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Table 4 Bias on the variance of the δ j 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

-0.05/-0.07

-0.05/-0.07

-0.06/-0.08

-0.09/-0.10

-0.09/-0.10

-0.09/-0.11

-0.10/-0.12

-0.10/-0.11

-0.09/-0.09

PMS-R

-0.08/-0.08

-0.08/-0.08

-0.08/-0.08

-0.13/-0.13

-0.13/-0.13

-0.13/-0.13

-0.16/-0.15

-0.15/-0.14

-0.15/-0.13

IMS

0.20/0.21

0.20/0.21

0.20/0.20

0.37/0.41

0.38/0.39

0.40/0.39

0.47/0.56

0.49/0.53

0.55/0.54

IMS-R

-0.03/-0.03

-0.03/-0.03

-0.03/-0.03

-0.05/-0.05

-0.05/-0.05

-0.04/-0.05

-0.06/-0.07

-0.06/-0.07

-0.03/-0.06

CIM

0.10/0.13

0.10/0.13

0.09/0.12

0.20/0.27

0.20/0.25

0.18/0.23

0.28/0.39

0.26/0.36

0.24/0.31

CIM-R

0.03/-0.03

0.02/-0.03

0.02/-0.02

0.05/0.06

0.05/0.05

0.03/0.03

0.07/0.07

0.06/0.06

0.06/0.04

ICS

-0.06/-0.06

-0.06/-0.06

-0.06/-0.06

-0.10/-0.09

-0.09/-0.09

-0.10/-0.09

-0.11/-0.11

-0.11/-0.10

-0.11/-0.10

LOG

0.16/0.16

0.16/0.16

0.16/0.15

0.28/0.31

0.29/0.29

0.30/0.28

0.38/0.43

0.40/0.40

0.44/0.37

LOG-R

-0.00/-0.00

-0.00/-0.00

-0.00/-0.00

-0.02/-0.01

-0.01/-0.02

-0.01/-0.02

-0.03/-0.03

-0.02/-0.03

0.00/-0.03

MOK

0.16/0.16

0.16/0.16

0.16/0.16

0.30/0.32

0.31/0.31

0.31/0.30

0.40/0.43

0.41/0.42

0.43/0.40

RAS

-0.22/-0.21

-0.23/-0.22

-0.22/-0.21

-0.34/-0.31

-0.34/-0.31

-0.34/-0.30

-0.39/-0.33

-0.39/-0.32

-0.40/-0.30

RAS-R

-0.18/-0.18

-0.18/-0.17

-0.18/-0.17

-0.28/-0.26

-0.28/-0.26

-0.28/-0.25

-0.33/-0.30

-0.32/-0.29

-0.32/-0.27

RAI

-0.22/-0.21

-0.22/-0.21

-0.22/-0.22

-0.19/-0.23

-0.19/-0.22

-0.20/-0.22

-0.19/-0.21

-0.19/-0.21

-0.20/-0.19

WORST

-0.01/0.08

-0.01/0.07

-0.01/0.08

0.11/0.26

0.09/0.25

0.06/0.22

0.20/0.43

0.13/0.37

0.06/0.30

NOIMP

0.00/0.00

0.00/0.00

0.00/0.00

0.00/0.00

0.01/0.01

0.01/0.00

0.01/0.00

0.01/0.00

0.03/0.00

LD

0.00/0.00

0.02/0.02

0.09/0.08

0.00/0.00

0.09/0.08

0.42/0.37

0.01/0.02

0.21/0.19

0.98/0.92

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