Hi, sorry for the delay in the response. I wanted to be certain that I give the correct answer, and during StanCon and traveling it’s more difficult to focus on details like this.
If you have in model block
Y_hijk[h] ~ normal(beta_0jkm[Plant4Day[h]]* X_hijk[h] + beta_1jkm[Plant4Day[h]], sigma_y);
and then you first had in generated quantities block
log_lik[h] = normal_lpdf(Y_hijk[h] |beta_0jkm[Plant4Day[h]]* X_hijk[h] + beta_1jkm[Plant4Day[h]], sigma_y);
If I understood correctly, your Y here is either growth rate or log of growth rate. In order to compare models for rate and log rate, when modeling log rate you need to include the Jacobian of the log transformation. For log(rate) the Jacobian is 1/rate. When working on density scale you would multiply by Jacobian. When you are working on log density scale you add log Jacobian, which is now log(1/rate)=-log(rate) and if your Y is log(rate), then you should have
log_lik[h] = normal_lpdf(Y_hijk[h] |beta_0jkm[Plant4Day[h]]* X_hijk[h] + beta_1jkm[Plant4Day[h]], sigma_y) - Y_hijk[h];
Alternatively you could have Y always to be rate and make another model with lognormal both in model and generated quantities block.