Table 3 Parameter estimates and 95% credibility intervals for longitudinal submodels under the joint modeling analysis (2)

Intercept (\(\beta _0\))

10.321

10.215

10.423

0.000

10.316

10.211

10.419

0.000

10.318

10.216

10.421

0.000

Spline\(_1\) (\(\beta _1\))

− 2.163

− 2.220

− 2.101

0.000

− 2.160

− 2.218

− 2.106

0.000

− 2.161

− 2.218

− 2.105

0.000

Spline\(_2\) (\(\beta _2\))

− 2.685

− 2.748

− 2.616

0.000

− 2.682

− 2.748

− 2.618

0.000

− 2.685

− 2.750

− 2.617

0.000

Spline\(_3\) (\(\beta _3\))

− 2.424

− 2.473

− 2.373

0.000

− 2.422

− 2.470

− 2.374

0.000

− 2.423

− 2.471

− 2.373

0.000

MHT\(_1\) \(\times\) Spline\(_1\) (\(\beta _4\))

0.302

0.183

0.419

0.000

0.301

0.189

0.412

0.000

0.293

0.181

0.410

0.000

MHT\(_1\) \(\times\) Spline\(_2\) (\(\beta _5\))

0.088

− 0.050

0.224

0.193

0.085

− 0.050

0.216

0.211

0.076

− 0.057

0.210

0.266

MHT\(_1\) \(\times\) Spline\(_3\) (\(\beta _6\))

0.229

0.124

0.332

0.000

0.231

0.129

0.330

0.000

0.223

0.121

0.328

0.000

MHT\(_2\) \(\times\) Spline\(_1\) (\(\beta _7\))

0.643

0.449

0.829

0.000

0.642

0.449

0.842

0.000

0.654

0.451

0.855

0.000

MHT\(_2\) \(\times\) Spline\(_2\) (\(\beta _8\))

0.253

0.024

0.479

0.033

0.252

0.023

0.483

0.029

0.265

0.027

0.492

0.025

MHT\(_2\) \(\times\) Spline\(_3\) (\(\beta _9\))

0.514

0.339

0.683

0.000

0.514

0.340

0.693

0.000

0.526

0.350

0.705

0.000

MP\(_1\) \(\times\) Spline\(_1\) (\(\beta _{10}\))

0.916

0.836

1.002

0.000

0.918

0.837

0.995

0.000

0.916

0.839

0.993

0.000

MP\(_1\) \(\times\) Spline\(_2\) (\(\beta _{11}\))

0.854

0.759

0.956

0.000

0.853

0.760

0.947

0.000

0.853

0.758

0.948

0.000

MP\(_1\) \(\times\) Spline\(_3\) (\(\beta _{12}\))

0.980

0.907

1.054

0.000

0.981

0.912

1.051

0.000

0.979

0.910

1.047

0.000

BMI (\(\delta _1\))

− 0.179

− 0.183

− 0.175

0.000

− 0.179

− 0.183

− 0.175

0.000

− 0.179

− 0.183

− 0.175

0.000

MHT\(_1\) (\(\delta _2\))

− 0.035

− 0.116

0.042

0.395

− 0.036

− 0.117

0.047

0.388

− 0.029

− 0.117

0.053

0.505

MHT\(_2\) (\(\delta _3\))

0.174

0.038

0.318

0.012

0.177

0.040

0.310

0.013

0.167

0.029

0.306

0.013

MP\(_1\) (\(\delta _4\))

− 0.508

− 0.560

− 0.457

0.000

− 0.510

− 0.561

− 0.457

0.000

− 0.509

− 0.558

− 0.457

0.000

\(\sigma\)

0.547

0.539

0.554

0.000

0.546

0.539

0.554

0.000

0.547

0.539

0.554

0.000

D[1, 1]

3.873

3.474

4.249

0.000

3.896

3.500

4.281

0.000

3.874

3.475

4.258

0.000

D[2, 1]

− 3.435

− 3.788

− 3.096

0.000

− 3.432

− 3.782

− 3.093

0.000

− 3.374

− 3.725

− 3.018

0.000

D[3, 1]

− 4.088

− 4.628

− 3.551

0.000

− 4.109

− 4.653

− 3.558

0.000

− 4.073

− 4.627

− 3.501

0.000

D[4, 1]

− 3.652

− 4.003

− 3.297

0.000

− 3.627

− 3.974

− 3.266

0.000

− 3.613

− 3.945

− 3.257

0.000

D[2, 2]

9.195

8.219

10.142

0.000

9.210

8.245

10.149

0.000

9.139

8.078

10.193

0.000

D[3, 2]

8.287

7.642

8.952

0.000

8.260

7.630

8.910

0.000

8.158

7.512

8.816

0.000

D[4, 2]

7.120

6.373

7.859

0.000

7.141

6.379

7.871

0.000

7.093

6.308

7.884

0.000

D[3, 3]

12.147

10.781

13.515

0.000

12.147

10.749

13.486

0.000

12.109

10.646

13.510

0.000

D[4, 3]

6.486

6.027

6.964

0.000

6.436

5.953

6.920

0.000

6.421

5.938

6.906

0.000

D[4, 4]

7.077

6.321

7.822

0.000

7.085

6.326

7.845

0.000

7.054

6.295

7.783

0.000