I understand that fixed vs. random effects have different meaning whether it be in biostatistics or econometrics. I recently came across a talk regarding fixed vs. random effects in the hierarchical setting, where the lecture slide is below:
The slide details $14$ different cancer treatment studies, indexed by $s$, with the data $x_{0s}$ and $x_{1s}$ following conditional Binomials. The effect size above, $\lambda_s$, is none other than the log relative risk ratio known in Biostatistics.
My questions are:
1) if our effect here is $\lambda_s$, would it be a fixed or random effect in this model?
2) If we removed the $\lambda_s|\mu, \tau^2 \sim N(\mu, \tau_2)$ part and instead replace it with $\theta_{1s} \sim U(0,1)$, would it now be a random effects model?
In general, if $\theta_{1s}$ and $\theta_{0s}$ are both random, does that imply we have $\lambda_s$ is a random effect? Thanks!
