Multilevel Functional Principal Component Analysis of Façade Sound Insulation Data

In this work we analize data from a sound insulation of façades study, the experiment consisting of independent measurements executed several times by different operators on the same residential building. Mathematically, data can be seen as functions of an acustic parameter over the spectrum of the frequencies. In these studies, it is important to assess the within and between group variability in the measurements of façade sound insulation. Moreover, in the engineering literature it is known that the indices of sound insulation are more variable at low frequencies, compared to higher frequencies. Therefore, we employ a multilevel functional principal component analysis (FPCA, Di et al~2009) to decompose the functional variance both at the data and at the group level. Our method allows ranking the performance of the operators on the basis of their measurements' variability and their different performances at either low frequency (relative high variability) and high frequency (relative low variability) spectra.