Multilevel Functional Principal Component Analysis of Façade Sound Insulation Data

This work analyses the 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 the 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 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 to higher frequencies (up to 5000 Hz), and therefore a multilevel functional model is employed to decompose the functional variance both at the measurament and at the group level. This decomposition also allows for the ranking of the laboratories on the basis of their measurement variability and their different performances at both the low frequencies (relative high variability) and over the whole spectrum. The former ranking is obtained via the principal component scores and the latter via the functional depth.