LGM age definition variables, standard error in intercept mean/variance

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LGM age definition variables, standard error in intercept mean/variance

In OpenMx, if I run a latent growth model with age definition variables and center my intercept at some age (by subtracting that number from each person's age), will the standard error of the intercept mean and variance depend on the number of people at or around that age? For example, if I have a longitudinal study that in the first wave a cross-section of people were recruited ages 10-40y and then followed every 5 years. Even if my total sample size was reasonable (1000) there are a lot less people at any given age, especially younger ages. So if I center the intercept at 20y, will the standard error of the intercept's mean and variance estimates be limited by the number of people with age 20y data? Does the issue get worse as I center to more and more specific ages such as 20.56y? Thanks