Multilevel Functional Principal Component Analysis of Façade Sound Insulation Data

This work analyzes data from an experimental study on façade sound insulation, consisting of independent repeated measurements executed by different laboratories on the same residential building. Mathematically, data can be seen as functions describing an acoustic parameter varying with frequency. The aim of this study is twofold. On one hand, considering the laboratory as the grouping variable, it is important to assess the within-group and between-group variability in the measurements. On the other hand, in building acoustics, it is known that sound insulation is more variable at low frequencies (from 50 to 100 Hz), compared with higher frequencies (up to 5000 Hz), and therefore, a multilevel functional model is employed to decompose the functional variance both at the measurement level and at the group level. This decomposition also allows for the ranking of the laboratories on the basis of measurement variability and performance at low frequencies (relative high variability) and over the whole spectrum. The former ranking is obtained via the principal component scores and the latter via an original Bayesian extension of the functional depth.