Vasdekis and Trichopoulou (2000), a discretization argument on age is used leading to a penalized least square estimation of a great number of parameters, that is one parameter for each year of age and gender. We propose to use a truncated polynomial spline of order 1 for each gender, which admits a mixed model spline representation for f. As far as socioeconomic characteristics are con- cerned, Chesher (1997) retained a multiplicative specification whereas Vasdekis and Trichopoulou (2000) chose the additive one. In the multiplicative model, a change in income for example would proportionally affect all the individual intakes whereas in the additive setting, they would be af- fected by the same value. Following Vasdekis and Trichopoulou (2000), we retained the additive specification since the difference between the two specifications may not be notable, and the addi- tive setting yields to a much simpler estimation procedure (linear model). Finally, time dependency is only introduced in Chesher (1998) to track changes with age within cohorts: this time depen- dency is directly introduced into the function f that is bivariately smoothed according to age and time (cf. Green and Silverman, 1994). Again, we adopt a simpler specification in which time is introduced as a dummy variable. All these assumptions yield an individual model of the form where the terms x$_{i,h,t}$β + z$_{i,h,t}$u stand for the mixed model spline representation of the function f, the term w$_{h,t}$γ denotes the socioeconomic effects, the term δ$_{t}$α the time effect, and ε$_{i,h,t}$ is the individual error term. Combining (2.1) and (2.2) , we obtain the final rescaled household model given by where Y$_{h,t}$ ≡ ∑ n$_{h,t}$ i =1 y$_{i,h,t}$/ √ n$_{h,t}$, X$_{h,t}$ ≡ ∑ n$_{h,t}$ i =1 x$_{i,h,t}$/ √ n$_{h,t}$, Z$_{h,t}$ ≡ ∑ n$_{h,t}$ i =1 z$_{i,h,t}$/ √ n$_{h,t}$, and ε$_{h,t}$ ≡ ∑ n$_{h,t}$ i =1 ε$_{i,h,t}$/ √ n$_{h,t}$. y$_{i,h,t}$ = x$_{i,h,t}$β + z$_{i,h,t}$u + w$_{h,t}$γ + δ$_{t}$α + ε$_{i,h,t}$, (2.2) Y$_{h,t}$ = X$_{h,t}$β + Z$_{h,t}$u + √ n$_{h,t}$w$_{h,t}$γ + √ n$_{h,t}$δ$_{t}$α + ε$_{h,t}$, (2.3) 8