Table 3 Open in new tab Simulations....

γ_{1} = 0

γ_{1} = 0.5

γ_{1} = 1

γ_{1} = 1.5

γ_{1} = 2

γ_{1} = 3

GEE (exchangeable)

MSE

μ₁

0.109

0.104

0.087

0.070

0.061

0.050

μ₂

0.111

0.106

0.091

0.076

0.067

0.062

μ₃

0.120

0.114

0.101

0.093

0.091

0.094

CI width

μ₁

1.273

1.247

1.141

1.035

0.958

0.868

μ₂

1.284

1.259

1.161

1.072

1.011

0.950

μ₃

1.317

1.295

1.219

1.169

1.153

1.165

Coverage

μ₁

0.948

0.947

0.950

0.948

0.947

μ₂

0.944

0.946

0.945

0.947

0.950

0.945

μ₃

0.942

0.944

0.947

0.945

0.942

0.941

mtram (binary)

MSE

μ₁

0.109

0.104

0.086

0.068

0.057

0.044

μ₂

0.110

0.106

0.091

0.074

0.064

0.055

μ₃

0.119

0.114

0.100

0.091

0.087

0.088

CI width

μ₁

1.251

1.254

1.150

1.042

0.958

0.847

μ₂

1.276

1.268

1.172

1.079

1.014

0.942

μ₃

1.343

1.303

1.230

1.178

1.162

1.184

Coverage

μ₁

0.953

0.951

0.949

0.953

0.952

μ₂

0.948

0.950

0.949

0.951

0.954

0.953

μ₃

0.947

0.948

0.950

0.951

0.953

0.955

mtram (continuous)

MSE

μ₁

0.074

0.067

0.045

0.029

0.019

0.009

μ₂

0.079

0.070

0.048

0.033

0.024

0.015

μ₃

0.082

0.075

0.056

0.046

0.038

0.033

CI width

μ₁

1.040

1.005

0.827

0.659

0.535

0.382

μ₂

1.061

1.020

0.853

0.705

0.602

0.485

μ₃

1.119

1.059

0.926

0.826

0.766

0.710

Coverage

μ₁

0.949

0.948

0.945

0.947

0.948

μ₂

0.945

0.948

0.949

0.948

0.947

0.951

μ₃

0.949

0.947

0.945

0.951

0.950

Table 3

Open in new tab

Simulations. MSE, widths, and coverages of 95% confidence intervals for three marginal effects. For dichotomized binary responses, results obtained from GEEs can be directly compared to results from marginal transformation models (first two blocks). The last block reports results of marginal transformation models fitted to continuous responses

			$γ_{1} = 0$	$γ_{1} = 0.5$	$γ_{1} = 1$	$γ_{1} = 1.5$	$γ_{1} = 2$	$γ_{1} = 3$
GEE (exchangeable)	MSE	μ₁	0.109	0.104	0.087	0.070	0.061	0.050
		μ₂	0.111	0.106	0.091	0.076	0.067	0.062
		μ₃	0.120	0.114	0.101	0.093	0.091	0.094
	CI width	μ₁	1.273	1.247	1.141	1.035	0.958	0.868
		μ₂	1.284	1.259	1.161	1.072	1.011	0.950
		μ₃	1.317	1.295	1.219	1.169	1.153	1.165
	Coverage	μ₁	0.948	0.947	0.947	0.950	0.948	0.947
		μ₂	0.944	0.946	0.945	0.947	0.950	0.945
		μ₃	0.942	0.944	0.947	0.945	0.942	0.941
mtram (binary)	MSE	μ₁	0.109	0.104	0.086	0.068	0.057	0.044
		μ₂	0.110	0.106	0.091	0.074	0.064	0.055
		μ₃	0.119	0.114	0.100	0.091	0.087	0.088
	CI width	μ₁	1.251	1.254	1.150	1.042	0.958	0.847
		μ₂	1.276	1.268	1.172	1.079	1.014	0.942
		μ₃	1.343	1.303	1.230	1.178	1.162	1.184
	Coverage	μ₁	0.953	0.951	0.949	0.953	0.953	0.952
		μ₂	0.948	0.950	0.949	0.951	0.954	0.953
		μ₃	0.947	0.948	0.950	0.951	0.953	0.955
mtram (continuous)	MSE	μ₁	0.074	0.067	0.045	0.029	0.019	0.009
		μ₂	0.079	0.070	0.048	0.033	0.024	0.015
		μ₃	0.082	0.075	0.056	0.046	0.038	0.033
	CI width	μ₁	1.040	1.005	0.827	0.659	0.535	0.382
		μ₂	1.061	1.020	0.853	0.705	0.602	0.485
		μ₃	1.119	1.059	0.926	0.826	0.766	0.710
	Coverage	μ₁	0.949	0.949	0.948	0.945	0.947	0.948
		μ₂	0.945	0.948	0.949	0.948	0.947	0.951
		μ₃	0.949	0.947	0.947	0.945	0.951	0.950

			$γ_{1} = 0$	$γ_{1} = 0.5$	$γ_{1} = 1$	$γ_{1} = 1.5$	$γ_{1} = 2$	$γ_{1} = 3$
GEE (exchangeable)	MSE	μ₁	0.109	0.104	0.087	0.070	0.061	0.050
		μ₂	0.111	0.106	0.091	0.076	0.067	0.062
		μ₃	0.120	0.114	0.101	0.093	0.091	0.094
	CI width	μ₁	1.273	1.247	1.141	1.035	0.958	0.868
		μ₂	1.284	1.259	1.161	1.072	1.011	0.950
		μ₃	1.317	1.295	1.219	1.169	1.153	1.165
	Coverage	μ₁	0.948	0.947	0.947	0.950	0.948	0.947
		μ₂	0.944	0.946	0.945	0.947	0.950	0.945
		μ₃	0.942	0.944	0.947	0.945	0.942	0.941
mtram (binary)	MSE	μ₁	0.109	0.104	0.086	0.068	0.057	0.044
		μ₂	0.110	0.106	0.091	0.074	0.064	0.055
		μ₃	0.119	0.114	0.100	0.091	0.087	0.088
	CI width	μ₁	1.251	1.254	1.150	1.042	0.958	0.847
		μ₂	1.276	1.268	1.172	1.079	1.014	0.942
		μ₃	1.343	1.303	1.230	1.178	1.162	1.184
	Coverage	μ₁	0.953	0.951	0.949	0.953	0.953	0.952
		μ₂	0.948	0.950	0.949	0.951	0.954	0.953
		μ₃	0.947	0.948	0.950	0.951	0.953	0.955
mtram (continuous)	MSE	μ₁	0.074	0.067	0.045	0.029	0.019	0.009
		μ₂	0.079	0.070	0.048	0.033	0.024	0.015
		μ₃	0.082	0.075	0.056	0.046	0.038	0.033
	CI width	μ₁	1.040	1.005	0.827	0.659	0.535	0.382
		μ₂	1.061	1.020	0.853	0.705	0.602	0.485
		μ₃	1.119	1.059	0.926	0.826	0.766	0.710
	Coverage	μ₁	0.949	0.949	0.948	0.945	0.947	0.948
		μ₂	0.945	0.948	0.949	0.948	0.947	0.951
		μ₃	0.949	0.947	0.947	0.945	0.951	0.950

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