Analyzing Longitudinal Data Using Gee-Smoothing Spline
This paper considers nonparametric regression to analyze longitudinal data. Some developments of nonparametric regression have been achieved for longitudinal or clustered categorical data. For exponential family distribution, Lin & Carroll [6] considered nonparametric regression for longitudin...
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| Format: | Article |
| Language: | English English |
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2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/7923/ http://psasir.upm.edu.my/id/eprint/7923/1/Analyzing%20Longitudinal%20Data%20Using%20Gee.pdf |
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| author | Ibrahim, Noor Akma Suliadi, |
| author_facet | Ibrahim, Noor Akma Suliadi, |
| author_sort | Ibrahim, Noor Akma |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper considers nonparametric regression to analyze longitudinal data. Some developments of nonparametric
regression have been achieved for longitudinal or clustered categorical data. For exponential family
distribution, Lin & Carroll [6] considered nonparametric regression for longitudinal data using GEE-Local Polynomial
Kernel (LPK). They showed that in order to obtain an efficient estimator, one must ignore within subject
correlation. This means within subject observations should be assumed independent, hence the working correlation
matrix must be an identity matrix. With Lin & Carroll [6], to obtain efficient estimates we should ignore
correlation that exist in longitudinal data, even if correlation is the interest of the study. In this paper we propose
GEE-Smoothing spline to analyze longitudinal data and study the property of the estimator such as the bias, consistency
and efficiency. We use natural cubic spline and combine with GEE of Liang & Zeger [5] in estimation.
We want to explore numerically, whether the properties of GEE-Smoothing spline are better than of GEE-Local
Polynomial Kernel that proposed by Lin & Carrol [6]. Using simulation we show that GEE-Smoothing Spline is
better than GEE-local polynomial. The bias of pointwise estimator is decreasing with increasing sample size. The
pointwise estimator is also consistent even with incorrect correlation structure, and the most efficient estimate is
obtained if the true correlation structure is used. |
| first_indexed | 2025-11-15T07:31:58Z |
| format | Article |
| id | upm-7923 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T07:31:58Z |
| publishDate | 2010 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-79232015-09-28T03:14:56Z http://psasir.upm.edu.my/id/eprint/7923/ Analyzing Longitudinal Data Using Gee-Smoothing Spline Ibrahim, Noor Akma Suliadi, This paper considers nonparametric regression to analyze longitudinal data. Some developments of nonparametric regression have been achieved for longitudinal or clustered categorical data. For exponential family distribution, Lin & Carroll [6] considered nonparametric regression for longitudinal data using GEE-Local Polynomial Kernel (LPK). They showed that in order to obtain an efficient estimator, one must ignore within subject correlation. This means within subject observations should be assumed independent, hence the working correlation matrix must be an identity matrix. With Lin & Carroll [6], to obtain efficient estimates we should ignore correlation that exist in longitudinal data, even if correlation is the interest of the study. In this paper we propose GEE-Smoothing spline to analyze longitudinal data and study the property of the estimator such as the bias, consistency and efficiency. We use natural cubic spline and combine with GEE of Liang & Zeger [5] in estimation. We want to explore numerically, whether the properties of GEE-Smoothing spline are better than of GEE-Local Polynomial Kernel that proposed by Lin & Carrol [6]. Using simulation we show that GEE-Smoothing Spline is better than GEE-local polynomial. The bias of pointwise estimator is decreasing with increasing sample size. The pointwise estimator is also consistent even with incorrect correlation structure, and the most efficient estimate is obtained if the true correlation structure is used. 2010 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/7923/1/Analyzing%20Longitudinal%20Data%20Using%20Gee.pdf Ibrahim, Noor Akma and Suliadi, (2010) Analyzing Longitudinal Data Using Gee-Smoothing Spline. WSEAS Transactions on Systems and Control . ISSN 1790-5117 http://www.wseas.us/e-library/conferences/2009/hangzhou/ACACOS/ACACOS02.pdf Spline theory English |
| spellingShingle | Spline theory Ibrahim, Noor Akma Suliadi, Analyzing Longitudinal Data Using Gee-Smoothing Spline |
| title | Analyzing Longitudinal Data Using Gee-Smoothing Spline |
| title_full | Analyzing Longitudinal Data Using Gee-Smoothing Spline |
| title_fullStr | Analyzing Longitudinal Data Using Gee-Smoothing Spline |
| title_full_unstemmed | Analyzing Longitudinal Data Using Gee-Smoothing Spline |
| title_short | Analyzing Longitudinal Data Using Gee-Smoothing Spline |
| title_sort | analyzing longitudinal data using gee-smoothing spline |
| topic | Spline theory |
| url | http://psasir.upm.edu.my/id/eprint/7923/ http://psasir.upm.edu.my/id/eprint/7923/ http://psasir.upm.edu.my/id/eprint/7923/1/Analyzing%20Longitudinal%20Data%20Using%20Gee.pdf |