Table 4.
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 longitudinal scenario using Poisson and negative binomial GLMM.
| σp | Outlier Dependent Poisson GLMM |
Zero Inflation Poisson GLMM |
||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
β1 = 0.01 |
β1 = 0.41 |
β1 = 0.92 |
β1 = 0.01 |
β1 = 0.41 |
β1 = 0.92 |
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| Type I (%) | Coverage (%) | Type II (%) | Coverage (%) | Type II (%) | Coverage (%) | Type I (%) | Coverage (%) | Type II (%) | Coverage (%) | Type II (%) | Coverage (%) | |
| 1.0 | 3.50 | 98.00 | 0.00 | 97.50 | 0.00 | 98.00 | 3.50 | 98.00 | 0.00 | 97.50 | 0.00 | 98.00 |
| 1.2 | 7.00 | 94.00 | 0.00 | 93.50 | 0.00 | 89.00 | 3.50 | 96.00 | 0.00 | 93.00 | 0.00 | 90.00 |
| 1.3 | 9.00 | 95.00 | 0.00 | 85.50 | 0.00 | 85.50 | 10.50 | 90.00 | 0.00 | 93.50 | 0.00 | 90.00 |
| 1.4 | 8.50 | 92.00 | 0.00 | 88.00 | 0.00 | 81.50 | 6.00 | 94.50 | 0.00 | 86.50 | 0.00 | 88.50 |
| 1.5 | 14.00 | 86.00 | 0.00 | 85.50 | 0.00 | 77.50 | 7.00 | 93.50 | 0.00 | 86.50 | 0.00 | 89.00 |
| 2.0 | 25.50 | 77.00 | 0.00 | 73.00 | 0.00 | 55.00 | 15.00 | 84.50 | 0.00 | 84.00 | 0.00 | 80.50 |
| 2.5 | 31.50 | 70.00 | 0.00 | 61.00 | 0.00 | 46.50 | 27.00 | 72.50 | 0.00 | 68.00 | 0.00 | 75.50 |
| 5.0 | 63.50 | 38.50 | 2.50 | 38.00 | 0.00 | 27.00 | 38.50 | 62.00 | 8.00 | 66.00 | 0.00 | 56.50 |
| 10.0 | 86.00 | 15.00 | 12.00 | 18.50 | 0.50 | 15.50 | — | — | — | — | — | — |
| 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 | 3.55 | 98.82 | 0.00 | 100.00 | 0.00 | 97.48 | 3.55 | 98.82 | 0.00 | 100.00 | 0.00 | 97.48 |
| 1.2 | 4.02 | 95.98 | 0.00 | 94.44 | 0.00 | 90.86 | 3.00 | 97.50 | 0.00 | 96.00 | 0.00 | 92.46 |
| 1.3 | 5.00 | 95.50 | 0.00 | 90.95 | 0.00 | 88.38 | 3.50 | 97.00 | 0.00 | 97.50 | 0.00 | 96.00 |
| 1.4 | 4.50 | 95.50 | 0.00 | 90.95 | 0.00 | 86.00 | 1.00 | 99.50 | 0.00 | 97.00 | 0.00 | 97.50 |
| 1.5 | 5.00 | 94.00 | 0.00 | 92.00 | 0.00 | 86.00 | 1.50 | 99.00 | 0.00 | 94.50 | 0.00 | 98.50 |
| 2.0 | 9.00 | 91.50 | 0.00 | 90.50 | 0.00 | 71.00 | 1.50 | 99.50 | 0.00 | 99.00 | 0.00 | 99.50 |
| 2.5 | 9.50 | 91.00 | 0.00 | 86.50 | 0.00 | 67.00 | 1.00 | 99.50 | 3.50 | 98.50 | 0.00 | 99.50 |
| 5.0 | 19.00 | 83.00 | 0.50 | 81.50 | 0.00 | 72.50 | 0.00 | 100.00 | 75.00 | 99.50 | 0.00 | 100.00 |
| 10.0 | 18.50 | 83.00 | 3.50 | 86.50 | 0.00 | 81.00 | — | — | — | — | — | — |
σp is defined as the ratio of the Pearson χ2 to its degrees of freedom