1. Fitting a Logit Model with a Polytomous Response Variable

2. Example: NA – Not available

3. The variables 1.Race – white, black 2.Age - < 22, ≥ 22 3.Father’s education – GS, some HS, HS grad, NA 4.Respondents Education - GS, some HS, HS grad – the response (dependent) variable

5. Techniques for handling Polytomous Response Variable Approaches 1.Consider the categories 2 at a time. Do this for all possible pairs of the categories. 2.Look at the continuation ratios i.1 vs 2 ii.1,2 vs 3 iii.1,2,3 vs 4 iv.etc

9. Causal or Path Analysis for Categorical Data

10. When the data is continuous, a causal pattern may be assumed to exist amongst the variables. The path diagram This is a diagram summarizing causal relationships. Straight arrows are drawn between a variable that has some cause and effect on another variable XY Curved double sided arrows are drawn between variables that are simply correlated X Y

11. Example 1 The variables – Job stress, Smoking, Heart Disease The path diagram Job Stress Heart Disease Smoking In Path Analysis for continuous variables, one is interested in determining the contribution along each path (the path coefficents)

12. Example 2 The variables – Job stress, Alcoholic Drinking, Smoking, Heart Disease The path diagram Job Stress Heart Disease Smoking Drinking

13. In analysis of categorical data there are no path coefficients but path diagrams can point to the appropriate logit analysis Example In this example the data consists of a two wave, two variable panel data for a sample of n =3398 schoolboys. It is looking at “membership” and “attitude towards” the leading crowd.

14. The path diagram: ABCD This suggest predicting B from A, then C from A and B and finally D from A, B and C.

18. Example 2 In this example we are looking at 1.Social Economic Status (SES) 2.Sex 3.IQ 4.Parental Encouragement for Higher Education (PE) 5.College Plans(CP)

20. The Path Diagram SES Sex IQ PE CP

21. The path diagram suggests 1.Predicting Parental Encouragement from Sex, SocioEconomic status, and IQ, then 2.Predicting College Plans from Parental Encouragement, Sex, SocioEconomic status, and IQ.

23. Logit Parameters: Model [ABC][ABD][ACD][BCD]

24. Two factor Interactions

27. Logit Parameters for Predicting College Plans Using Model 9: [ABCD][BCE][AE][DE]