Model fitting in (n+1) dimensions.
Conventionally, fitting a mathematical model to empirically derived data is achieved by varying model parameters to minimize the deviations between expected and observed values in the dependent dimension. However, when functions to be fit are multivalued (e.g., an ellipse), conventional model fitting procedures fail. A novel (n+1)-dimensional [(n+1)-D] model fitting procedure is presented which can solve such problems by transforming the n-D model and data into (n+1)-D space and then minimizing deviations in the constructed dimension. While the (n+1)-D procedure provides model fits identical to those obtained with conventional methods for single-valued functions, it also extends parameter estimation to multivalued functions.
Slotnick
Scott D
SD
Department of Psychology, Harvard University, Cambridge, Massachusetts 02138, USA. slotnick@wjh.harvard.edu
D000465:Algorithms; D003627:Data Interpretation, Statistical; D016014:Linear Models; D008432:Mathematical Computing; D015233:Models, Statistical; D011589:Psychology, Experimental / Q000706:statistics & numerical data*