§7.2: The Proportional Odds Model for Ordinal Response

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Presentation transcript:

§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=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 X1, X2 , … XN predictor variables Find the distribution of Y in terms of the X’s Y 1-Disagree 2-Neutral 3-Agree Probability P(Y=1|x’s) P(Y=2|x’s) P(Y=3|x’s)

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

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?

Proportional Odds vs. More Complicated Model 9 parameters Y 1 x1 x2 Y=1 a11 b11 b12 Y=2 a21 b21 b22 Y=3 a31 b31 b32 Y=4 n/a Proportional Odds 5 parameters Y 1 x1 x2 Y=1 α11 β11 β 12 Y=2 α21 Y=3 α31 Y=4 n/a

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