Table 3 Specification tests for various estimators
Correlation | Residuals | Hosmer-Lemeshow (F) test | Copas test | |||
|---|---|---|---|---|---|---|
LP vs residuals | Skewness | Kurtosis | Determination | Validation | ||
OLS raw scale @ | 1.00 | 4.33 | 32.74 | 0.0001 | 0.0001 | 0.996(0.993, 0.998) |
OLS log scale @ | 0.03 | 0.25 | 3.58 | 0.0001 | 0.0001 | 1.079(1.063, 1.094) |
LMM log scale @ | 0.008 | 0.25 | 3.76 | 0.0001 | 0.0001 | 1.054(1.036, 1.072) |
Treatment effects model: log scale | 0.150 | 0.27 | 3.58 | 0.0001 | 0.0001 | 1.043(1.025, 1.062) |
GLM: family(Poisson), link(log) # | 0.0001 | 2.37 | 13.41 | 0.0001 | 0.0001 | 0.940(0.899, 0.981) |
GLM: family(negative binomial), link(log) # | 0.0001 | 1.59 | 8.14 | 0.0001 | 0.0001 | 0.967(0.926, 1.008) |
GLM: family(gamma), link(log) # | 0.0001 | 1.26 | 6.60 | 0.0001 | 0.0001 | 0.923(0.882, 0.965) |
GLM: family(inverse Gaussian), link(log) # | 0.0002 | 0.20 | 4.98 | 0.0001 | 0.0001 | 0.776(0.717, 0.835) |
EEE: raw scale | 0.002 | 4.25 | 32.44 | 0.0001 | 0.002 | 0.956(0.957,0.958) |
Skew- t regression: log scale | 0.0001 | 0.31 | 3.59 | 0.0001 | 0.0001 | 1.085(1.065, 1.105) |
Skew normal regression: log scale | 0.0001 | 0.32 | 3.56 | 0.0001 | 0.0001 | 1.134 (1.113, 1.155 |
FMM: raw scale | 0.0001 | 4.68 | 33.70 | 0.0001 | 0.0001 | 0.795(0.737, 0.852) |