Fig. 3

Illustration of regression and successive time-to-event models. Three types of modeling of a longitudinal count variable are shown: a linear regression model with individual effect (left), a bilinear regression model without individual effect (center) and a successive time-to-event model with two phases. For each model, observations were generated for six individuals belonging to two groups (points). Bold lines represent the average dynamics of the variable for each group, and thin lines the dynamics of each individual. For both regression models (linear with individual effect and non-linear without individual effect), the values generated at successive time points for a given individual are non-monotonous, unlike for the successive time-to-event model. In the context of phyllochron, the longitudinal variable corresponds to the number of visible leaves, the groups correspond to conditions or genotypes, and the individuals are plants. In the successive time-to-event model, segments (the duration between two jumps) of bold lines correspond to the parameters \((\mu _{y,\,lsg,\,f})_f\) while segments of thin lines correspond to the random variables \((Y_{y,\,lsg,\,p,\,f})_f\)