Jjf. Commandeur et al., A distance-based variety of nonlinear multivariate data analysis, including weights for objects and variables, PSYCHOMETRI, 64(2), 1999, pp. 169-186
In the distance approach to nonlinear multivariate data analysis the focus
is on the optimal representation of the relationships between the objects i
n the analysis. In this paper two methods are presented for including weigh
ts in distance-based nonlinear multivariate data analysis. In the first met
hod weights are assigned to the objects while the second method is concerne
d with differential weighting of groups of variables. When each analysis va
riable defines a group the latter method becomes a variable weighting metho
d Far objects the weights are assumed to be given; for groups of variables
they may be given, or estimated. These weighting schemes can also be combin
ed and have several important applications. For example, they make it possi
ble to perform efficient analyses of large data sets, to use the distance-b
ased variety of nonlinear multivariate data analysis as an addition to logl
inear analysis of multiway contingency tables, and to do stability studies
of the solutions by applying the bootstrap on the objects or the variables
in the analysis. These and other applications are discussed, and an efficie
nt algorithm is proposed to minimize the corresponding loss function.