Throughout this section, we’ve been interested in determining how aware respondents are about the practice of neighbourhood policing near their homes. We’ve already explored the significance of the effects of independent variables like sex, health, and education on neighpol1. Now, we are curious what the odds are that a respondent is aware there is a neighbourhood policing program in place in their neighbourhood. Odds are similar to a probability, but have slightly different properties. You might have heard of them if you’ve watched horse racing! They are related to the chances of something happening – so a horse with odds of 4 to 1 is expected to win once and lose four times if it ran five times. In regard to a respondent being aware of a neighbourhood policing program, the odds are the chances that they have heard of it compared to the chances of that they have not heard.
Remember that neighpol1 is a variable that catalogues answers to the following question: “Before this interview, were you aware that there was a Neighbourhood Policing Team in your local area?” Respondents could have only answered “yes” or “no” to this question, making neighpol1 a binary variable, with just two possible categories.
In the other sections of this site, we analyze continuous dependent variables. However, neighpol1 is binary. If the dependent variable is categorical and binary, meaning that the outcome can be either 0 or 1, we can use the binary logistic regression method to illustrate trends in our data. Logistic regression is a statistical analysis that is very similar to linear regression. You may recall from other sections that linear regression allows us to model the relationship between two (or more) variables and predict certain values of the dependent variable. Because binary logistic regression is used when dependent variables are binary, this test allows us to predict the odds of certain values of the dependent variable.
We will focus on the following explanatory (or independent) variables:
sex: Sex of respondent
age: Age of respondent
ethngrp2: Respondent’s ethnic group
relig2a: Respondent’s religion
remploy: Employment status of respondent
educat3: Highest level of education of respondent
health2: Health status of respondent
Notice that some of these categorical variables have more than two categories and some are binary, meaning that they only have two categories. For example, the variable relig2a, concerning a respondent’s religion, has several categories, as there are more than two possible religious affiliations. The variable sex, concerning the sex of the respondent, is binary, as there are only two possible responses to this question (i.e. Male or Female). The variable age is continuous, as the age of a respondent can be any number between 16 (the youngest age of respondents in the CSEW) and 105 (the oldest age of respondents in the CSEW 2011-2012).
First, we may want to investigate if age has a relationship with our outcome variable, neighpol1. To do so, we are going to use logistic regression to look at the relationship between the neighpol1 (our dependent or outcome variable Y) and age (our independent variable X). This analysis can be found under the "Simple Logistic Regression" tab.