Analysis of growth curve data by using cubic smoothing splines

Nummi, Tapio; Koskela, Laura

doi:10.1080/02664760801923964

Cited by 10 publications

(3 citation statements)

References 12 publications

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“…We now consider the case of dependent errors, that is, Cov( ɛ ) =σ 2 R . In this setting, the penalized least squares criterion is Q = ( g − y )′ H ( g − y ) +α g ′ K g , with H = R −1 and the analog of is In line with Nummi and Koskela (2007), when R has an appropriate special form, it can be seen that the equation for reduces to . This is a very important simplification, since spline estimates in this case are simple linear functions of the observations.…”

Section: Fitting a Cubic Smoothing Splinementioning

confidence: 99%

Testing for Cubic Smoothing Splines under Dependent Data

et al. 2011

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In most research on smoothing splines the focus has been on estimation, while inference, especially hypothesis testing, has received less attention. By defining design matrices for fixed and random effects and the structure of the covariance matrices of random errors in an appropriate way, the cubic smoothing spline admits a mixed model formulation, which places this nonparametric smoother firmly in a parametric setting. Thus nonlinear curves can be included with random effects and random coefficients. The smoothing parameter is the ratio of the random-coefficient and error variances and tests for linear regression reduce to tests for zero random-coefficient variances. We propose an exact F-test for the situation and investigate its performance in a real pine stem data set and by simulation experiments. Under certain conditions the suggested methods can also be applied when the data are dependent.

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Section: Fitting a Cubic Smoothing Splinementioning

confidence: 99%

Testing for Cubic Smoothing Splines under Dependent Data

et al. 2011

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“…It is common in such settings to model the rows of

U

as a user‐specified vector‐valued function

u (t) \in ℝ^{k}

of time

t

, the

i

th row of

U

then being

u^{T} (t_{i})

. Polynomial bases

u^{T} (t) = (1, t, t^{2}, \dots, t^{k - 1})

are prevalent, particularly in the foundational work of Potthoff and Roy (1964), Rao (1965), Grizzle and Allen (1969) and others, but splines (Nummi & Koskela, 2008) or other basis constructions (Izenman & Williams, 1989) could be used as well. In longitudinal studies, model () might be used when modeling profiles, while model () could be used when modeling just profile differences.…”

Section: Introductionmentioning

confidence: 99%

Envelopes for multivariate linear regression with linearly constrained coefficients

Cook,

Forzani,

Liu

2023

Scandinavian J Statistics

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A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and longitudinal data. Envelope methods have been proposed to improve the estimation efficiency in unconstrained multivariate linear models, but have not yet been developed for constrained models. We pursue that development in this article. We first compare the standard envelope estimator with the standard estimator arising from a constrained multivariate model in terms of bias and efficiency. To further improve efficiency, we propose a novel envelope estimator based on a constrained multivariate model. We show the advantage of our proposals by simulations and by studying the probiotic capacity to reduced Salmonella infection.This article is protected by copyright. All rights reserved.

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“…, y n . A set of covariance matrices satisfying the condition (4) can be generated using the formulas discussed in [12] and [13]. As a special case these structures include, for example, R = XDX + I, where X = [1, x], 1 = (1, .…”

Section: Cubic Smoothing Splinesmentioning

confidence: 99%

Testing linearity in semiparametric regression models

Nummi

Pan

Mesue

2013

Statistics and Its Interface

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One of the fundamental assumptions of a basic multiple linear regression model is that the contribution of each of the model terms is strictly linear. In many cases, this may be an excessive simplification of the complicated relationships. Moreover, it may be difficult or impossible to test the hypothesized model against all possible kinds of relevant alternative models. Therefore, tests that perform well under more general circumstances are also required. This paper considers the semiparametric model, where the contribution of one of the model terms may not be strictly linear, and also proposes an exact F-test for the situation. The method also allows dependent error terms. The performance of the proposed test is illustrated by simulation experiments and in real air pollution and health data.

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Analysis of growth curve data by using cubic smoothing splines

Cited by 10 publications

References 12 publications

Testing for Cubic Smoothing Splines under Dependent Data

Testing for Cubic Smoothing Splines under Dependent Data

Envelopes for multivariate linear regression with linearly constrained coefficients

Testing linearity in semiparametric regression models

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