Scenario | Parameter | Negative binomial | Transformed data | ||
---|---|---|---|---|---|
 |  |  | Raw | Natural logarithm | Square root |
1 | PE relative bias% | -10.35 | -16.14 | -5.41 | -5.32 |
 | Variance | 0.0098 | 0.0138 | 0.0145 | 0.0137 |
 | MSE | 0.011 | 0.0168 | 0.0148 | 0.014 |
2 | PE relative bias% | -10.8 | -17.21 | -1.13 | -2.55 |
 | Variance | 0.0108 | 0.0136 | 0.0198 | 0.0183 |
 | MSE | 0.0126 | 0.0181 | 0.0198 | 0.0184 |
3 | PE relative bias% | -5.33 | -7.65 | 8.45 | 12.43 |
 | Variance | 0.0052 | 0.0118 | 0.0115 | 0.012 |
 | MSE | 0.0056 | 0.0126 | 0.0124 | 0.014 |
4 | PE relative bias% | -9.3 | -16.93 | 9.75 | 9.7 |
 | Variance | 0.0067 | 0.0107 | 0.0205 | 0.0152 |
 | MSE | 0.0081 | 0.0153 | 0.022 | 0.0167 |
5 | PE relative bias% | -8.28 | -18.37 | -10.46 | -10.92 |
 | Variance | 0.0114 | 0.0135 | 0.0133 | 0.0136 |
 | MSE | 0.0129 | 0.0207 | 0.0156 | 0.0161 |
6 | PE relative bias% | -19.51 | -30.33 | -21.06 | -22.33 |
 | Variance | 0.0148 | 0.0138 | 0.0162 | 0.0161 |
 | MSE | 0.0254 | 0.0394 | 0.0285 | 0.03 |
7 | PE relative bias% | -8.02 | -14.27 | 0.41 | 2.54 |
 | Variance | 0.0095 | 0.012 | 0.0158 | 0.0122 |
 | MSE | 0.0112 | 0.0172 | 0.0158 | 0.0124 |
8 | PE relative bias% | -5.89 | -15.66 | 9.03 | 7.11 |
 | Variance | 0.009 | 0.0107 | 0.016 | 0.0131 |
 | MSE | 0.01 | 0.0181 | 0.0185 | 0.0146 |
9 | PE relative bias% | 17.53 | 3.26 | 27.01 | 26.74 |
 | Variance | 0.0129 | 0.0105 | 0.0126 | 0.0118 |
 | MSE | 0.0144 | 0.0106 | 0.0162 | 0.0154 |
10 | PE relative bias% | 8.55 | -0.51 | 31.12 | 27.35 |
 | Variance | 0.0165 | 0.0145 | 0.025 | 0.0225 |
 | MSE | 0.017 | 0.0145 | 0.0314 | 0.0275 |
11 | PE relative bias% | 30.36 | 27.17 | 62.05 | 66.58 |
 | Variance | 0.0104 | 0.0134 | 0.0144 | 0.015 |
 | MSE | 0.0154 | 0.0174 | 0.0351 | 0.0388 |
12 | PE relative bias% | 19.56 | 16.28 | 57.01 | 55.29 |
 | Variance | 0.0118 | 0.0157 | 0.0193 | 0.0183 |
 | MSE | 0.0144 | 0.0175 | 0.0416 | 0.0392 |
13 | PE relative bias% | 13.24 | 7.84 | 18.41 | 18.51 |
 | Variance | 0.0213 | 0.0185 | 0.0176 | 0.0183 |
 | MSE | 0.0229 | 0.0191 | 0.0207 | 0.0215 |
14 | PE relative bias% | 7.22 | -2.79 | 17.15 | 15.39 |
 | Variance | 0.0217 | 0.0172 | 0.027 | 0.0255 |
 | MSE | 0.0223 | 0.0173 | 0.0306 | 0.0284 |
15 | PE relative bias% | 28.41 | 23.59 | 45.99 | 48.25 |
 | Variance | 0.0154 | 0.0182 | 0.0178 | 0.0188 |
 | MSE | 0.0236 | 0.0239 | 0.0394 | 0.0425 |
16 | PE relative bias% | 22.69 | 19.99 | 51.97 | 50 |
 | Variance | 0.0216 | 0.0205 | 0.0262 | 0.023 |
 | MSE | 0.0281 | 0.0256 | 0.0604 | 0.0546 |