Table 4 Estimated values of fixed effects and measures of heterogeneity for the two-level logistic regression, under random effects variance values 0.2 and 0.5

\(\mathbf {\sigma ^{2}_{u}=0.2}\)

True values:

0.500

-1.500

0.300

-0.300

0.0570

1.532

0.3176

0.3294

1.667

10

5

0.542

-1.502

0.376

-0.382

0.042

1.417

0.209

0.392

1.334

20

0.488

-1.508

0.300

-0.290

0.056

1.524

0.322

0.337

1.669

50

0.500

-1.503

0.303

-0.285

0.055

1.519

0.323

0.340

1.665

100

0.492

-1.498

0.298

-0.292

0.059

1.541

0.324

0.329

1.699

250

0.507

-1.527

0.290

-0.315

0.054

1.514

0.304

0.333

1.605

50

5

0.539

-1.508

0.320

-0.255

0.067

1.590

0.354

0.322

1.882

20

0.481

-1.461

0.298

-0.290

0.054

1.508

0.312

0.347

1.636

50

0.489

-1.510

0.299

-0.261

0.060

1.546

0.344

0.337

1.763

100

0.528

-1.506

0.302

-0.350

0.061

1.553

0.296

0.306

1.627

250

0.565

-1.487

0.300

-0.328

0.052

1.501

0.293

0.333

1.559

100

5

0.532

-1.511

0.334

-0.343

0.062

1.559

0.299

0.306

1.657

20

0.505

-1.518

0.312

-0.293

0.058

1.534

0.322

0.331

1.683

50

0.505

-1.496

0.297

-0.300

0.057

1.532

0.317

0.329

1.665

100

0.498

-1.503

0.309

-0.284

0.058

1.537

0.328

0.333

1.705

250

0.498

-1.497

0.302

-0.313

0.055

1.517

0.306

0.332

1.614

300

5

0.503

-1.505

0.292

-0.325

0.046

1.461

0.281

0.352

1.485

20

0.498

-1.509

0.296

-0.297

0.056

1.525

0.318

0.333

1.657

50

0.495

-1.499

0.301

-0.299

0.057

1.528

0.317

0.332

1.659

100

0.501

-1.495

0.303

-0.306

0.056

1.526

0.313

0.330

1.644

250

0.496

-1.498

0.296

-0.301

0.057

1.528

0.317

0.331

1.658

500

5

0.489

-1.499

0.299

-0.300

0.041

1.424

0.279

0.384

1.450

20

0.494

-1.506

0.299

-0.299

0.057

1.531

0.318

0.330

1.666

50

0.494

-1.503

0.298

-0.294

0.057

1.531

0.321

0.332

1.674

100

0.499

-1.503

0.298

-0.284

0.057

1.530

0.326

0.335

1.689

250

0.481

-1.499

0.301

-0.291

0.058

1.533

0.323

0.332

1.683

\(\mathbf {\sigma ^{2}_{u}=0.5}\)

True values:

0.500

-1.500

0.300

-0.300

0.1319

1.963

0.3821

0.2057

2.669

10

5

0.497

-1.500

0.310

-0.297

0.106

1.816

0.367

0.242

2.323

20

0.519

-1.489

0.291

-3.332

0.125

1.925

0.366

0.207

2.493

50

0.516

-1.497

0.313

-0.332

0.126

1.930

0.367

0.206

2.509

100

0.430

-1.490

0.300

-0.230

0.130

1.920

0.410

0.230

2.770

250

0.480

-1.500

0.290

-0.250

0.130

1.950

0.400

0.220

2.770

50

5

0.500

-1.440

0.330

-0.240

0.100

1.780

0.390

0.270

2.360

20

0.490

-1.500

0.290

-0.270

0.130

1.960

0.390

0.210

2.760

50

0.480

-1.500

0.300

-0.270

0.140

1.990

0.400

0.210

2.820

100

0.480

-1.510

0.310

-0.300

0.130

1.950

0.380

0.210

2.650

250

0.520

-1.500

0.300

-0.270

0.120

1.920

0.390

0.220

2.630

100

5

0.500

-1.460

0.290

-0.290

0.130

1.930

0.380

0.220

2.610

20

0.540

-1.510

0.280

-0.310

0.140

1.990

0.380

0.200

2.720

50

0.480

-1.500

0.300

-0.290

0.130

1.960

0.390

0.210

2.680

100

0.510

-1.500

0.300

-0.330

0.140

1.990

0.370

0.190

2.670

250

0.470

-1.500

0.300

-0.270

0.130

1.950

0.390

0.210

2.720

300

5

0.520

-1.500

0.330

-0.310

0.140

1.990

0.380

0.200

2.700

20

0.490

-1.500

0.300

-0.300

0.130

1.940

0.380

0.210

2.620

50

0.500

-1.490

0.290

-0.320

0.130

1.960

0.380

0.200

2.610

100

0.470

-1.500

0.300

-0.270

0.130

1.950

0.390

0.210

2.710

250

0.498

-1.499

0.299

-0.302

0.131

1.960

0.381

0.206

2.656

500

5

0.510

-1.500

0.290

-0.290

0.130

1.940

0.380

0.210

2.620

20

0.500

-1.500

0.310

-0.300

0.130

1.950

0.380

0.210

2.640

50

0.500

-1.500

0.300

-0.280

0.130

1.970

0.390

0.210

2.720

100

0.504

-1.501

0.298

-0.286

0.132

1.963

0.388

0.209

2.706

250

0.508

-1.499

0.299

-0.269

0.131

1.959

0.394

0.213

2.743