Confidence Intervals for Semiparametric Regression Curves Based on the Truncated Spline Estimator for Longitudinal Data
DOI:
https://doi.org/10.54065/likelihood.1483Keywords:
Semiparametric Regression, Longitudinal Data, Truncated Spline, Pointwise Confidence Interval, Weighted Least Squares, Infant GrowthAbstract
Confidence intervals are required to quantify uncertainty in an estimated regression curve, but their construction becomes more complex when the model combines parametric and nonparametric components for repeated measurements. This study develops a pointwise confidence interval for a semiparametric regression curve based on a truncated spline estimator for continuous longitudinal data. The parametric component was specified as linear, whereas the unknown age effect was represented by a truncated-power spline. Model parameters were estimated using weighted least squares, spline order and knots were selected through generalized cross-validation, and a Student's t pivotal quantity was used when the common variance scale was unknown. The procedure was applied to 252 height measurements from 16 infants aged 0-24 months in Surabaya, comprising eight male and eight female infants. The selected model was a second-order truncated spline with four knots at 4, 8, 12, and 16 months. It produced a GCV value of 8.8505, an MSE of 8.2975, and a coefficient of determination of 91.0469%. The fitted curve indicated the largest average monthly increase during 0-4 months and the smallest during 16-24 months. The sex coefficient indicated an estimated constant mean-height difference of 0.4926 cm, rather than a difference in growth velocity. The proposed interval is conditional on the selected spline specification, normal-error assumption, and diagonal working covariance. Consequently, the empirical results are illustrative and should not be interpreted as simultaneous-band coverage or as a population growth standard.
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