4 Lec - للترجمة.pptx

Ordinal a n d MultinomialLogistic Regression Ordinal logistic regression • It is a statistical analysis method that can be used to model the relationship between an ordinal response variable and one or more explanatory variables. • Ordinal logistic regression is used to model ordinal outcome varia...

Ordinal a n d MultinomialLogistic Regression Ordinal logistic regression • It is a statistical analysis method that can be used to model the relationship between an ordinal response variable and one or more explanatory variables. • Ordinal logistic regression is used to model ordinal outcome variables, in which the log odds of the outcomes are modeled as a linear combination of the predictor variables. • An ordinal variable is a categorical variable for which there is a clear ordering of the category levels. • It is used when there are 3 or more ordered categories. 1. It consists of multiple binary logistics and combines the results to a single model with one less than the number of categories 2. This combined model constrains the coefficients to be the same requiring an extra assumption called the proportional odds assumption. 3. Multiple binary logistic regressions (Odds ratio of 1 vs. 2,3 = odds ratio of 1,2 vs. 3). 4. It produces multiple intercepts in the output. A. One less than the number of categories b. intercepts are not generally interpreted. 5. Since we have multiple categories, we need to interpret the odds ratio as the effect of being in a higher category relative to a low category (or vice versa). Example • A study looks at factors that influence the decision of whether to apply to graduate school. College juniors are asked if they are unlikely, somewhat likely, or very likely to apply to graduate school. Hence, our outcome variable has three categories. Data on parental educational status, whether the undergraduate institution is public or private, and current GPA is also collected. The researchers have reason to believe that the "distances" between these three points are not equal. For example, the "distance" between "unlikely" and "somewhat likely" may be shorter than the distance between "somewhat likely" and "very likely". Interpreting the odds ratio • Parental Education: For students whose parents did attend college, the odds of being more likely (i.e., very or somewhat likely versus unlikely) to apply is 2.85 times that of students whose parents did not go to college, holding constant all other variables. • School Type: For students in public school, the odds of being more likely (i.e., very or somewhat likely versus unlikely) to apply is 5.71% lower [i.e., (1 -0.943) x 100%] than private school students, holding constant all other variables. • GPA: For every one unit increase in student's GPA the odds of being more likely to apply (very or somewhat likely versus unlikely) is multiplied 1.85 times (i.e., increases 85%), holding constant all other variables. Multinomial logistic regression • Multinomial logistic regression is used to model nominal outcome variables, in which the log odds of the outcomes are modeled as a linear combination of the predictor variables. Pname1 log =BX Pname2 • There is no proportional odds assumption Example • Entering high school students make program choices among general program, vocational program and academic program. Their choice might be modeled using their writing score and their social economic status. • As compared to high SES students, low SES students are approximately 3 times higher likely (OR=3.199) to select general program rather than academic program. • For every one unit increase in the writing score, the student will be 11% less likely (OR=0.893) to select vocation program rather than academic program. • 11%?? • (1-0.89)*100=.11*100=11%