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APPLIED DATA ANALYSIS IN CRIMINAL JUSTICE CJ 525 MONMOUTH UNIVERSITY Juan P. Rodriguez
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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
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Lecture 8 Multivariate Analysis With Logistic Regression
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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
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A Bivariate Example Relationship between political orientation and gun ownership Use the GSS98 dataset
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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
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A Bivariate Example
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OWNGUN is a categorical variable with 2 values: NO & YES The remaining values are coded as missing
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A Bivariate Example POLVIEWS should be numerical It is really an ordinal variable but it can be considered numeric
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A Bivariate Example Second Step: Test the relationship Analyze Regression Binary Logistic Dependent:OWNGUN Covariates:POLVIEWS OK
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A Bivariate Example
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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
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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
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Graphing the Regression line Find the predicted probabilities for different values of the independent variable Plot the values
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Graphing the Regression line
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Graph is central portion of sigmoid curve: probability of 0.2 to 0.5
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Graphing the Regression line The model Chi Square tests if the model predicts occurrence better than simple chance: P<0.001
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Multivariate Logistic Regression Ensure all variables are structured correctly
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Multivariate Logistic Regression
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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
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Recoding CHILDS
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Multivariate Logistic Regression
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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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Making Predictions
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Graphing the equation
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Multivariate Logistic Regression
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