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Table 5 Bias on the σ 2 parameters as a function of the rate of missing data per item (π), the value of the correlation coefficient ρ between the latent variable Θ and the propensity to have missing data ξ for each method for handling missing data (results for w = 0/w = 1)

From: Imputation by the mean score should be avoided when validating a Patient Reported Outcomes questionnaire by a Rasch model in presence of informative missing data

  π= 10% π= 20% π= 30%
Method ρ= 0.0 ρ= -0.4 ρ= -0.9 ρ= 0.0 ρ= -0.4 ρ= -0.9 ρ= 0.0 ρ= -0.4 ρ= -0.9
PMS 0.61/0.58 0.61/0.58 0.62/0.57 1.27/1.14 1.27/1.14 1.26/1.11 1.64/1.58 1.59/1.57 1.56/1.50
PMS-R 0.34/0.35 0.34/0.35 0.34/0.34 0.62/0.64 0.62/0.62 0.61/0.62 0.85/0.86 0.82/0.86 0.79/0.81
IMS -0.15/-0.14 -0.15/-0.15 -0.15/-0.16 -0.24/-0.24 -0.24/-0.24 -0.27/-0.27 -0.28/-0.29 -0.30/-0.29 -0.34/-0.32
IMS-R -0.23/-0.22 -0.23/-0.23 -0.22/-0.23 -0.38/-0.38 -0.37/-0.38 -0.38/-0.39 -0.45/-0.47 -0.46/-0.46 -0.46/-0.48
CIM 0.59/0.57 0.60/0.58 0.62/0.58 1.15/1.09 1.17/1.13 1.20/1.14 1.54/1.48 1.55/1.56 1.55/1.60
CIM-R 0.32/0.28 0.33/0.29 0.35/0.30 0.59/0.50 0.61/0.52 0.62/0.52 0.80/0.64 0.78/0.66 0.78/0.65
ICS 0.32/0.33 0.32/0.33 0.33/0.33 0.57/0.59 0.57/0.61 0.56/0.57 0.76/0.77 0.74/0.78 0.71/0.74
LOG 0.19/0.20 0.19/0.20 0.18/0.18 0.22/0.22 0.22/0.24 0.16/0.19 0.18/0.16 0.13/0.18 0.02/0.07
LOG-R -0.03/-0.13 -0.03/-0.03 -0.03/-0.04 -0.12/-0.12 -0.13/-0.12 -0.15/-0.15 -0.20/-0.23 -0.22/-0.22 -0.27/-0.29
MOK 0.30/0.31 0.30/0.31 0.30/0.29 0.54/0.56 0.55/0.57 0.54/0.55 0.75/0.74 0.72/0.76 0.69/0.73
RAS 0.26/0.28 0.26/0.28 0.28/0.27 0.49/0.50 0.49/0.53 0.49/0.53 0.65/0.67 0.62/0.70 0.60/0.70
RAS-R 0.04/0.05 0.04/0.05 0.05/0.04 0.06/0.07 0.07/0.09 0.07/0.09 0.10/0.09 0.08/0.10 0.07/0.09
RAI 0.29/0.31 0.29/0.31 0.30/0.30 1.12/0.92 1.12/0.95 1.11/0.95 1.53/1.40 1.49/1.42 1.46/1.41
WORST -0.25/-0.21 -0.16/-0.13 -0.04/-0.03 -0.42/-0.27 -0.30/-0.25 -0.15/-0.11 -0.50/-0.47 -0.42/-0.36 -0.28/-0.14
NOIMP 0.01/0.02 0.01/0.02 0.02/0.02 0.00/0.01 0.01/0.02 0.00/-0.00 0.02/0.00 -0.00/0.01 -0.01/-0.01
LD 0.01/0.02 0.02/0.02 -0.00/-0.01 0.02/0.02 0.01/0.02 -0.05/-0.04 0.03/0.03 -0.02/0.02 -0.14/-0.12
FC 0.01/0.01 0.01/0.01 0.02/0.01 0.00/0.00 0.01/0.02 0.01/0.01 0.01/0.00 0.00/0.01 0.01/0.01