backfit function

Backfit from scores to configuration

Backfit from PNSS or PCA scores to a representative configuration

backfit(scores, x, type="pnss", size=1)

Arguments

• scores: n x p matrix of scores
• x: An object that is the output of either pnss3d (if type="pnss") or procGPA (if type="pca")
• type: Either "pnss" for PNSS or "pca" for PCA
• size: The centroid size of the backfitted configuration. The default is 1 but one can rescale the backfitting if desired.

Returns

A k x m matrix of co-ordinates of the backfitted configuration

References

Dryden, I.L., Kim, K., Laughton, C.A. and Le, H. (2019). Principal nested shape space analysis of molecular dynamics data. Annals of Applied Statistics, 13, 2213-2234.

Jung, S., Dryden, I.L. and Marron, J.S. (2012). Analysis of principal nested spheres. Biometrika, 99, 551-568.

Author(s)

Ian Dryden

See Also

pns, pns4pc, plot3darcs

Examples

ans <- pnss3d( macf.dat, sphere.type="BIC", n.pc=8)
y <- backfit( ans$PNS$scores[1,] , ans ,type="pnss")
riemdist( macf.dat[,,1] , y )  #should be close to zero

ans2 <- procGPA( macf.dat, tangentcoords="partial")
y <- backfit( ans2$scores[1,] , ans2 ,type="pca")
riemdist( macf.dat[,,1] , y )  #should be close to zero