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Lets say i want to identify the effect of some categorical variables x1 x2 x3 on a numeric y. I got data from 3 waves on the same individuals, but there are missing values on some variables because of two things:

  • x2 is measured only in wave 2 (for example some kind of personality test)
  • x3 is missing for individuals with x1 == 0 (for example x1 is employment status (employed yes or no) and x3 is occupational status(isco or something like that)

Doing a linear regression on y, listwise deletion will eliminate all individuals in wave 1 and 3 as well as everyone with x1 == 0.

What would be the best approach to get reliable estimates for all variables of interest?

Would it be correct to set the missing data to some arbitrary value, e.g. x2 == 88 for wave 1 and 3 (as "not measured" category) and x3 == 99 for people with x1 == 0 (as "not applicable" category) and include it in the regression? I would think the autocorrelation biases my estimates, as the x2=88 is essentially a year effect and x1 and x3 are now correlated highly as well.

Or should i estimate different models for my variables, e.g. one for x3 on y for wave 1 to 3 and one for x2 on y for wave 2?

Some R-Code for plausibility:

rm(list=ls())
set.seed(555)

x1 <- round(runif(1000,0,1))
x2 <- round(runif(1000,1,5))
x3 <- round(runif(1000,1,5))
y <- round(x1*5+x2*5+x3*5+runif(1000,0,10))
w <- round(runif(1000,1,3))
dat <- as.data.frame(cbind(x1,x2,x3,y,w))
dat$x2[dat$w != 2] <- NA
dat$x3[dat$x1 == 1] <- NA
m1 <- lm(y~as.factor(x1)+as.factor(w), data=dat)
m2 <- lm(y~as.factor(x3)+as.factor(w), data=dat)
m3 <- lm(y~as.factor(x1)+as.factor(x2), data=dat)
m4 <- lm(y~as.factor(x3)+as.factor(x2), data=dat)
summary(m1)
summary(m2)
summary(m3)
summary(m4)

dat$x2[is.na(dat$x2)] <- 88
dat$x3[is.na(dat$x3)] <- 99
mf <- lm(y~as.factor(x1)+as.factor(x2)+as.factor(x3)+as.factor(w), data=dat)
summary(mf)

The coefficient of x1 is rather different in mf vs. m1, though the x'es are uncorrelated without its relevance for y and in both regressions all observations are used.

This is directly related to 1 but in my opinion not solved, as there was just one method suggested and no real description of the mechanism. I mean, this seems like some real fundamental "problem" and something i seem to have missed in introductory statistics, as there should be a relatively trivial and intuitive answer.

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