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Table 4 Simulation results from PLSI mixed-effects model and linear mixed-effects model

From: A family of partial-linear single-index models for analyzing complex environmental exposures with continuous, categorical, time-to-event, and longitudinal health outcomes

Variable

True rank

True coefficient

PLSI ME rank

PLSI ME estimate

PLSI ME 95% CI

PLSI ME Proportion of contribution (%)

Linear ME rank

Linear ME original estimate

Linear ME original 95% CI

Linear ME normed estimate

Linear ME normed 95% CI

Identity link function

 Environmental factors

  a-Tocopherol

1

0.560

1

0.584

(0.469, 0.698)

34.1

1

0.590

(0.456, 0.723)

0.580

(0.519, 0.642)

  g-tocopherol

2

0.490

2

0.481

(0.396, 0.566)

23.1

2

0.490

(0.401, 0.579)

0.482

(0.439, 0.525)

  Retinyl-palmitate

3

0.420

3

0.402

(0.284, 0.520)

16.2

3

0.408

(0.302, 0.513)

0.401

(0.336, 0.467)

  Retinol

7

0.140

7

0.091

(−0.025, 0.206)

0.8

7

0.088

(−0.011, 0.186)

0.086

(0.027, 0.145)

  3,3,4,4,5-pncb

8

0.070

8

0.054

(−0.067, 0.175)

0.3

8

0.058

(−0.047, 0.164)

0.057

(0.000, 0.114)

  PCB194

6

−0.210

6

−0.225

(−0.378, − 0.072)

5.1

6

− 0.236

(− 0.372, − 0.099)

−0.232

(− 0.303, − 0.160)

  2.3.4.6.7.8.hxcdf

5

− 0.280

5

− 0.236

(− 0.344, − 0.128)

5.6

5

−0.241

(− 0.331, − 0.151)

−0.237

(− 0.295, − 0.179)

  trans.b.carotene

4

− 0.350

4

− 0.386

(− 0.475, − 0.297)

14.9

4

−0.392

(− 0.486, − 0.298)

−0.386

(− 0.433, − 0.339)

 Covariates

  Intercept

 

0.000

 

−0.069

(−0.426, 0.287)

  

−0.074

(−0.486, 0.339)

  

  Age

 

0.005

 

0.011

(0.004, 0.019)

  

0.011

(0.005, 0.018)

  

  Sex (female)

 

−0.076

 

−0.121

(− 0.245, 0.003)

  

−0.125

(− 0.302, 0.051)

  

 Race/Ethnicity

  Non-Hispanic white

 

Ref

 

Ref

   

Ref

   

  Non-Hispanic black

 

−0.138

 

−0.225

(−0.368, − 0.082)

  

− 0.231

(− 0.450, − 0.012)

  

  Mexican American

 

0.175

 

0.030

(−0.123, 0.184)

  

0.027

(−0.195, 0.249)

  

  Other race

 

0.409

 

0.086

(−0.231, 0.403)

  

0.081

(−0.395, 0.557)

  

  Other Hispanic

 

0.355

 

0.811

(0.463, 1.158)

  

0.811

(0.322, 1.300)

  

  Time effect

 

1.000

 

0.978

(0.951, 1.005)

  

0.978

(0.947, 1.008)

  

Quadratic link function

 Environmental factors

  a-Tocopherol

1

0.560

1

0.558

(0.500, 0.617)

31.2

1

0.526

(0.288, 0.764)

0.614

(0.565, 0.664)

  g-tocopherol

2

0.490

2

0.499

(0.453, 0.544)

24.9

3

0.333

(0.176, 0.489)

0.389

(0.324, 0.454)

  Retinyl-palmitate

3

0.420

3

0.422

(0.363, 0.482)

17.8

4

0.279

(0.090, 0.467)

0.325

(0.242, 0.409)

  Retinol

7

0.140

7

0.167

(0.108, 0.227)

2.8

8

−0.006

(−0.181, 0.169)

−0.007

(−0.078, 0.064)

  3,3,4,4,5-pncb

8

0.070

8

0.073

(0.024, 0.122)

0.5

6

0.216

(0.027, 0.405)

0.252

(0.164, 0.341)

  PCB194

6

−0.210

6

−0.209

(−0.269, − 0.149)

4.4

2

0.378

(0.137, 0.619)

0.441

(0.352, 0.531)

  2.3.4.6.7.8.hxcdf

5

−0.280

5

−0.268

(−0.327, − 0.209)

7.2

7

− 0.061

(− 0.221, 0.100)

−0.071

(− 0.141, − 0.001)

  trans.b.carotene

4

− 0.350

4

− 0.335

(− 0.388, − 0.283)

11.3

5

−0.273

(− 0.44, − 0.106)

−0.319

(− 0.381, − 0.257)

 Covariates

  Intercept

 

0.000

 

0.877

(0.653, 1.100)

  

2.202

(1.478, 2.925)

  

  Age

 

0.005

 

0.007

(0.004, 0.009)

  

−0.023

(−0.035, −0.011)

  

  Sex (female)

 

−0.076

 

−0.061

(−0.158, 0.036)

  

−0.150

(−0.465, 0.165)

  

 Race/Ethnicity

  Non-Hispanic white

 

Ref

 

Ref

   

Ref

   

  Non-Hispanic black

 

−0.138

 

−0.078

(−0.206, 0.050)

  

−0.004

(−0.395, 0.387)

  

  Mexican American

 

0.175

 

0.219

(0.081, 0.358)

  

0.323

(−0.070, 0.717)

  

  Other race

 

0.409

 

0.642

(0.372, 0.911)

  

0.095

(−0.763, 0.953)

  

  Other Hispanic

 

0.355

 

0.152

(−0.093, 0.397)

  

−0.125

(−0.976, 0.726)

  

  Time effect

 

1.000

 

1.014

(0.987, 1.041)

  

1.013

(0.983, 1.044)

  
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Environmental Health

ISSN: 1476-069X