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Annexes 205allows an acceleration of the cognitive decline among oldest subjects. The intercept, linearand quadratic coefficients for age were subject-specific random coefficients to take intoaccount intra-subject correlation. We added a Brownian motion to account for individualdeviations from this quadratic evolution and thus relaxed the parametric form of the model.The test-specific models defined the flexible links between the psychometric tests and thelatent cognitive factor. The hypothesis is that a test-specific nonlinear transformation of eachtest is a noisy measure of the latent cognitive factor. More specifically, the value of thenonlinear transformation of each test at age t equalled:- the latent cognitive level at age t,- plus test-specific covariates effects, which account for the effect of the covariates onthe ability to pass this test after adjustment on the cognitive level,- plus a test-and-subject-specific random effect, which accounts for inter-individualvariations of ability to pass this test after adjustment on the latent cognitive level andeffects of covariates,- plus an independent test-specific measurement error.The nonlinear test-specific transformations which link each psychometric test with the latentcommon cognitive factor were parametric functions depending on parameters to be estimatedsimultaneously with the other parameters in the model. The chosen flexible transformationswere Beta Cumulative Distribution Functions which offer a large variety of shapes (concave,convex or sigmoid) using only two estimated parameters per test. The complete methodologywas previously detailed in Proust et al. [22] and is described in Appendix.7