applied data analysis in criminal justice
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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 - PowerPoint PPT PresentationTRANSCRIPT
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 Association – Multivariate Analysis Comparing Group Means – Bivariate Multivariate Analysis - Regression
Lecture 8
Multivariate AnalysisWith Logistic Regression
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
A Bivariate Example
Relationship between political orientation and gun ownership
Use the GSS98 dataset
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
A Bivariate Example
A Bivariate Example
A Bivariate Example
A Bivariate Example
•OWNGUN is a categorical variable with 2 values: NO & YES
•The remaining values are coded as missing
A Bivariate Example
•POLVIEWS should be numerical
•It is really an ordinal variable but it can be considered numeric
A Bivariate Example
Second Step: Test the relationship Analyze
Regression Binary Logistic
Dependent: OWNGUN Covariates: POLVIEWS OK
A Bivariate Example
A Bivariate Example
A Bivariate Example
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
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
Graphing the Regression line
Find the predicted probabilities for different values of the independent variable
Plot the values
Graphing the Regression line
Graphing the Regression line
Graphing the Regression line
Graphing the Regression line
Graphing the Regression line
Graphing the Regression line
Graphing the Regression line
Graphing the Regression line
Graphing the Regression line
Graphing the Regression line
Graph is central portion of sigmoid curve: probability of 0.2 to 0.5
Graphing the Regression line
The model Chi Square tests if the model predicts occurrence better than simple chance: P<0.001
Multivariate Logistic Regression
Ensure all variables are structured correctly
Multivariate Logistic Regression
Multivariate Logistic Regression
Multivariate Logistic Regression
Multivariate Logistic Regression
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
Recoding CHILDS
Recoding CHILDS
Recoding CHILDS
Recoding CHILDS
Recoding CHILDS
Recoding CHILDS
Recoding CHILDS
Multivariate Logistic Regression
Multivariate Logistic Regression
Multivariate Logistic Regression
Multivariate Logistic Regression
Multivariate Logistic Regression
Multivariate Logistic Regression
Multivariate Logistic Regression
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
Making Predictions
Making Predictions
Making Predictions
Making Predictions
Making Predictions
Making Predictions
Graphing the equation
Graphing the equation
Graphing the equation
Graphing the equation
Multivariate Logistic Regression