1. APPLIED DATA ANALYSIS IN CRIMINAL JUSTICE CJ 525 MONMOUTH UNIVERSITY Juan P. Rodriguez

2. Perspective Research Techniques Accessing, Examining and Saving Data Univariate Analysis – Descriptive Statistics Constructing (Manipulating) Variables Association – Bivariate Analysis Association – Multivariate Analysis Comparing Group Means – Bivariate Multivariate Analysis - Regression

3. Lecture 8 Multivariate Analysis With Logistic Regression

4. Logistic Regression Analyzes relationships of multiple independent variables to one dependent variable Unlike in linear regression, the dependent variable must be binary, a categorical variable with 2 categories If the variable is not binary, it can be recoded to a binary form It estimates the probability that an event will occur

5. A Bivariate Example Relationship between political orientation and gun ownership Use the GSS98 dataset

6. A Bivariate Example First Step: Examine the structure of the dependent and independent variables. Ensure that: The dependent variable, OWNGUN, is binary The independent variable, POLVIEWS, is numerical

7. A Bivariate Example

10. OWNGUN is a categorical variable with 2 values: NO & YES The remaining values are coded as missing

11. A Bivariate Example POLVIEWS should be numerical It is really an ordinal variable but it can be considered numeric

12. A Bivariate Example Second Step: Test the relationship Analyze Regression Binary Logistic Dependent:OWNGUN Covariates:POLVIEWS OK

13. A Bivariate Example

16. The logistic regression coefficients (B) indicate the direction and strength of the relationship They represent the effect of a one unit change in the level of POLVIEWS on the log-odds of OWNGUN. The relationship is positive (0.19): the more conservative a person is, the more likely he/she will own a gun The odds ratio (Exp(B)) is how many times higher the odds of occurrence are for each one-unit increase in POLVIEWS: 1.21

17. Making Predictions What is the probability of gun ownership for someone extremely conservative (POLVIEWS=7)? Log-odds = A + B(X) Odds = Exp(A + B(X)) But Probability = Odss/1 + Odds Probability = (Exp(A+b(X))/1+Exp(A+B(X)) Probability = (Exp(-1.379+0.19(7))/(1+Exp(- 1.379+0.19(7)) = 0.95/1.95 = 0.49

18. Graphing the Regression line Find the predicted probabilities for different values of the independent variable Plot the values

19. Graphing the Regression line

28. Graph is central portion of sigmoid curve: probability of 0.2 to 0.5

29. Graphing the Regression line The model Chi Square tests if the model predicts occurrence better than simple chance: P<0.001

30. Multivariate Logistic Regression Ensure all variables are structured correctly

31. Multivariate Logistic Regression

35. Childs is the number of children in the family We want to know if having ANY children influences gun ownership CHILDS needs to be recoded

36. Recoding CHILDS

43. Multivariate Logistic Regression

50. Many variables are statistically significant: Conservative values increase likelihood of owning a gun Having children increases the probability of having a gun

51. Making Predictions

57. Graphing the equation

61. Multivariate Logistic Regression