Table 3.
Percentage of simulations with Χ1 Type I and II errors and in which parameter coverage included the true parameter given true values of 0.01, 0.41, and 0.92 for the cross-sectional scenario using the negative binomial regression model and negative binomial GLMM.
| σp | Outlier Dependent Negative Binomial |
Zero Inflation Negative Binomial |
||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
β1 = 0.01 |
β1 = 0.41 |
β1 = 0.92 |
β1 = 0.01 |
β1 = 0.41 |
β1 = 0.92 |
|||||||
| Type I (%) | Coverage (%) | Type II (%) | Coverage (%) | Type II (%) | Coverage (%) | Type I (%) | Coverage (%) | Type II (%) | Coverage (%) | Type II (%) | Coverage (%) | |
| 1.0 | 3.00 | 95.50 | 0.50 | 93.00 | 0.00 | 91.50 | 3.00 | 95.50 | 0.50 | 93.00 | 0.00 | 91.50 |
| 1.2 | 3.50 | 95.00 | 3.00 | 90.00 | 0.00 | 82.00 | 3.50 | 96.50 | 4.50 | 92.50 | 0.00 | 94.00 |
| 1.3 | 3.00 | 97.50 | 3.50 | 91.00 | 0.00 | 79.00 | 5.00 | 94.50 | 5.50 | 93.00 | 0.00 | 92.50 |
| 1.4 | 6.00 | 93.00 | 3.00 | 89.50 | 0.00 | 80.50 | 6.00 | 94.50 | 8.50 | 96.00 | 0.00 | 93.50 |
| 1.5 | 7.00 | 94.50 | 5.50 | 90.50 | 0.00 | 77.50 | 5.00 | 94.00 | 10.00 | 95.00 | 0.00 | 93.50 |
| 2.0 | 6.00 | 94.00 | 17.50 | 85.50 | 0.00 | 73.00 | 3.00 | 97.50 | 33.50 | 97.50 | 0.00 | 96.00 |
| 2.5 | 7.50 | 93.50 | 24.00 | 85.00 | 0.00 | 67.50 | 2.00 | 98.50 | 60.50 | 99.00 | 0.00 | 95.00 |
| 5.0 | 15.50 | 84.00 | 46.50 | 80.50 | 0.00 | 59.00 | 5.00 | 95.00 | 93.00 | 97.50 | 34.50 | 98.50 |
| 10.0 | 22.50 | 78.00 | 61.00 | 77.50 | 11.00 | 54.50 | — | — | — | — | — | — |
| σp | Negative Binomial GLMM |
Negative Binomial GLMM |
||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
β1 = 0.01 |
β1 = 0.41 |
β1 = 0.92 |
β1 = 0.01 |
β1 = 0.41 |
β1 = 0.92 |
|||||||
| Type I (%) | Coverage (%) | Type II (%) | Coverage (%) | Type II (%) | Coverage (%) | Type I (%) | Coverage (%) | Type II (%) | Coverage (%) | Type II (%) | Coverage (%) | |
| 1.0 | 0.52 | 99.48 | 7.33 | 97.38 | 0.00 | 96.88 | 0.52 | 99.48 | 7.33 | 97.38 | 0.00 | 96.88 |
| 1.2 | 0.51 | 99.49 | 8.59 | 96.46 | 0.00 | 91.96 | 1.52 | 98.99 | 11.00 | 96.00 | 0.00 | 97.47 |
| 1.3 | 0.50 | 99.50 | 12.63 | 95.96 | 0.00 | 91.96 | 1.02 | 97.46 | 12.56 | 98.49 | 0.00 | 97.50 |
| 1.4 | 2.00 | 98.00 | 13.50 | 98.50 | 0.00 | 89.95 | 3.02 | 97.49 | 13.00 | 95.50 | 0.00 | 96.97 |
| 1.5 | 0.50 | 99.50 | 21.00 | 96.00 | 0.00 | 86.93 | 0.50 | 99.50 | 19.00 | 98.50 | 0.00 | 96.00 |
| 2.0 | 2.00 | 98.00 | 30.50 | 93.50 | 0.00 | 84.50 | 2.00 | 99.00 | 43.00 | 96.50 | 0.00 | 97.50 |
| 2.5 | 1.00 | 98.50 | 38.50 | 92.00 | 0.00 | 80.00 | 2.00 | 98.50 | 59.50 | 98.00 | 0.00 | 96.00 |
| 5.0 | 7.50 | 93.00 | 62.00 | 89.50 | 3.00 | 73.50 | 5.03 | 94.97 | 88.94 | 96.48 | 18.00 | 98.50 |
| 10.0 | 13.50 | 88.00 | 79.00 | 91.00 | 23.00 | 67.50 | — | — | — | — | — | — |
σp is defined as the ratio of the Pearson χ2 to its degrees of freedom