Abstract
Our interest is the analysis of quantitative magnetic resonance image (MRI) data, most relevant in current human brain research. When generalized additive models (GAM) are fitted to such data, the backfitting algorithm of S-Plus tends to fail due to serial correlation and concurvity. To accommodate for condition problems of the system matrix we introduce the new concept of relaxed iterative projection generalized additive models (RIP-GAM). While the RIP algorithm (also in S-Plus) does not seem to run into numerical troubles for our data set, backfitting has slow or no convergence in some instances. In standard situations, however, both procedures give the same estimation results.
Because little is known about the functional relationships between the quantitative MRI parameters such as mean diffusivity, magnetization transfer ratio or forward transfer rate and qualitative lesion-related (binary) variables from clinical MRI diagnostics, more exploratory evidence is required. Hence we fit GAMs and when necessary RIP-GAMs. In addition we apply classification trees for the validation of the selected variables. Even for a simple one-step lookahead procedure we obtain stable results which support the fitted GAMs. In conclusion, both nonparametric techniques are valuable tools for quantitative MRI research.
