# More complex than simple and multiple regressions?

I am currently in an Econometrics class that requires us to write a research paper that showcases our skills in regression/ modeling. What is slightly more complex than simple and multiple regressions that I may be able to learn and utilize in my research project? I realize that the model depends on the research question, but I'd like to learn different types of modeling anyhow.

Thanks.

Welcome to the wonderful world of econometrics! Most introductory econometrics courses will extend Ordinary Least Squares (OLS) by considering binary outcomes models such as the logit and probit.

Whilst OLS is typically restricted to modelling continuous outcomes bound between $-\infty$ and $\infty$, in research one will often come across data where this is not the case. The most elementary extension is the binary (yes/no) outcome data.

This data takes the form of a yes/no (coded 1/0). Clearly, OLS runs into several problems. First and foremost (for your purposes) is the fact that you can predict outcomes outside of the range $[0,1]$. The simplest solution: logistic regression.

Logistic regression estimates the probability that $y=1$ conditional on your explanatory variables. It does this creating a mapping of your regression equation $\beta_0 + \beta_1 x$ on to the space $[0,1]$ by considering: $$\ln \left( \frac{P(y=1)}{1-P(y=1)} \right) = \beta_0 + \beta_1x$$ Depending on what data you can find (and what software you have available - for example EViews, R, Stata and SPSS all have built in routines for logistic regression) this might be an interesting way to proceed.

• (+1). Since the OP tells us in her profile that she studies Psychology, Discrete Outcomes models will be even more useful to her than classic linear regression. And indeed, although in Econometrics there is still a slight preference for the Probit model, outside Econometrics the use of the Logit model has literally exploded in the last 15 years. – Alecos Papadopoulos Sep 15 '15 at 14:51

For a list of methods used in applied econometrics you can take a look at the ReplicationWiki (that I work on). Many of them have data and code so you can easily try them out. (The example is with instrumental variables, replace this method in the search form with any other from the list to search for examples for them.)

I would recommend taking a copy of Stock and Watson's Introduction to Econometrics, which provides a fairly easy to grasp overview of many such techniques. A selection includes:

• binary outcome models (as mentioned by Alan): logit, probit, linear probability
• panel data models and fixed effects
• non-linear regression, including dummy variables and interaction effects
• instrumental variables and two-stage least squares models.