Outcome to Probability where Probability resembles a Sigmoid Function:

where,

O = Outcome “is identical to” (or “≡”) the following:

$O=e_{[\nabla ]}^{a+b_{i}x},\frac{Prob\left(sim\right)}{1-\left|Prob\left(sim\right)\right|}=e_{[\nabla ]}^{a+b_{i}x};Prob=\frac{1}{1+e_{[\nabla ]}^{-\left(a+b_{i}x\right)}}$ ;

$Tr{i}_{{\theta }_1}=\frac{\text{Probability}\left(\text{Score1}\right)}{\text{Probability}\left(\text{ScoreGreaterthan1}\right)}$ ;

$Tr{i}_{{\theta }_2}=\frac{\text{Probability}\left(\text{Score1or2}\right)}{\text{Probability}\left(\text{ScoreGreaterthan2}\right)}$ ; and

$Tr{i}_{{\theta }_3}=\frac{\text{Probability}\left(\text{Score1},\text{2or3}\right)}{\text{Probability}\left(\text{ScoreGreaterthan3}\right)}$ ; thus,

“The Trichotomous Power Analysis Tri-Ordinal Trilogistic Model” is:

$e_{[\nabla ]}\left(Tr{i}_{{\theta }_{1,2,3}}\right)={\alpha }_{1,2,3}-{\beta }_{[\nabla ]}$

where, $e_{[\nabla ]}\left({\theta }_{1,2,3}\right)=Tr{i}_{{\nabla }_{1,2,3}}$ ; ${\alpha }_{1,2,3}=b_1,b_2$ and $b_3$ ; and ${\beta }_{[\nabla ]}$ = The G-TPA Progression Line.