Table 1 Bias, standard deviation and mean absolute deviation of the estimates of the logit discrete choice model with contextual group effects and the logit endogenous social interactions model with closed groups
From: Partial identification of nonlinear peer effects models with missing data
Group size | No. of groups | Bias: \({\bar{\theta }}-{\theta}\left(\bar{\theta }=\tfrac{ {\textstyle \sum _{s}} {\hat{\theta }}_{s}}{S}\right)\) | STD: \(\sqrt{\tfrac{ {\textstyle \sum _{s}} ({\hat{\theta }}_{s}-{\bar{\theta }})^{2}}{S-1}}\) | MAD: \(\tfrac{ {\textstyle \sum _{s}} \left| {\hat{\theta }}_{s}-\theta \right| }{S}\) | Average time (secs) | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
k | b | d | k | b | d | k | b | d | |||
Logit with contextual group effects (\(J=0\)) | |||||||||||
 5 | 50 | \(-\)0.03 | 0.03 | 0.00 | 0.21 | 0.20 | 0.17 | 0.17 | 0.17 | 0.13 | 0.02 |
 5 | 100 | \(-\)0.03 | 0.01 | 0.04 | 0.18 | 0.18 | 0.14 | 0.13 | 0.11 | 0.11 | 0.02 |
 5 | 200 | \(-\)0.03 | 0.01 | 0.00 | 0.12 | 0.11 | 0.10 | 0.10 | 0.08 | 0.08 | 0.02 |
 5 | 500 | 0.00 | 0.00 | 0.01 | 0.07 | 0.07 | 0.05 | 0.06 | 0.05 | 0.04 | 0.04 |
 5 | 1000 | 0.00 | 0.01 | 0.00 | 0.05 | 0.04 | 0.05 | 0.04 | 0.03 | 0.04 | 0.07 |
 5 | 2500 | 0.00 | 0.00 | 0.00 | 0.03 | 0.03 | 0.03 | 0.03 | 0.02 | 0.02 | 0.13 |
Logit endogenous social interactions model (closed groups) | |||||||||||
 5 | 50 | 0.09 | 0.04 | 0.02 | 0.29 | 0.18 | 0.22 | 0.24 | 0.15 | 0.17 | 0.03 |
 5 | 100 | 0.11 | 0.01 | \(-\)0.03 | 0.24 | 0.17 | 0.12 | 0.20 | 0.14 | 0.10 | 0.03 |
 5 | 200 | 0.02 | 0.03 | \(-\)0.01 | 0.16 | 0.12 | 0.10 | 0.12 | 0.10 | 0.08 | 0.04 |
 5 | 500 | 0.05 | 0.01 | \(-\)0.01 | 0.10 | 0.06 | 0.06 | 0.09 | 0.05 | 0.05 | 0.07 |
 5 | 1000 | 0.03 | 0.00 | \(-\)0.01 | 0.07 | 0.06 | 0.03 | 0.06 | 0.04 | 0.03 | 0.08 |
 5 | 2500 | 0.05 | 0.00 | \(-\)0.03 | 0.04 | 0.03 | 0.02 | 0.05 | 0.03 | 0.03 | 0.14 |
 10 | 50 | 0.05 | 0.00 | \(-\)0.02 | 0.25 | 0.12 | 0.15 | 0.21 | 0.10 | 0.11 | 0.03 |
 10 | 100 | 0.01 | 0.00 | \(-\)0.02 | 0.19 | 0.09 | 0.10 | 0.15 | 0.07 | 0.08 | 0.03 |
 10 | 200 | 0.00 | \(-\)0.01 | \(-\)0.01 | 0.12 | 0.07 | 0.08 | 0.10 | 0.06 | 0.07 | 0.04 |
 10 | 500 | 0.00 | \(-\)0.01 | \(-\)0.03 | 0.09 | 0.05 | 0.04 | 0.07 | 0.04 | 0.05 | 0.07 |
 10 | 1000 | \(-\)0.01 | 0.00 | \(-\)0.03 | 0.06 | 0.03 | 0.03 | 0.05 | 0.02 | 0.03 | 0.12 |
 10 | 2500 | \(-\)0.03 | 0.00 | \(-\)0.02 | 0.04 | 0.02 | 0.02 | 0.04 | 0.02 | 0.02 | 0.25 |
 25 | 50 | 0.02 | 0.01 | 0.04 | 0.26 | 0.08 | 0.12 | 0.21 | 0.06 | 0.09 | 0.03 |
 25 | 100 | \(-\)0.01 | 0.00 | \(-\)0.03 | 0.18 | 0.07 | 0.08 | 0.14 | 0.05 | 0.06 | 0.05 |
 25 | 200 | \(-\)0.07 | 0.00 | \(-\)0.04 | 0.09 | 0.05 | 0.05 | 0.09 | 0.04 | 0.06 | 0.07 |
 25 | 500 | \(-\)0.06 | 0.00 | \(-\)0.03 | 0.07 | 0.04 | 0.04 | 0.08 | 0.03 | 0.04 | 0.14 |
 25 | 1000 | \(-\)0.05 | 0.00 | \(-\)0.03 | 0.05 | 0.02 | 0.03 | 0.06 | 0.02 | 0.03 | 0.26 |
 25 | 2500 | \(-\)0.05 | 0.00 | \(-\)0.03 | 0.03 | 0.01 | 0.01 | 0.06 | 0.01 | 0.03 | 0.59 |