Self Modeling Nonlinear Regression

Lawton, William H.; Sylvestre, Edward A.; Maggio, Mary S.

doi:10.1080/00401706.1972.10488942

Cited by 124 publications

(49 citation statements)

References 6 publications

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“…One of the most frequently used nonparametric models to analyse longitudinal data is the 'shape invariant model' proposed by Lawton, Sylvestre and Maggio [18] y . This nonlinear model has the following form…”

Section: Spline Modelsmentioning

confidence: 99%

Pharmacodynamics of controlled release verapamil in patients with hypertension: an analysis using spline functions

Aarons

Baxter

Gupta³

2004

Biopharm & Drug Disp

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Section: Spline Modelsmentioning

confidence: 99%

Pharmacodynamics of controlled release verapamil in patients with hypertension: an analysis using spline functions

Aarons

Baxter

Gupta³

2004

Biopharm & Drug Disp

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“…A nonparametric method is proposed in Ramsay and Silverman [7]: the original series is split into individual cycles and each cycle is treated as an independent curve. A more efficient method is semiparametric shape-invariant modeling [4][5][6]10].…”

Section: Introductionmentioning

confidence: 99%

Semiparametric shape-invariant models for periodic data

Hürtgen

Gervini

2009

Journal of Applied Statistics

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This article presents a novel shape-invariant modeling approach to quasi-periodic data. We propose a dynamic semiparametric method that estimates the common cycle shape in a nonparametric way and the individual phase and amplitude variability in a parametric way. An efficient algorithm to compute the estimators is proposed. The behavior of the estimators is studied by simulation and by a real-data example.circadian rhythms, nonparametric regression, spline smoothing,

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“…Existing methods for analyzing functional data include selfmodeling regression (Lawton, Sylvestre, and Maggio, 1972) or shape invariant models (SIM) and time warping procedures. The SIM assumes curves have a common shape, modeled nonparametrically, and curve-specific differences in Time (seconds)…”

Section: Introductionmentioning

confidence: 99%

Self Modeling with Flexible, Random Time Transformations

Brumback¹,

Lindstrom²

2004

Biometrics

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Methods for modeling sets of complex curves where the curves must be aligned in time (or in another continuous predictor) fall into the general class of functional data analysis and include self-modeling regression and time-warping procedures. Self-modeling regression (SEMOR), also known as a shape invariant model (SIM), assumes the curves have a common shape, modeled nonparametrically, and curve-specific differences in amplitude and timing, traditionally modeled by linear transformations. When curves contain multiple features that need to be aligned in time, SEMOR may be inadequate since a linear time transformation generally cannot align more than one feature. Time warping procedures focus on timing variability and on finding flexible time warps to align multiple data features. We draw on these methods to develop a SIM that models the time transformations as random, flexible, monotone functions. The model is motivated by speech movement data from the University of Wisconsin X-ray microbeam speech production project and is applied to these data to test the effect of different speaking conditions on the shape and relative timing of movement profiles.

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Self Modeling Nonlinear Regression

Cited by 124 publications

References 6 publications

Pharmacodynamics of controlled release verapamil in patients with hypertension: an analysis using spline functions

Pharmacodynamics of controlled release verapamil in patients with hypertension: an analysis using spline functions

Semiparametric shape-invariant models for periodic data

Self Modeling with Flexible, Random Time Transformations

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