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APPLIED DATA ANALYSIS IN CRIMINAL JUSTICE

APPLIED DATA ANALYSIS IN CRIMINAL JUSTICE. CJ 525 MONMOUTH UNIVERSITY Juan P. Rodriguez. Perspective. Research Techniques Accessing, Examining and Saving Data Univariate Analysis – Descriptive Statistics Constructing (Manipulating) Variables Association – Bivariate Analysis

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APPLIED DATA ANALYSIS IN CRIMINAL JUSTICE

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  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

  8. A Bivariate Example

  9. A Bivariate Example

  10. A Bivariate Example • 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

  14. A Bivariate Example

  15. A Bivariate Example

  16. A Bivariate Example 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

  20. Graphing the Regression line

  21. Graphing the Regression line

  22. Graphing the Regression line

  23. Graphing the Regression line

  24. Graphing the Regression line

  25. Graphing the Regression line

  26. Graphing the Regression line

  27. Graphing the Regression line

  28. Graphing the Regression line 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

  32. Multivariate Logistic Regression

  33. Multivariate Logistic Regression

  34. Multivariate Logistic Regression

  35. Multivariate Logistic Regression 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

  37. Recoding CHILDS

  38. Recoding CHILDS

  39. Recoding CHILDS

  40. Recoding CHILDS

  41. Recoding CHILDS

  42. Recoding CHILDS

  43. Multivariate Logistic Regression

  44. Multivariate Logistic Regression

  45. Multivariate Logistic Regression

  46. Multivariate Logistic Regression

  47. Multivariate Logistic Regression

  48. Multivariate Logistic Regression

  49. Multivariate Logistic Regression

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

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