# Solved – Baseline adjustment in growth models: Random Intercept or Baseline Covariate

Let's say I have outcome data at four time-points (baseline, 3 months, 6 months, 12 months) which I want to regress on an explicit time variable (\$t_1 = 0\$, \$t_2 = 1\$, \$t_3 = 2\$, \$t_4 = 3\$) to understand linear change.

I typically adjust for baseline differences in the outcome using a random intercept, e.g.:

\$\$Y_{it} = beta_0 + beta_1Time_{it} + U_i + e_{it} \$\$

Where \$i\$ = subject, \$t\$ = time, \$B_0\$ is a fixed intercept, \$B_1\$ is the slope of the explicit time variable, \$U_i\$ is the random intercept, and \$e\$ is subject- and time-varying error.

However, my supervisor adjusts for baseline differences by including the baseline measurement as a covariate and a random intercept, e.g.,:

\$\$Y_{it} = beta_0 + beta_1Time_{it} + beta_2Baseline_i + U_i + e_{it} \$\$

I know that other people adjust for baseline variation in the outcome by just including baseline measurement as a covariate and no random intercept.

My questions are:

1. Which of the above approaches is valid for adjusting for baseline differences (if any) and why?
2. In particular, is it appropriate to adjust for baseline variation with a random intercept and no baseline covariate, and why?
3. Do you have any references on the topic?
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