# Quality of the Representation of Variables by Biplot This function returns an object of the class `qbpca`. It is a simple measure of the quality of biplot representation of the variables. The observed (in the data) and projected (under biplot reduction) correlations are computed. ```r qbpca(x, bpca) ``` ## Arguments - `x`: A `data.frame` or `matrix` object. - `bpca`: A object of the class `bpca`. ## Details This function binds the vectors of observed (from the matrix or data.frame) and projected (under biplot reduction) correlations for all variables. ## Returns An object of class `qbpca` and `data.frame` with two columns: - **obs**: A vector of the observed correlations for all variables. - **var.rb**: A vector of the projected correlations for all variables determined under biplot reduction). ## Author(s) Faria, J. C. Allaman, I. B. Demétrio C. G. B. ## References Johnson, R. A. and Wichern, D. W. (1988) **Applied multivariate statistical analysis**. Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 6 ed. ## See Also `bpca` ## Examples ```r ## ## Example 1 ## Example of 'var.rb=TRUE' parameter as a measure of the quality of the biplot - 2d ## oask <- devAskNewPage(dev.interactive(orNone=TRUE)) ## Differences between methods of factorization # SQRT bp1 <- bpca(gabriel1971, meth='sqrt', var.rb=TRUE) qbp1 <- qbpca(gabriel1971, bp1) plot(qbp1, main='sqrt - 2d \n (poor)') # JK bp2 <- bpca(gabriel1971, meth='jk', var.rb=TRUE) qbp2 <- qbpca(gabriel1971, bp2) plot(qbp2, main='jk - 2d \n (very poor)') # GH bp3 <- bpca(gabriel1971, meth='gh', var.rb=TRUE) qbp3 <- qbpca(gabriel1971, bp3) plot(qbp3, main='gh - 2d \n (good)') # HJ bp4 <- bpca(gabriel1971, meth='hj', var.rb=TRUE) qbp4 <- qbpca(gabriel1971, bp4) plot(qbp4, main='hj - 2d \n (good)') ## ## Example 2 ## Example of 'var.rb=TRUE' parameter as a measure of the quality of the biplot - 3d ## ## Differences between methods of factorization # SQRT bp1 <- bpca(gabriel1971, meth='sqrt', d=1:3, var.rb=TRUE) qbp1 <- qbpca(gabriel1971, bp1) plot(qbp1, main='sqrt - 3d \n (poor)') # JK bp2 <- bpca(gabriel1971, meth='jk', d=1:3, var.rb=TRUE) qbp2 <- qbpca(gabriel1971, bp2) plot(qbp2, main='jk - 3d \n (very poor)') # GH bp3 <- bpca(gabriel1971, meth='gh', d=1:3, var.rb=TRUE) qbp3 <- qbpca(gabriel1971, bp3) plot(qbp3, main='gh - 3d \n (whow!)') # HJ bp4 <- bpca(gabriel1971, meth='hj', d=1:3, var.rb=TRUE) qbp4 <- qbpca(gabriel1971, bp4) plot(qbp4, main='hj - 3d \n (whow!)') devAskNewPage(oask) ```

qbpca function