1. ERIC CANEN, M.S. UNIVERSITY OF WYOMING WYOMING SURVEY & ANALYSIS CENTER EVALUATION 2010: EVALUATION QUALITY SAN ANTONIO, TX NOVEMBER 13, 2010 What Am I Supposed to Do With Three-Way Crosstabs? An Introduction to Log Linear Models

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3. 3 Situation What effects? Community Level Communities

4. 4 Set Up Matched Communities Pre-Ordinance Post-Ordinance Pre/PostVariables of Interest Would be Seen as cool for smoking Tried smoking during lifetime Friends Smoke Parents Have Favorable Attitude toward Smoking Smoked during past 30 days

5. 5 Design Matched Communities Pre/PostEach Variable of Interest 222 X X

6. 6 Expectations (Hypotheses)

7. 7 NOTE: Hypothetical Data

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10. 10 Analysis Rows Columns Layers Try: Cross Tabulation

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13. Expected Cell Probabilities: P(AB) = P(A) * P(B) Expected Cell Counts: E(n ab ) = n * P(AB) Expected Cell Probabilities: P(AB|C) = P(A|C) * P(B|C) Expected Cell Counts: E(n ab |C) = n * P(AB|C) Expected Cell Probabilities: P(ABC) = P(A) * P(B) * P(C) Expected Cell Counts: E(n abc ) = n * P(ABC) 13

14. 14 Analysis Consider: Logistic Regression

15. 15 Analysis Loglinear Models Alternative to Crosstabs Model Based Higher Order Terms Modeling Cell Counts Related to ANOVA Relationship between variables Generalize Linear Models

16. Assumptions Data represent cross tabulated counts No expected cell counts are zero cell counts and no more than 20% of the cells have expected cell counts <=5 If sample size was fixed then the cell counts are expected to follow a multinomial distribution If sample size was not fixed then cell counts are expected to follow a Poisson distribution Models look at relationships or association, like correlation (r statistic) 16

17. Program Commands SAS  Proc CatMod procedure  Proc GenMod procedure R  loglin() function  glm() function Stata  poisson command (Poison regression)  glm command SPSS/PASW  GENLOG  GENLIN 17

18. 18 Saturated Model Or perfect fit model

19. 19 In SPSS: Analyze  Loglinear  General

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25. 25 GENLOG ordinance PREPOSTORD FUD1_dichot /MODEL=POISSON /PRINT=FREQ RESID ADJRESID ZRESID DEV ESTIM CORR COV /PLOT=RESID(ADJRESID) NORMPROB(ADJRESID) /CRITERIA=CIN(95) ITERATE(20) CONVERGE(0.001) DELTA(.5) /DESIGN ordinance PREPOSTORD FUD1_dichot FUD1_dichot*PREPOSTORD FUD1_dichot*ordinance PREPOSTORD*ordinance FUD1_dichot*PREPOSTORD*ordinance. Run Syntax

26. 26 Complete Independence Model

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28. 28 NOTE: All main effects… No interactions

29. 29 GENLOG ordinance PREPOSTORD FUD1_dichot /MODEL=POISSON /PRINT=FREQ RESID ADJRESID ZRESID DEV ESTIM CORR COV /PLOT=RESID(ADJRESID) NORMPROB(ADJRESID) /CRITERIA=CIN(95) ITERATE(20) CONVERGE(0.001) DELTA(.5) /DESIGN ordinance PREPOSTORD FUD1_dichot. Run Syntax

30. 30 Block Independence Models Testing whether one factor is independent of the relationship between two other factors

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32. 32 NOTE: Only one interaction effect

33. 33 GENLOG ordinance PREPOSTORD FUD1_dichot /MODEL=POISSON /PRINT=FREQ RESID ADJRESID ZRESID DEV ESTIM CORR COV /PLOT=RESID(ADJRESID) NORMPROB(ADJRESID) /CRITERIA=CIN(95) ITERATE(20) CONVERGE(0.001) DELTA(.5) /DESIGN ordinance PREPOSTORD FUD1_dichot PREPOSTORD*ordinance. Run Syntax

34. 34 Partial Independence Models Testing whether one factor shares or mediates relationships between the other two factors

35. 35 NOTE: This is the equivalent to what was being done in the original three-way crosstabs example

36. 36 NOTE: There are two interaction effects and they share a single factor

37. 37 GENLOG ordinance PREPOSTORD FUD1_dichot /MODEL=POISSON /PRINT=FREQ RESID ADJRESID ZRESID DEV ESTIM CORR COV /PLOT=RESID(ADJRESID) NORMPROB(ADJRESID) /CRITERIA=CIN(95) ITERATE(20) CONVERGE(0.001) DELTA(.5) /DESIGN ordinance PREPOSTORD FUD1_dichot PREPOSTORD*ordinance PREPOSTORD*FUD1_dichot. Run Syntax

38. 38 Uniform Association Model Testing whether the association between any two of the variables is the same at all levels of the third variable.

39. 39 NOTE: All three two way interaction effects are present in the model

40. 40 GENLOG ordinance PREPOSTORD FUD1_dichot /MODEL=POISSON /PRINT=FREQ RESID ADJRESID ZRESID DEV ESTIM CORR COV /PLOT=RESID(ADJRESID) NORMPROB(ADJRESID) /CRITERIA=CIN(95) ITERATE(20) CONVERGE(0.001) DELTA(.5) /DESIGN ordinance PREPOSTORD FUD1_dichot PREPOSTORD*ordinance PREPOSTORD*FUD1_dichot FUD1_dichot*ordinance. Run Syntax

41. 41 Showing the Effect

42. 42 NOTE: Hypothetical Data

43. 43 NOTE: Hypothetical Data

44. 44 NOTE: Hypothetical Data

45. 45 Complete independence model:

46. 46 Complete independence model:

47. 47 Complete independence model:

48. 48 Uniform Association Model:

49. 49 Uniform Association Model:

50. 50 Uniform Association Model:

51. Tips and Tricks Plot both the observed and expected values for all models Consider if you want to work forward (independent  block  partial  uniform  saturated) or backward (saturated  uniform  block  partial  independent) Backward maybe quicker Example of non-significant and inconclusive result 51 Run Syntax