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Table 1 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 not extreme missingness probabilities (M1) 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

0.439

0.034

0.035

0.674

0.340

0.034

0.033

0.670

 

Working models for Y:

Five covariates with logit link

 

Working models for δ:

Five covariates with logit link

CE

0.388

0.036

0.036

0.948

0.286

0.038

0.036

0.924

PMI

0.387

0.030

0.032

0.954

0.287

0.034

0.032

0.930

NNMI MLR (5,0.4,0.4;0.2)

0.387

0.032

0.033

0.952

0.288

0.036

0.033

0.936

NNMI MLR (5,0.1,0.7;0.2)

0.389

0.033

0.034

0.956

0.288

0.035

0.033

0.930

NNMI MLR (5,0.7,0.1;0.2)

0.386

0.032

0.033

0.956

0.290

0.036

0.034

0.926

NNMI CLR (5,0.4,0.4;0.2)

0.385

0.032

0.033

0.948

0.294

0.036

0.034

0.916

NNMI CLR (5,0.1,0.7;0.2)

0.381

0.032

0.033

0.944

0.295

0.037

0.034

0.928

NNMI CLR (5,0.7,0.1;0.2)

0.390

0.032

0.033

0.950

0.294

0.037

0.034

0.936

 

Working models for Y:

Three covariates with logit link

  

(misspecified scenario 1)

 

Working models for δ:

Five covariates with logit link

CE

0.311

0.057

0.057

0.760

0.288

0.041

0.041

0.932

PMI

0.464

0.037

0.038

0.454

0.285

0.032

0.031

0.922

NNMI MLR (5,0.4,0.4;0.2)

0.410

0.036

0.039

0.932

0.290

0.035

0.033

0.926

NNMI MLR (5,0.1,0.7;0.2)

0.407

0.036

0.039

0.940

0.290

0.035

0.033

0.932

NNMI MLR (5,0.7,0.1;0.2)

0.408

0.035

0.039

0.930

0.291

0.035

0.033

0.928

NNMI CLR (5,0.4,0.4;0.2)

0.415

0.036

0.038

0.896

0.292

0.034

0.033

0.940

NNMI CLR (5,0.1,0.7;0.2)

0.412

0.036

0.039

0.916

0.292

0.035

0.033

0.934

NNMI CLR (5,0.7,0.1;0.2)

0.413

0.035

0.039

0.926

0.291

0.035

0.034

0.954

 

Working models for Y:

Five covariates with logit link

 

Working models for δ:

Three covariates with logit link

  

(misspecified scenario 2)

CE

0.389

0.032

0.033

0.954

0.285

0.033

0.032

0.942

PMI

0.387

0.030

0.032

0.954

0.287

0.034

0.032

0.930

NNMI MLR (5,0.4,0.4;0.2)

0.393

0.032

0.033

0.962

0.292

0.035

0.033

0.936

NNMI MLR (5,0.1,0.7;0.2)

0.402

0.034

0.035

0.936

0.289

0.035

0.033

0.926

NNMI MLR (5,0.7,0.1;0.2)

0.389

0.031

0.033

0.960

0.297

0.036

0.034

0.936

NNMI CLR (5,0.4,0.4;0.2)

0.387

0.031

0.032

0.958

0.298

0.035

0.033

0.936

NNMI CLR (5,0.1,0.7;0.2)

0.382

0.031

0.033

0.956

0.298

0.035

0.034

0.940

NNMI CLR (5,0.7,0.1;0.2)

0.392

0.031

0.033

0.954

0.302

0.035

0.034

0.920

  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