Simulated correlations with different magnitudes and noise and recovered them.
- partial pooling is better for all but tau/ndt parameter
# alpha/boundary
```r
# correlations for panels below
> p_grid[, .(r = round(cor(sim_cor, recovered_cor_nopool), 4)), keyby = .(met, e)]
met e r
1: pearson 1 0.9993
2: pearson 5 0.9931
3: pearson 9 0.9894
4: pearson 13 0.9391
5: pearson 17 0.9535
6: spearman 1 0.9996
7: spearman 5 0.9907
8: spearman 9 0.9874
9: spearman 13 0.9795
10: spearman 17 0.9686
> p_grid[, .(r = round(cor(sim_cor, recovered_cor_pool), 4)), keyby = .(met, e)]
met e r
1: pearson 1 0.9998
2: pearson 5 0.9962
3: pearson 9 0.9960
4: pearson 13 0.9697
5: pearson 17 0.9855
6: spearman 1 0.9995
7: spearman 5 0.9931
8: spearman 9 0.9930
9: spearman 13 0.9880
10: spearman 17 0.9766
# larger abs deviation from true value
t = 8.6945, df = 209, p-value = 1.029e-15
# larger SEs for no-pooling
t = 5.0574, df = 104, p-value = 1.835e-06
```
![[alpha-bound 1.png]]
# tau/ndt
```r
# correlations for panels below
> p_grid[, .(r = round(cor(sim_cor, recovered_cor_nopool), 4)), keyby = .(met, e)]
met e r
1: pearson 1 1.0000
2: pearson 5 0.9996
3: pearson 9 0.9988
4: pearson 13 0.9952
5: pearson 17 0.9970
6: spearman 1 1.0000
7: spearman 5 0.9994
8: spearman 9 0.9988
9: spearman 13 0.9969
10: spearman 17 0.9960
> p_grid[, .(r = round(cor(sim_cor, recovered_cor_pool), 4)), keyby = .(met, e)]
met e r
1: pearson 1 1.0000
2: pearson 5 0.9996
3: pearson 9 0.9989
4: pearson 13 0.9940
5: pearson 17 0.9973
6: spearman 1 0.9999
7: spearman 5 0.9993
8: spearman 9 0.9990
9: spearman 13 0.9965
10: spearman 17 0.9959
# no diff in deviation
t = -0.007922, df = 209, p-value = 0.9937
# no difference in SE
t = 0.86532, df = 104, p-value = 0.3889
```
![[tau-ndt 1.png]]
# beta/bias
```r
# correlations for panels below
> p_grid[, .(r = round(cor(sim_cor, recovered_cor_nopool), 4)), keyby = .(met, e)]
met e r
1: pearson 1 0.9989
2: pearson 2 0.9967
3: pearson 3 0.9912
4: pearson 4 0.9821
5: pearson 5 0.9866
6: spearman 1 0.9989
7: spearman 2 0.9953
8: spearman 3 0.9900
9: spearman 4 0.9845
10: spearman 5 0.9827
> p_grid[, .(r = round(cor(sim_cor, recovered_cor_pool), 4)), keyby = .(met, e)]
met e r
1: pearson 1 0.9991
2: pearson 2 0.9973
3: pearson 3 0.9907
4: pearson 4 0.9878
5: pearson 5 0.9905
6: spearman 1 0.9988
7: spearman 2 0.9951
8: spearman 3 0.9917
9: spearman 4 0.9886
10: spearman 5 0.9825
# larger abs deviation from true value
t = 4.5721, df = 309, p-value = 6.995e-06
# larger SEs for no-pooling
t = 3.9775, df = 154, p-value = 0.0001069
```
![[beta-bias 1.png]]
# delta/drift
```r
# correlations for panels below
> p_grid[, .(r = round(cor(sim_cor, recovered_cor_nopool), 4)), keyby = .(met, e)]
met e r
1: pearson 1 0.8723
2: pearson 3 0.5252
3: pearson 5 0.3604
4: pearson 7 0.3899
5: pearson 9 0.2182
6: spearman 1 0.9497
7: spearman 3 0.8066
8: spearman 5 0.7972
9: spearman 7 0.5895
10: spearman 9 0.4286
> p_grid[, .(r = round(cor(sim_cor, recovered_cor_pool), 4)), keyby = .(met, e)]
met e r
1: pearson 1 0.9631
2: pearson 3 0.8403
3: pearson 5 0.4730
4: pearson 7 0.5479
5: pearson 9 0.5882
6: spearman 1 0.9629
7: spearman 3 0.8730
8: spearman 5 0.7805
9: spearman 7 0.6522
10: spearman 9 0.5356
# larger abs deviation from true value
t = 6.5905, df = 409, p-value = 1.354e-10
# larger SEs for no-pooling
t = 4.6021, df = 204, p-value = 7.342e-06
```
![[delta-drift 2.png]]