]` is used to compute the p-value for observation `NewX[i,]` and class `b`. ## References Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. **Journal of Statistical Software 78(4)**, 1--19. doi:10.18637/jss.v078.i04 Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. **Electronic Journal of Statistics 2**, 468--493, available at [http://dx.doi.org/10.1214/08-EJS245](http://dx.doi.org/10.1214/08-EJS245). Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at [http://boris.unibe.ch/id/eprint/53585](http://boris.unibe.ch/id/eprint/53585). ## Author(s) Niki Zumbrunnen niki.zumbrunnen@gmail.com Lutz Dümbgen lutz.duembgen@stat.unibe.ch [www.imsv.unibe.ch/duembgen/index_ger.html](www.imsv.unibe.ch/duembgen/index_ger.html) ## See Also `pvs, pvs.gaussian, pvs.knn, pvs.wnn` ## Examples ```r X <- iris[c(1:49, 51:99, 101:149), 1:4] Y <- iris[c(1:49, 51:99, 101:149), 5] NewX <- iris[c(50, 100, 150), 1:4] pvs.logreg(NewX, X, Y, tau.o=1, pen.method="vectors", progress=TRUE) # A bigger data example: Buerk's hospital data. ## Not run: data(buerk) X.raw <- as.matrix(buerk[,1:21]) Y.raw <- buerk[,22] n0.raw <- sum(1 - Y.raw) n1 <- sum(Y.raw) n0 <- 3*n1 X0 <- X.raw[Y.raw==0,] X1 <- X.raw[Y.raw==1,] tmpi0 <- sample(1:n0.raw,size=3*n1,replace=FALSE) tmpi1 <- sample(1:n1 ,size= n1,replace=FALSE) Xtrain <- rbind(X0[tmpi0[1:(n0-100)],],X1[1:(n1-100),]) Ytrain <- c(rep(1,n0-100),rep(2,n1-100)) Xtest <- rbind(X0[tmpi0[(n0-99):n0],],X1[(n1-99):n1,]) Ytest <- c(rep(1,100),rep(2,100)) PV <- pvs.logreg(Xtest,Xtrain,Ytrain,tau.o=2,progress=TRUE) analyze.pvs(Y=Ytest,pv=PV,pvplot=FALSE) ## End(Not run) ```

pvs.logreg function