Semiparametric models for the analysis of longitudinal weight measurement data
ORSAMA, ANNA-LEENA (2011)
2011
Tilastotiede - Statistics
Informaatiotieteiden yksikkö - School of Information Sciences
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Hyväksymispäivämäärä
2011-05-31
Julkaisun pysyvä osoite on
https://urn.fi/urn:nbn:fi:uta-1-21414
https://urn.fi/urn:nbn:fi:uta-1-21414
Tiivistelmä
This thesis discusses semiparametric regression models that provide a flexible tool for modelling longitudinal data. Nonparametric models can be used for exploring data when parametric assumptions are too restricted to provide an adequate fit. In this thesis splines, piecewise defined polynomials, are discussed with emphasis on penalised splines. A penalised spline model can be connected to the widely known linear mixed-effects models that are a powerful tool for analysing clustered unbalanced data. Partitioning spline components into fixed effects and random effects, fusion between a parametric and a nonparametic model can be obtained. The advantage is that through the linear mixed-effect model presentation a nonparametric fit can be extended to account for the longitudinal nature of the data.
For model estimation and inference, likelihood based methods maximum likelihood and restricted maximum likelihood are discussed. Testing the significance of a spline model involves testing if a variance component of the corresponding LME model is zero. Testing is nonstandard since basic assumptions do not hold; in longitudinal data measurements are not independent or identically distributed and under the null hypothesis the test parameter is on the boundary of its parameter space.
The presented theory is applied to longitudinal weight measurements data to explore the weekly rhythm of weight. The rhythm is explored in the population level and in two subgroups; among subjects who have lost weight and among subjects who have gained weight. We find a rhythm that shows weight to be higher after weekends, on Sundays and on Mondays, and decrease during weekdays. Furthermore, in the whole population level and in the loss group, there seems to be a slight but significant increase in the end of the week, on Fridays and Saturdays. There is no difference in the shape of the estimated profile curves between the groups.
Asiasanat:linear mixed-effects model, penalised spline, semiparametric regression, weekly rhythm
For model estimation and inference, likelihood based methods maximum likelihood and restricted maximum likelihood are discussed. Testing the significance of a spline model involves testing if a variance component of the corresponding LME model is zero. Testing is nonstandard since basic assumptions do not hold; in longitudinal data measurements are not independent or identically distributed and under the null hypothesis the test parameter is on the boundary of its parameter space.
The presented theory is applied to longitudinal weight measurements data to explore the weekly rhythm of weight. The rhythm is explored in the population level and in two subgroups; among subjects who have lost weight and among subjects who have gained weight. We find a rhythm that shows weight to be higher after weekends, on Sundays and on Mondays, and decrease during weekdays. Furthermore, in the whole population level and in the loss group, there seems to be a slight but significant increase in the end of the week, on Fridays and Saturdays. There is no difference in the shape of the estimated profile curves between the groups.
Asiasanat:linear mixed-effects model, penalised spline, semiparametric regression, weekly rhythm