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Table 3 Specification tests for various estimators

From: A review of statistical estimators for risk-adjusted length of stay: analysis of the Australian and new Zealand intensive care adult patient data-base, 2008–2009

  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)
  1. LP, linear predictor. @, standardised residuals [13]. #, Deviance residuals [68].