I am working on a project using the Young Lives longitudinal dataset, a longitudinal survey of children aged 1-15 (followed through time in 5 separate rounds) My RQ is investigating the impact of early childhood stunting on a PPVT reading score variable at age 15. Specifically, my independent variable is stunting at age 1 or age 5, where stunting refers to possessing a height-for-age z score two standard deviations less than the population mean at age 1 or age 5.

My dependent variable is an outcome variable in 1 period (i.e., time-invariant), however my independent variable, varies between periods as an individual can be stunted at age 1, then not stunted at age 5, and vice versa.

For my model so far, I am using the following general model:

PPVTage15= B0 + B1*(Indicator Variable for age 1 or age 5) + B2*(indicator variable for stunting) + B3*(age 1 or age 5)*(stunting) + ci ( a set of control covariates)

As my model is a panel dataset, with 5 instances of each individual, I was curious about using panel fixed effects to eliminate time invariant heterogeneity in individuals. However, my outcome variable, for a PPVT score at age 15, is time invariant. My questions are as follows:

1) Can I use individual fixed effects in this model estimation? (with the STATA fe command)
2) In my dataset, I also have data on PPVT scores for the individual at period 3 (at age 12). Although I am currently using a time invariant dependent variable of PPVT score at age 15, one solution to my problem would be to use this outcome to generate variance in the dependent variable. However, I do not have a PPVT score measured in every period. For this reason, would it be worthwhile using the PPVT score in round 3?
3)Would you recommend any other way to control for unobserved individual heterogeneity if I cannot used fixed effects?

Thank you