A Multinomial Ordinal Probit Model with Singular Value Decomposition Method for a Multinomial Trait

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="419832.fig.001a" src="https://static.hindawi.com/articles/jps/volume-2012/419832/figures/419832.fig.001a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Estimates of SNP effects by the proposed method</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="419832.fig.001b" src="https://static.hindawi.com/articles/jps/volume-2012/419832/figures/419832.fig.001b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b><svg height="10.325" id="M186" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.75 10.325" width="11.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑃</tspan>
</text>
</g>
</g>
</svg> values of testing SNP effects (<svg height="14.9125" id="M187" style="vertical-align:-3.2955pt" version="1.1" viewbox="0 0 42.362499 14.9125" width="42.362499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.9125)">
<g transform="translate(72,-60.07)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">l</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">o</tspan>
<tspan style="font-size: 12.50px; " x="18.291889" y="0">g</tspan>
</text>
<text transform="matrix(1,0,0,-1,-47.41,60.25)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">0</tspan>
</text>
</g>
</g>
</svg>(<i>P </i>value)) </td></tr></table></td></tr></table>

<table>Analysis of the simulated data sets with multinomial ordinal probit model with SVD.</table>

Journal of Probability and Statistics

fig1

Figure 1

Figure 1: A Multinomial Ordinal Probit Model with Singular Value Decomposition Method for a Multinomial Trait 