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I think you will have to take a look at random effects (see How to account for participants in a study design?).

I think you will have to take a look at random effects (see How to account for participants in a study design?).

I can not upload plots from here but if you execute the code then you get a grapgh with on the horizontal axis the simulated initial heights and on the vertical axis the estimated/predicted values for each person, the red line is the bisector.

I can not upload plots from here but if you execute the code then you get a graph with on the horizontal axis the simulated initial (i.e. in the first year) heights and on the vertical axis the estimated/predicted values for each person in the first year, the red line is the bisector.

The idea is that you have, for a number of people $N$, a number of height measurements in different years, so $h_{iy},i=1, 2 \dots, N, y=1, 2, \dots 10$. Each $h_{iy}$ depends on the height in the first year (which depends on the person $i$) and increases with the years (the rate of increase can also depend on the person $i$), so you have something like $h_{iy} = \beta_{1i} + \beta_{2i} y + \epsilon$, where the coefficients $\beta_{1i}, \beta_{2i}$ depend on the person (hence the subscipt $i$), but if you can estimate such an equation, then you have one regression line for each person and you can look, for that single person, which points are 'far away' from that individual person's regression line.

The first one gives you the fixed effects $\beta_k$ (compare them to the values used in the simulation), the second one gives you the best linear unbiased prediction (blup) of the random effect for each person of your data set.

Compare now the 'estimated fixed effects + the blup predictors of the random effects' for each person to your input (simulated data), first for the intercept:

The idea is that you have, for a number of people $N$, a number of height measurements in different years $y$, so $h_{iy},i=1, 2 \dots, N, y=1, 2, \dots 10$. Each $h_{iy}$ depends on the height in the first year (which depends on the person $i$) and increases with the years (the rate of increase can also depend on the person $i$), so you have something like $h_{iy} = \beta_{1i} + \beta_{2i} y + \epsilon$, where the coefficients $\beta_{1i}, \beta_{2i}$ depend on the person (hence the subscipt $i$), but if you can estimate such an equation, then you have one regression line for each person and you can look, for that single person, which points are 'far away' from that individual person's own regression line.

The first one gives you the fixed effects $\beta_k$ (compare them to the values used in the simulation), the second one gives you the best linear unbiased prediction (blup) of the random effect for each person of your dataset.

Compare now the 'estimated fixed effects + the blup predictors of the random effects' for each person to your input (in this case simulated) data, first for the intercept: