Slotnick Scott D
Department of Psychology, Harvard University, Cambridge, Massachusetts 02138, USA.
Behav Res Methods Instrum Comput. 2003 May;35(2):322-4. doi: 10.3758/bf03202559.
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.
传统上，通过改变模型参数以最小化因变量维度中预期值与观测值之间的偏差，从而使数学模型与经验得出的数据相拟合。然而，当要拟合的函数是多值函数时（例如椭圆），传统的模型拟合程序就会失效。本文提出了一种新颖的（n + 1）维[（n + 1）-D]模型拟合程序，该程序可以通过将n维模型和数据转换到（n + 1）维空间，然后最小化在构建维度中的偏差来解决此类问题。虽然（n + 1）-D程序提供的模型拟合与用传统方法对单值函数获得的拟合相同，但它也将参数估计扩展到了多值函数。
