Table 14 Empirical Type I error for OTE \({\theta }_{1}=0\) and HTE \({\theta }_{3}=0\) based on 1,000 simulations using naïve standard error estimator provided by gee function using R. The number of clusters \(I=8\), the total time steps is \(J=5\), the cluster size is \(m=40\) for each cluster, the prevalence of \({X}_{ijk}\) is 50% when estimating HTE, \({\gamma }_{j}=0.1\left(j-1\right)\) for \(j=\mathrm{1,2},\mathrm{3,4},5\), and \({\theta }_{0}={\text{log}}\left(0.15/0.85\right)\)
| Â | Estimating OTE | Estimating HTE | Estimating HTE | |||
|---|---|---|---|---|---|---|
Data generating Procedure | \({\text{logit}}\left({\mu }_{ijk}\right)={\theta }_{0}+{\gamma }_{j}\) | \({\text{logit}}\left({\mu }_{ijk}\right)={\theta }_{0}+{\gamma }_{j}\) | \({\text{logit}}\left({\mu }_{ijk}\right)={\theta }_{0}+{\gamma }_{j}+{\text{log}}\left(1.68\right){W}_{ij}+{\text{log}}\left(1.5\right){X}_{ijk}\) | |||
| Â | \(\alpha =0.1\) | \(\alpha =0.05\) | \(\alpha =0.1\) | \(\alpha =0.05\) | \(\alpha =0.1\) | \(\alpha =0.05\) |
\(\rho =1\) | \(0.052\) | \(0.060\) | \(0.054\) | \(0.057\) | \(0.036\) | \(0.043\) |
\(\rho =0.5\) | \(0.279\) | \(0.174\) | \(0.048\) | \(0.048\) | \(0.047\) | \(0.048\) |