# Theoretical Framework: The Proportional Odds Model

The Proportional Odds Model

A binary logistic regression model estimates the odds and the probability of experiencing an event for the dichotomous outcome variable on a set of predictors. The logistic regression model is defined as: ln(Y′) = logit [π(x)] = ln = α + β1X1 + β2X2 + …+ βpXp. (1) where logit [π(x)] is the log odds of success, and the odds is a ratio between the probability of having an event and the probability of not having that event.

By extending binary logistic regression, the proportional odds (PO) model estimates the odds and the probabilities of being at or below a particular category when the outcome variable is ordinal. The ordinal regression model can be expressed on the

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j =1, 2, … J -1. αj are the cut points, and β1, β2 …βp are the logit coefficients. This PO model estimates different cut points, but the effect of any predictor is assumed to be the same across these cut points. To estimate the cumulative odds of being at or below the jth category, this model can be rewritten

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This study surveyed high school students, parents, teachers, school counselors and administrators, and assessed 9th graders’ algebraic skills and reasoning. It was designed to keep track of high school students from grade nine to postsecondary school education and their choice of future careers. In the 2009 base year data, 21,444 high school students, from a national sample of 944 schools, participated in the study. Students were asked to provide information regarding basic demographics, school and home experience, such as math and science activities, coursework, and time spent on different activities, mathematics and science attitude, mathematics and science self-efficacy, their feelings about math and science teacher, and future educational and life plans after secondary