# Ordered logistic regression works

\begin{aligned} \log\left[ \frac { P( \operatorname{A} \geq \operatorname{B} ) }{ 1 - P( \operatorname{A} \geq \operatorname{B} ) } \right] &= \alpha_{1} + \beta_{1}(\operatorname{continuous\_1}) + \beta_{2}(\operatorname{continuous\_2}) \\ \log\left[ \frac { P( \operatorname{B} \geq \operatorname{C} ) }{ 1 - P( \operatorname{B} \geq \operatorname{C} ) } \right] &= \alpha_{2} + \beta_{1}(\operatorname{continuous\_1}) + \beta_{2}(\operatorname{continuous\_2}) \end{aligned}

\begin{aligned} \log\left[ \frac { P( \operatorname{A} \geq \operatorname{B} ) }{ 1 - P( \operatorname{A} \geq \operatorname{B} ) } \right] &= \alpha_{1} + \beta_{1}(\operatorname{continuous\_1})\ + \\ &\quad \beta_{2}(\operatorname{continuous\_2}) \\ \log\left[ \frac { P( \operatorname{B} \geq \operatorname{C} ) }{ 1 - P( \operatorname{B} \geq \operatorname{C} ) } \right] &= \alpha_{2} + \beta_{1}(\operatorname{continuous\_1})\ + \\ &\quad \beta_{2}(\operatorname{continuous\_2}) \end{aligned}

\begin{aligned} P( \operatorname{A} \geq \operatorname{B} ) &= \Phi[\alpha_{1} + \beta_{1}(\operatorname{continuous\_1}) + \beta_{2}(\operatorname{continuous\_2})] \\ P( \operatorname{B} \geq \operatorname{C} ) &= \Phi[\alpha_{2} + \beta_{1}(\operatorname{continuous\_1}) + \beta_{2}(\operatorname{continuous\_2})] \end{aligned}

\begin{aligned} P( \operatorname{A} \geq \operatorname{B} ) &= \Phi[\alpha_{1} + \beta_{1}(\operatorname{continuous\_1})\ + \\ &\qquad\ \beta_{2}(\operatorname{continuous\_2})] \\ P( \operatorname{B} \geq \operatorname{C} ) &= \Phi[\alpha_{2} + \beta_{1}(\operatorname{continuous\_1})\ + \\ &\qquad\ \beta_{2}(\operatorname{continuous\_2})] \end{aligned}

\begin{aligned} \log\left[ \frac { P( \operatorname{A} \geq \operatorname{B} ) }{ 1 - P( \operatorname{A} \geq \operatorname{B} ) } \right] &= 1.09 + 0.03(\operatorname{continuous\_1}) - 0.03(\operatorname{continuous\_2}) \\ \log\left[ \frac { P( \operatorname{B} \geq \operatorname{C} ) }{ 1 - P( \operatorname{B} \geq \operatorname{C} ) } \right] &= 2.48 + 0.03(\operatorname{continuous\_1}) - 0.03(\operatorname{continuous\_2}) \end{aligned}


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equatiomatic documentation built on Jan. 30, 2021, 9:06 a.m.