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§7.2: The Proportional Odds Model for Ordinal Response

§7.2: The Proportional Odds Model for Ordinal Response. Warm Up. Give an example of an ORDINAL variable Suppose p(Y=1)=0.5, p(Y=2)=0.3, p(Y=3)=0.2. Find P(Y ≤2). What is logit( P(Y ≤2))? What is logit( P(Y ≤3))?. Our Goal. Y – ORDINAL response variable

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§7.2: The Proportional Odds Model for Ordinal Response

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  1. §7.2: The Proportional Odds Modelfor Ordinal Response

  2. Warm Up • Give an example of an ORDINAL variable • Suppose p(Y=1)=0.5, p(Y=2)=0.3, p(Y=3)=0.2. Find P(Y≤2). • What is logit(P(Y≤2))? • What is logit(P(Y≤3))?

  3. Our Goal • Y – ORDINAL response variable • X1, X2 , … XN predictor variables • Find the distribution of Y in terms of the X’s

  4. Proportional Odds Model • Express “Cumulative Logit” as a linear combination of predictor variables.

  5. You Try • For the ordinal variable you came up with earlier, what are two predictor variables? • Write out the model with your example variables Logit(P(Y≤j|x’s)=αj + β1x1+ β2x2 • How many αj’s are in your model?

  6. Proportional Odds vs. More Complicated Model

  7. Score Test • Compares Proportional Odds Model to more complicated model • Null Hypothesis – Proportional Odds appropriate • Alternative Hypothesis – More complicated model is needed.

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