. Author manuscript; available in PMC: 2014 Jan 17.

Published in final edited form as: Multivariate Behav Res. 2013 Jan 17;47(6):840–876. doi: 10.1080/00273171.2012.732901

TABLE 7.

Coverage Rate of Latent Interaction Effect (Statistical Power = 0.7)

Sample Size

Distribution

CPI

GAPI

UPI

LMS

100

Normal

0.947 ^*

0.903 ^*

0.954 ^*

0.923 ^*

0.932 ^*

0.904 ^*

0.948 ^*

Uniform

0.923 ^*

0.880

0.960 ^*

0.931 ^*

0.948 ^*

0.915 ^*

0.927 ^*

0.910 ^*

0.856

0.925 ^*

0.891

0.914 ^*

0.869

0.956 ^*

0.888

0.807

0.929 ^*

0.876

0.918 ^*

0.871

0.962 ^*

χ_{1}^{2}

0.822

0.724

0.933 ^*

0.904 ^*

0.931 ^*

0.898

0.924 ^*

200

Normal

0.956 ^*

0.941 ^*

0.956 ^*

0.949 ^*

0.958 ^*

0.941 ^*

0.958 ^*

Uniform

0.940 ^*

0.902 ^*

0.955 ^*

0.946 ^*

0.959 ^*

0.947 ^*

0.932 ^*

0.892

0.891

0.918 ^*

0.899

0.917 ^*

0.893

0.931 ^*

0.879

0.864

0.930 ^*

0.887

0.926 ^*

0.875

0.913 ^*

χ_{1}^{2}

0.691

0.672

0.924 ^*

0.928 ^*

0.933 ^*

0.922 ^*

0.755

500

Normal

0.955 ^*

0.947 ^*

0.952 ^*

0.955 ^*

0.954 ^*

0.952 ^*

0.950 ^*

Uniform

0.956 ^*

0.916 ^*

0.958 ^*

0.956 ^*

0.963 ^*

0.955 ^*

0.943 ^*

0.849

0.901 ^*

0.931 ^*

0.909 ^*

0.935 ^*

0.908 ^*

0.870

0.811

0.874

0.899

0.868

0.906 ^*

0.869

0.813

χ_{1}^{2}

0.375

0.479

0.916 ^*

0.926 ^*

0.921 ^*

0.269

1000

Normal

0.954 ^*

0.953 ^*

0.960 ^*

0.947 ^*

0.951 ^*

0.964 ^*

Uniform

0.953 ^*

0.941 ^*

0.958 ^*

0.962 ^*

0.956 ^*

0.958 ^*

0.946 ^*

0.855

0.935 ^*

0.932 ^*

0.920 ^*

0.932 ^*

0.921 ^*

0.841

0.741

0.879

0.923 ^*

0.896

0.924 ^*

0.900

0.735

χ_{1}^{2}

0.149

0.266

0.913 ^*

0.918 ^*

0.926 ^*

0.922 ^*

0.049

5000

Normal

0.947 ^*

0.943 ^*

0.944 ^*

0.951 ^*

0.945 ^*

0.950 ^*

0.943 ^*

Uniform

0.955 ^*

0.930 ^*

0.958 ^*

0.960 ^*

0.957 ^*

0.960 ^*

0.950 ^*

0.776

0.946 ^*

0.940 ^*

0.930 ^*

0.944 ^*

0.931 ^*

0.763

0.667

0.907 ^*

0.937 ^*

0.923 ^*

0.935 ^*

0.921 ^*

0.649

χ_{1}^{2}

0.000

0.003

0.927 ^*

0.946 ^*

0.936 ^*

0.945 ^*

0.000

Coverage Rate of Latent Interaction Effect (Statistical Power = 0.9)

Sample Size

Distribution

CPI

GAPI

UPI

LMS

100

Normal

0.928 ^*

0.891

0.949 ^*

0.919 ^*

0.937 ^*

0.905 ^*

0.931 ^*

Uniform

0.941 ^*

0.879

0.970 ^*

0.945 ^*

0.949 ^*

0.922 ^*

0.939 ^*

0.906 ^*

0.844

0.921 ^*

0.876

0.914 ^*

0.865

0.954 ^*

0.870

0.815

0.912 ^*

0.877

0.888

0.838

0.952 ^*

χ_{1}^{2}

0.785

0.706

0.904 ^*

0.873

0.890

0.866

0.915 ^*

200

Normal

0.933 ^*

0.908 ^*

0.950 ^*

0.942 ^*

0.951 ^*

0.931 ^*

0.956 ^*

Uniform

0.942 ^*

0.908 ^*

0.959 ^*

0.950 ^*

0.956 ^*

0.946 ^*

0.944 ^*

0.857

0.881

0.886

0.884

0.892

0.876

0.920 ^*

0.839

0.851

0.909 ^*

0.892

0.904 ^*

0.877

0.899

χ_{1}^{2}

0.667

0.671

0.879

0.863

0.882

0.865

0.732

500

Normal

0.957 ^*

0.943 ^*

0.957 ^*

0.945 ^*

0.950 ^*

0.951 ^*

Uniform

0.938 ^*

0.921 ^*

0.949 ^*

0.948 ^*

0.952 ^*

0.937 ^*

0.836

0.900

0.899

0.891

0.892

0.884

0.843

0.779

0.858

0.898

0.903 ^*

0.891

0.888

0.803

χ_{1}^{2}

0.392

0.511

0.914 ^*

0.920 ^*

0.921 ^*

0.923 ^*

0.238

1000

Normal

0.945 ^*

0.941 ^*

0.945 ^*

0.949 ^*

0.948 ^*

0.952 ^*

Uniform

0.936 ^*

0.921 ^*

0.945 ^*

0.952 ^*

0.946 ^*

0.952 ^*

0.955 ^*

0.794

0.902 ^*

0.900

0.894

0.898

0.895

0.776

0.739

0.886

0.895

0.887

0.895

0.888

0.681

χ_{1}^{2}

0.157

0.295

0.905 ^*

0.912 ^*

0.906 ^*

0.913 ^*

0.043

5000

Normal

0.952 ^*

0.951 ^*

0.946 ^*

0.951 ^*

0.945 ^*

0.953 ^*

0.960 ^*

Uniform

0.945 ^*

0.925 ^*

0.938 ^*

0.943 ^*

0.936 ^*

0.940 ^*

0.728

0.934 ^*

0.921 ^*

0.907 ^*

0.916 ^*

0.898

0.700

0.639

0.910 ^*

0.931 ^*

0.921 ^*

0.931 ^*

0.916 ^*

0.572

χ_{1}^{2}

0.000

0.006

0.917 ^*

0.935 ^*

0.932 ^*

0.938 ^*

0.000

Note. ML means maximum likelihood. SB means Satorra-Bentler correction.

means (Coverage Rate > 0.9) criterion met.

Note. ML means maximum likelihood. SB means Satorra-Bentler correction.

means (Coverage Rate > 0.9) criterion met.