The K-systems Niche
Biological Sciences, Southeastern Louisiana University
Last modified: June 7, 2006
Traditional multivariate statistical approaches operate on variables, generally across the entire data set. The computational approach to K-systems analysis (KSA) is conceptually orthogonal to this, as it operates on (often tiny) pieces of combinations of variables (states and substates), searching for consistent patterns as broad as a particular level within a main effect (and never broader) to as narrow as a single cell of a complex interaction. Consequently, the fundamental computational unit in K-systems analysis is the event instead of the variable. In the field of ecology, events are real, whereas variables are usually sloppy dissections of events.
In traditional approaches to reconstructability analysis (RA) that explore behavior of a system function, the system function and predictor variables are either discrete, or they are binned into discrete variables. In K-systems analysis, the system function is metric (quantitative) and the predictor variables may or may not be metric. When predictor variables are metric, a preprocessing cluster analysis is necessary so that all possible (highly constrained) states and (less constrained) substates can be constructed. As in other RA approaches, KSA uses maximum entropy criteria to determine a modelís information content. An enormous advantage of KSA is that it is not constrained by an assumed (linear, additive) model and nonlinearities, if important, are crisply captured. A disadvantage of KSA is that it cannot associate the importance of an event with a Type I error rate. Moreover, the results of KSA are sensitive to the method of granulation, and the current method is theoretically and computationally suboptimal (via measures of system accuracy and least squares). Other problems with KSA include sensitivity to (a) outliers, (b) surrogate variables, and (c) extraneous variables. Fortunately, outliers can be screened with residual diagnostics of ANOVA or multiple regression, surrogate variables can be combined to form factor scores in factor analysis, and extraneous variables can be screened by the savvy investigator. Bottom line: for data sets suited to ANOVA, multiple regression, or a combination of the two (ANCOVA, multi-source regression), it is highly likely that K-systems analysis will extract potent information missed or distorted by these other routines.