Growth charts are widely used in pediatric care for assessing childhood bodysize measurements (e.g., height or weight). The existing growth charts screenone body size at a single given age. However, when a child has multiplemeasures over time and exhibits a growth path, how to assess those measuresjointly in a rigorous and quantitative way remains largely undeveloped in theliterature. In this paper, we develop a new method to construct growth chartsfor growth paths. A new estimation algorithm using alternating regressions isdeveloped to obtain principal component representations of growth paths (sparsefunctional data). The new algorithm does not rely on strong distributionassumptions and is computationally robust and easily incorporates subject levelcovariates, such as parental information. Simulation studies are conducted toinvestigate the performance of our proposed method, including comparisons toexisting methods. When the proposed method is applied to monitor the pubertygrowth among a group of Finnish teens, it yields interesting insights.
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