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Table 2 Simulation results from probability estimation for Y, where Y is generated using a logit link function with five covariates, δ is generated using a logit link function with extreme missingness probabilities (M2) based on five covariates, N = 400

From: A nonparametric multiple imputation approach for missing categorical data

 

Pr(Y=1)=0.386

Pr(Y=2)=0.288

Method

Est

SD

SE

CR

Est

SD

SE

CR

FO

0.386

0.023

0.024

0.960

0.286

0.023

0.023

0.934

CC

0.425

0.031

0.033

0.802

0.374

0.033

0.033

0.250

 

Working models for Y:

Five covariates with logit link

 

Working models for δ:

Five covariates with logit link

CE

0.378

0.102

0.080

0.946

0.288

0.108

0.076

0.902

PMI

0.385

0.034

0.036

0.950

0.288

0.036

0.033

0.922

NNMI MLR (5,0.4,0.4;0.2)

0.389

0.039

0.040

0.946

0.297

0.043

0.040

0.906

NNMI MLR (5,0.1,0.7;0.2)

0.399

0.042

0.045

0.942

0.292

0.041

0.039

0.918

NNMI MLR (5,0.7,0.1;0.2)

0.385

0.038

0.039

0.936

0.302

0.044

0.042

0.916

NNMI CLR (5,0.4,0.4;0.2)

0.384

0.037

0.038

0.938

0.304

0.042

0.040

0.918

NNMI CLR (5,0.1,0.7;0.2)

0.372

0.038

0.039

0.926

0.307

0.043

0.042

0.918

NNMI CLR (5,0.7,0.1;0.2)

0.395

0.038

0.039

0.944

0.305

0.043

0.041

0.908

 

Working models for Y:

Three covariates with logit link

  

(misspecified scenario 1)

 

Working models for δ:

Five covariates with logit link

CE

0.302

0.234

0.184

0.946

0.287

0.117

0.084

0.910

PMI

0.495

0.039

0.042

0.258

0.288

0.032

0.031

0.932

NNMI MLR (5,0.4,0.4;0.2)

0.436

0.051

0.053

0.852

0.295

0.042

0.040

0.914

NNMI MLR (5,0.1,0.7;0.2)

0.431

0.052

0.054

0.878

0.293

0.041

0.040

0.932

NNMI MLR (5,0.7,0.1;0.2)

0.433

0.050

0.053

0.858

0.296

0.042

0.041

0.924

NNMI CLR (5,0.4,0.4;0.2)

0.440

0.047

0.049

0.806

0.297

0.040

0.039

0.924

NNMI CLR (5,0.1,0.7;0.2)

0.429

0.046

0.048

0.852

0.299

0.042

0.039

0.926

NNMI CLR (5,0.7,0.1;0.2)

0.441

0.050

0.051

0.806

0.297

0.041

0.040

0.920

 

Working models for Y:

Five covariates with logit link

 

Working models for δ:

Three covariates with logit link

  

(misspecified scenario 2)

CE

0.386

0.050

0.048

0.960

0.286

0.043

0.040

0.894

PMI

0.385

0.034

0.036

0.950

0.288

0.036

0.033

0.922

NNMI MLR (5,0.4,0.4;0.2)

0.398

0.038

0.040

0.952

0.301

0.041

0.039

0.906

NNMI MLR (5,0.1,0.7;0.2)

0.426

0.042

0.045

0.858

0.294

0.039

0.037

0.922

NNMI MLR (5,0.7,0.1;0.2)

0.392

0.037

0.038

0.942

0.312

0.043

0.040

0.882

NNMI CLR (5,0.4,0.4;0.2)

0.390

0.035

0.038

0.954

0.307

0.040

0.039

0.912

NNMI CLR (5,0.1,0.7;0.2)

0.377

0.037

0.039

0.940

0.307

0.041

0.040

0.924

NNMI CLR (5,0.7,0.1;0.2)

0.401

0.036

0.037

0.938

0.313

0.041

0.039

0.912

  1. Est: Estimates of probabilities; SD: Empirical standard deviation; SE: Estimate of standard error; CR: Coverage rate of 95% confidence intervals; FO: fully observed; CC: Complete Cases; CE: Calibration estimator; PMI: Parametric Multiple Imputation; NNMI MLR (NN,ω 1,ω 2;ω 3): the NNMI method using Multinomial Logistic Regressions, NN is the number of nearest neighbors and weights are ω 1,ω 2, and ω 3; NNMI CLR : the NNMI method using Cumulative Logistic Regressions; K = 10 imputed datasets are used for PMI and NNMI methods