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Self‐Modeling for Two‐Dimensional Response Curves
Author(s) -
Ladd William M.,
Lindstrom Mary J.
Publication year - 2000
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2000.00089.x
Subject(s) - parameterized complexity , parametric statistics , mathematics , parametric equation , affine transformation , transformation (genetics) , function (biology) , parametric model , variable (mathematics) , coordinate system , computer science , algorithm , geometry , mathematical analysis , statistics , biochemistry , chemistry , evolutionary biology , biology , gene
Summary. Two‐dimensional response curves are an important experimental outcome in speech kinematics and other areas of research. These parameterized curves are usually obtained by recording the two‐dimensional location of an object over time. In this setting, time is the independent variable and the x and y locations on specified coordinate axes define the multivariate response. Collections of such parameterized curves can be obtained either from one subject or from a number of different subjects, each producing one or several realizations of the response curve. When only one dependent variable is observed over time and no parametric model is specified, self‐modeling regression (SEMOR) is an attractive modeling approach. SEMOR assumes that each of a collection of curves differs from a smooth, average shape function by some simple parametric transformation of the coordinate axes (usually linear). We will describe the extension of SEMOR to two‐dimensional parameterized curves using affine transformations of a two‐dimensional, time‐parameterized shape function.