Mixed modeling for irregularly sampled and correlated functional data: Speech science applications

The speech sciences often employ complex experimental designs requiring models with multiple covariates and crossed random effects. For curve-like data such as time-varying signals, single-time-point feature extraction is commonly used as data reduction technique to make the data amenable to statistical hypothesis testing, thereby discarding a wealth of information. The present paper discusses the application of functional linear mixed models, a functional analogue to linear mixed models. This type of model allows for the holistic evaluation of curve dynamics for data with complex correlation structures due to repeated measures on subjects and stimulus items. The nonparametric, spline-based estimation technique allows for correlated functional data to be observed irregularly, or even sparsely. This means that information on variation in the temporal domain is preserved. Functional principal component analysis is used for parsimonious data representation and variance decomposition. The basic functionality and usage of the model is illustrated based on several case studies with different data types and experimental designs. The statistical method is broadly applicable to any types of data that consist of groups of curves, whether they are articulatory or acoustic time series data, or generally any types of data suitably modeled based on penalized splines.