Title: Sources of error
Course: UGQuants (SSPS) > Section: Correlation and Regression

Sources of error

There are many ways for error to creep into our regression models.  In his Basic Econometrics (Ch2), Damodar Gujarati points to several sources of difficulty:

 | Intrinsic randomness in human behaviour
 | Vagueness of theory
 | Unavailability of data
 | Core variables versus peripheral variables
 | Poor proxy variables
 | Parsimony
 | Wrong form (might not be linear)

The first of these is the concern of all social scientists. Individuals do not behave as machines. Their behaviour is at times unpredictable, which means that at best we can seek to identify general trends and relationships between variables. Our ability to identify these trends and relationships depends in large part on the quality of the data that we have; the extent to which it represents the population we are interested in; and the extent to which it was collected in a rigorous manner, without influence from the researcher, or the research instrument (in this case usually a survey).  In addition, we might be dealing with data that we have not collected ourselves and as such the types of variables that interest us are not necessarily those that have been collected by previous researchers. Sometimes we find ourselves using proxy variables that we think get to the heart of the matter but are in fact imperfect indicators of what we want to use.  We might, for example, use political interest as a proxy for engagement, or self-professed political engagement as a proxy for political knowledge.  Furthermore, just as we might find ourselves struggling with data, so too might we find that we are less than clear on the relationship that we are seeking to detect.  Here, our knowledge of theory and our ability to identify the core variables that are of interest will help us.  Last, we might find that even if we are clear on what we expect to find and have good quality data, the relationship between our variables might not be linear. This is not the end of the world if it is non-linear, as there are different tests we can use, but it does mean that some of the simpler ones we have learned about here may be inappropriate. As is usually the case, we must be mindful of the data that we have and be guided by it, rather than use the few tests we can regardless of whether they are appropriate or not.