with curve features. Let us go back now to the original problem of a one-factor design, where the sample of n individuals can be separated into I groups, with group i containing J$_{i}$ individuals. For subject j in group i we observe certain variable (e.g. mass) at time points t$_{ij}$ 1 , . . . , t$_{ijν}$$_{ij}$ , obtaining observations y$_{ij}$ 1 , . . . , y$_{ijν}$$_{ij}$ . The number of observations ν$_{ij}$ as well as the time points may change from individual to individual. We assume where { x$_{ij}$ ( t ) } are underlying smooth curves, no directly observable, and { ε$_{ijk}$ } are i.i.d. N (0 , σ $^{2}$) random errors independent of the underlying x$_{ij}$ ( t ) s. Observational model (5), which treats the smooth curves { x$_{ij}$ ( t ) } as latent variables, is the usual way to bridge functional data analysis and longitudinal data analysis (M¨uller, 2008). As discussed in Section 2, we can write x$_{ij}$ ( t ) = z$_{ij}$ { w − 1 ij ( t ) } for a warped process z$_{ij}$ ( t ) and a warping function w$_{ij}$ ( t ) . These will inherit the dependence structure of the x$_{ij}$ s, so we can assume with { α$_{i}$ ( t ) } and { β$_{ij}$ ( t ) } zero-mean random factors independent of each other and among themselves. For the main factor α ( t ) and the residual term β ( t ) we assume expansions analogous to (4): z$_{ij}$ ( t ) = µ ( t ) + α$_{i}$ ( t ) + β$_{ij}$ ( t ) , j = 1 , . . . , J$_{i}$, i = 1 , . . . , I, (6) α ( t ) = p ∑ k =1 U$_{k}$φ$_{k}$ ( t ) , (7) y$_{ijk}$ = x$_{ij}$ ( t$_{ijk}$ ) + ε$_{ijk}$, (5) 3 The warped ANOVA model 7