Section B.6 Motivating Multiple Regression
So we have seen that we can fit models with just one predictor. We can build better models by expanding the number of predictors (although keep in mind you should also aim to build models as parsimonious as possible).
Another reason why it is important to think about additional variables in your model is to control for spurious correlations (although here you may also want to use your common sense when selecting your variables!). You must have heard before that correlation does not equal causation. Just because two things are associated, we cannot assume that one is the cause for the other. Typically we see how the pilots switch the secure-the-belt button when there is turbulence. These two things are associated, they tend to come together. But the pilots are not causing the turbulences by pressing a switch! The world is full of spurious correlations, associations between two variables that should not be taken too seriously.
Looking only at covariation between a pair of variables can be misleading. It may lead you to conclude that a relationship is more important than it really is. This is no trivial matter, but one of the most important ones we confront in research and policy.
It’s not an exaggeration to say that most quantitative explanatory research is about trying to control for the presence of confounders, variables that may explain away observed associations. Think about any criminology question: Does marriage reduce crime? Or is it that people which get married are different from those that don’t (and are those pre-existing differences that are associated with less crime)? Do gangs lead to more crime? Or is it that young people that join gangs are more likely to be offenders to start with? Are the police being racist when they stop and search more members of ethnic minorities? Or is it that there are other factors (i.e., offending, area of residence, time spent in the street) that, once controlled, would mean there is no ethnic disproportionality in stop and searches? Does a particular program reduce crime? Or is the observed change due to something else?
These things also matter for policy. [275], for example, argued that signs of incivility (or antisocial behaviour) in a community lead to more serious forms of crime later on as people withdraw to the safety of their homes when they see those signs of incivilities, and this leads to a reduction in informal mechanisms of social control. Many policies to tackle antisocial behaviour are very much informed by this model and were heavily influenced by broken windows theory.
But is the model right? [264] argue it is not entirely correct. They tried to show that there are other confounding factors (poverty, collective efficacy) that explain the association of signs of incivility and more serious crime. In other words, the reason why you see antisocial behaviour in the same communities that you see crime is because other structural factors explain both of those outcomes. They also argue that perceptions of antisocial behaviour are not just produced by observed antisocial behaviour, but also by stereotypes about social class and race. If you believe them, then the policy implications are that only tackling antisocial behaviour won’t help you to reduce crime (as [275] has argued). So as you can see this stuff matters for policy not just for theory.
Multiple regression is one way of checking the relevance of competing explanations. You could set up a model where you try to predict crime levels with an indicator of broken windows and an indicator of structural disadvantage. If after controlling for structural disadvantage you see that the regression coefficient for broken windows is still significant, you may be onto something, particularly if the estimated effect is still large. If, on the other hand, the t test for the regression coefficient of your broken windows variable is no longer significant, then you may be tempted to think that perhaps [264] were onto something.
