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\begin{table}[t]
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\caption*{\  \textbf{Table S1. Type I error rates of seven tests with 1,000 individuals for trait with five categories at nominal significance  level  0.05.}}
\centering
\begin{tabular}{ccllllllllll}\hline
&\multicolumn{9}{c}{\qquad \qquad \qquad \qquad \textbf{Scenario}}\\\cline{3-12}
$\bm{\rho}$&\bf{Test}&  \bf{1}&\bf{2} &\bf{ 3 }&\bf{4} &\bf{ 5} & \bf{6} & \bf{7}& \bf{8 }& \bf{9} & \bf{10} \\\hline
0&  MIT &0.060&	0.054&	0.062&	0.046	&0.032&	0.058	&0.052&	0.052&	0.054&	0.046\\
&aMIT&0.062&0.058&0.058&0.042&	0.030&	0.056	&0.054&	0.052&	0.058&	0.050\\
&Score&0.046	&0.040&	0.046&	0.044&	0.046&	0.036&	0.054&	0.048	&0.062&	0.044\\
&$\mathrm{SKAT}$-$\mathrm{O_{B}}$&0.062&	0.044&	0.050&	0.040&	0.038 &	0.042&	0.032&	0.034&	0.050&	0.030\\
&$\mathrm{aSPU_{B}}$&0.052&	0.060&	0.066&	0.038	&0.060&	0.034&	0.048&	0.062&	0.042&	0.048\\
&$\mathrm{GFLM_{B}}$&0.040&	0.032&	0.044&	0.050	&0.038&	0.038&	0.053&	0.034&	0.048&	0.032\\
&$\mathrm{KLT_{B}}$&0.046&	0.044&	0.046&	0.042&	0.040&	0.038&	0.050&	0.038&	0.050	&0.034\\
0.5& MIT &0.062&	0.056&	0.058&	0.052&	0.052	&0.046&	0.054&	0.056&	0.050&	0.066\\
&aMIT&0.064&	0.052&	0.052&	0.048&	0.056&	0.044	&0.052&	0.058&	0.044&	0.064\\
&Score&0.054&	0.044&	0.046&	0.038	&0.034	&0.050&	0.038&	0.058&	0.040&	0.046\\
&$\mathrm{SKAT}$-$\mathrm{O_{B}}$&0.046&	0.042&	0.054&	0.038&	0.032&	0.046&	0.040&	0.054&	0.052&	0.056\\
&$\mathrm{aSPU_{B}}$&0.060&	0.052&	0.057&	0.046&	0.050&	0.046&	0.046&	0.052&	0.060&	0.060\\
&$\mathrm{GFLM_{B}}$&0.048&	0.038&	0.036&	0.054&	0.034&	0.038&	0.046&	0.046&	0.048&	0.044\\
&$\mathrm{KLT_{B}}$&0.058	&0.042&	0.042&	0.054	&0.036&	0.058&	0.034&	0.046&	0.042&	0.036\\
0.9& MIT &0.046 &	0.066 &	0.044 &	0.050 &	0.066 &	0.054 &	0.054 &	0.066 &	0.044 &	0.052\\
&aMIT&0.048&	0.066&	0.046&	0.050&	0.066&	0.048&	0.050	&0.068&	0.046&	0.054\\
&Score&0.044&	0.048&	0.044&	0.044&	0.062&	0.050&	0.040&	0.044&	0.038&	0.044\\
&$\mathrm{SKAT}$-$\mathrm{O_{B}}$&0.046&	0.038&	0.030&	0.048&	0.046&	0.040&	0.050&	0.056&	0.054&	0.048\\
&$\mathrm{aSPU_{B}}$&0.048&	0.062&	0.050&	0.048&	0.044	&0.054&	0.050&	0.054&	0.066	&0.052\\
&$\mathrm{GFLM_{B}}$&0.046&	0.052&	0.048&	0.043&	0.048	&0.032&	0.054&	0.038&	0.042&0.048\\
&$\mathrm{KLT_{B}}$&0.032&	0.056&	0.042&	0.040&	0.048&	0.040&	0.056&	0.044&	0.038&	0.042\\
\hline
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