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