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Table 3 Bias on the v parameter 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 -0.04/-0.08 -0.04/-0.08 -0.03/-0.07 -0.04/-0.13 -0.04/-0.13 -0.05/-0.14 -0.05/-0.15 -0.08/-0.18 -0.11/-0.22
PMS-R 0.00/-0.03 -0.00/-0.03 -0.00/-0.03 0.00/-0.06 -0.00/-0.07 -0.03/-0.09 -0.00/-0.09 -0.03/-0.12 -0.07/-0.16
IMS 0.00/0.04 -0.03/0.02 -0.05/-0.00 0.00/0.08 -0.05/0.04 -0.12/-0.03 -0.00/0.13 -0.09/0.04 -0.19/-0.06
IMS-R 0.00/0.00 -0.02/-0.02 -0.04/-0.04 0.00/-0.00 -0.03/-0.03 -0.08/-0.08 -0.00/0.00 -0.06/-0.05 -0.13/-0.13
CIM 0.04/0.04 0.03/0.03 0.04/0.04 0.06/0.06 0.06/0.06 0.04/0.04 0.07/0.09 0.03/0.05 -0.00/0.00
CIM-R 0.02/0.04 0.01/0.03 0.01/0.04 0.03/0.01 0.01/0.00 0.01/-0.02 0.03/0.02 -0.01/-0.02 -0.05/-0.07
ICS 0.00/-0.02 -0.00/-0.03 -0.00/-0.03 0.00/-0.06 -0.01/-0.05 -0.03/-0.07 -0.00/-0.06 -0.03/-0.10 -0.07/-0.14
LOG 0.00/0.03 -0.02/0.01 -0.03/-0.01 0.00/0.05 -0.04/0.01 -0.11/-0.05 -0.00/0.09 -0.08/0.01 -0.19/-0.10
LOG-R 0.00/-0.00 -0.02/-0.01 -0.03/-0.03 0.00/-0.00 -0.03/-0.03 -0.08/-0.08 -0.00/0.00 -0.06/-0.06 -0.14/-0.13
MOK -0.01/0.01 -0.02/0.00 -0.03/-0.00 -0.02/0.02 -0.04/0.01 -0.08/-0.02 -0.03/0.05 -0.08/0.00 -0.13/-0.05
RAS 0.00/-0.06 -0.00/-0.06 0.01/-0.06 0.00/-0.12 -0.00/-0.11 -0.00/-0.12 -0.00/-0.17 -0.01/-0.18 -0.02/-0.20
RAS-R 0.00/-0.04 -0.01/-0.05 -0.01/-0.05 0.00/-0.08 0.01/-0.09 -0.03/-0.11 -0.00/-0.12 -0.03/-0.14 -0.06/-0.17
RAI 0.00/-0.06 -0.00/-0.06 0.00/-0.06 0.00/-0.06 0.00/-0.06 -0.00/-0.07 -0.00/-0.08 -0.02/-0.11 -0.05/-0.15
WORST 0.23/0.23 0.22/0.20 0.21/0.19 0.38/0.36 0.36/0.34 0.33/0.31 0.45/0.44 0.41/0.40 0.36/0.35
NOIMP 0.00/0.00 -0.01/-0.01 -0.02/-0.02 0.00/-0.00 -0.02/-0.02 -0.06/-0.06 -0.00/0.00 -0.05/-0.04 -0.11/-0.11
LD 0.00/-0.00 -0.10/-0.08 -0.21/-0.19 0.00/-0.00 -0.20/-0.19 -0.45/-0.42 -0.00/-0.00 -0.31/-0.29 -0.70/-0.67
FC 0.00/-0.00 0.00/-0.00 -0.00/0.00 -0.00/-0.00 -0.00/0.00 0.00/0.00 -0.00/0.00 -0.00/0.00 0.00/0.00