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Table 1 Simulation results for n = 500

From: Latent class distributional regression for the estimation of non-linear reference limits from contaminated data sources

\(\alpha _1\)

c

LCDR

GOLD

NAIVE

Integrated error

0.6

20

− 0.185

(2.837)

− 0.160

(0.942)

26.60

(1.223)

15

− 0.318

(3.365)

− 0.172

(0.936)

19.33

(1.160)

10

− 0.924

(3.753)

− 0.169

(0.945)

12.81

(1.087)

5

− 1.997

(3.897)

− 0.179

(0.936)

7.410

(0.980)

0.7

20

− 0.496

(2.528)

− 0.110

(0.863)

21.86

(1.225)

15

− 0.711

(2.885)

− 0.106

(0.859)

15.66

(1.146)

10

− 1.596

(3.297)

− 0.090

(0.858)

10.19

(1.058)

5

− 2.895

(3.810)

− 0.103

(0.858)

5.760

(0.958)

0.8

20

− 0.563

(2.168)

− 0.082

(0.821)

16.18

(1.205)

15

− 0.991

(2.459)

− 0.089

(0.824)

11.40

(1.129)

10

− 2.112

(2.943)

− 0.064

(0.825)

7.243

(1.030)

5

− 3.599

(3.645)

− 0.062

(0.825)

3.967

(0.921)

Integrated squared error

0.6

20

17.05

(17.81)

3.792

(2.770)

747.43

(74.07)

15

22.15

(26.54)

3.804

(2.788)

397.42

(50.93)

10

28.59

(39.72)

3.843

(2.799)

177.19

(31.74)

5

42.32

(57.01)

3.788

(2.759)

61.99

(16.77)

0.7

20

13.06

(11.57)

3.253

(2.325)

509.10

(61.96)

15

16.31

(17.00)

3.250

(2.330)

264.13

(41.33)

10

23.82

(29.69)

3.258

(2.352)

114.47

(24.89)

5

41.57

(56.00)

3.238

(2.310)

39.07

(13.05)

0.8

20

9.919

(8.52)

2.869

(2.154)

284.09

(45.34)

15

13.16

(12.49)

2.883

(2.183)

143.68

(29.81)

10

21.86

(26.45)

2.883

(2.168)

60.38

(17.29)

5

45.80

(58.75)

2.880

(2.176)

20.39

(8.814)

  1. Reported are the means and standard deviations of the integrated error and the integrated squared error over all simulation runs for latent class distributional regression (LCDR), “gold standard” (GOLD) and “naive” fit (NAIVE)