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November 6th, 2015

### How to Use Regression Analysis Effectively

So, you want to use regression analysis in your paper? While statistical modeling can add great authority to your paper and to the conclusions you draw, it is also easy to use incorrectly.

The worst case scenario can occur when you think you’ve done everything right and therefore reach a strong conclusion based on an improperly conceived model. This guide presents a series of suggestions and considerations that you should take into account before you decide to use regression analysis in your paper.

The best regression model is based on a strong theoretical foundation that demonstrates not just that A and B are related, but why A and B are related.

Before you start, ask yourself two important questions: is your research question a good fit for regression analysis? And, do you have access to good data?

### 1. Is Your Research Question a Good Fit for Regression Analysis?

This depends on many different factors. Are you trying to explain something that is primarily described by numerical values? This is a key question to ask yourself before you decide to use regression. Although there are various ways to use regression analysis to describe non-numerical outcomes (e.g., dichotomous yes/no or probabilistic outcomes), they become more complicated and you will need to have a much deeper understanding of the underlying principles of regression in order to use them effectively.

Before you start, consider whether or not your dependent variable is numerical. Some examples:

• Number of years a politician serves in Senate
• Life expectancy
• Age at birth of first child

At the same time, you need to make sure that there is sufficient variation in your dependent variable and that the variation occurs in a normal pattern.

For example, you would have a problem if you tried to predict the likelihood of someone being elected as president because almost no one is elected as president. As a result, there is virtually no variation on the dependent variable.

Before you can conduct any type of analysis, you need a good data set. Not all data sets are easily suited to regression analysis without considerable manipulation.

Some things to consider before you decide to use regression:

• Are most of your independent variables numerical in nature? The best data set for regression will have variables that are primarily described by numbers that vary on a continuous scale. On the other hand, if most of your variables are categorical, you might consider using a different method of analysis (e.g., Chi-squared).
• Are there enough cases (n) in your data set? Particularly if you think you might use multiple regression, where multiple independent variables are used to predict a single dependent variable, you need to have a sufficient number of cases in your sample to obtain significant results. A general rule of thumb is that you need at least 20 cases per independent variable in your model. So if your model includes 5 independent variables, you need a minimum of 100 cases.

Keep in mind that your independent variables need to meet the same criteria for normality and variability as your dependent variable.

Once you decide to proceed with a regression model in your analysis, there are a three key concepts to keep in mind as you design your model to avoid making an easily preventable mistake that could send your conclusions way off track.

• Parsimony
• Internal Validity
• Multicollinearity

Each is described in more detail below.

### Parsimony

In statistics, the principle of parsimony is based on the idea that when possible, the simplest model with the fewest independent variables should be used when a model with more variables offers only slightly more explanatory value. In other words, one should not add variables to a model that do not increase the ability of the model to explain something.

Only add variables to a model if they significantly increase the ability of the model to explain something.

If you add too many variables to your model, you can unwittingly introduce major problems to your analysis.

In the extreme case, you must consider that your R2 value will always increase with the addition of new variables: so if you examine R2 alone, you can be duped into thinking that you have a great model simply by dumping in more and more predictor variables.

There are two good ways to address this problem: use an Adjusted R2 to compare models with different numbers of predictors, and use stepwise regression to analyze the explanatory impact of each variable as it is added to the model.

• Adjusted R2 takes into consideration the number of variables used in the model, and only increases when the addition of a new variable explains more than would random chance alone. So although a model with 10 variables might have a very high R2 value, the Adjusted R2 could actually be much lower than a model with fewer variables. Selecting your model based on Adjusted R2 helps you select a more parsimonious model that is less likely to have other problems (e.g., see multicollinearity below).
• Stepwise Regression is a computational method of assessing the additional explanatory value of each variable as they are added to the model in different orders. It can be used to parse out superfluous variables from a model, however it needs to be used carefully and in concert with theoretical guidance to avoid overfitting your data.

A good rule of thumb as you consider different models is that you should always have a good reason to add a predictor variable to your model, and if you can’t come up with a good theoretical explanation as to why A influences B, then leave out A!

### Internal Validity

Internal validity is the degree to which one factor can be said to cause another factor based on three basic criteria:

1. Temporal precedence, i.e., the “cause” precedes the “effect.”
2. Covariation, i.e., the “cause” and “effect” are demonstrably related.
3. Nonspuriousness, i.e., there are no plausible alternative explanations for the observed covariation caused by a confounding variable.

In many cases, internal validity becomes an issue in the form of a “chicken and egg” problem.

For example, let’s say you are considering the relationship between obesity and depression (a common example). If you want to include depression as an independent variable to explain obesity in your model, you first need to consider the question:

If you have no clear theoretical guidance to show that, in fact, depression usually precedes obesity (temporal precedence), you could introduce a significant problem to your model if the relationship is in fact the other way around: depression being the result of obesity.

Therefore, as you craft your model it is important to have a theoretical basis for the inclusion of each variable.

### Multicollinearity

Multicollinearity occurs when the independent variables in a multiple regression model are highly correlated with one another. This can be a problem in several ways:

• It reduces the parsimony of your model if the two variables are highly similar (e.g., two different variables that effectively measure the same thing);
• Multicollinearity can lead to erratic changes in the coefficients (measured effect) of predictor variables;
• As a result, it can be difficult to interpret the results of a model with high multicollinearity among predictors. Specifically, it becomes impossible to discern the individual effect of different regressors.

An example of variables that are going to be highly multicollinear are any variables that effectively measure the same thing. One way to show this, for the purposes of an example, is to imagine converting categorical data into a series of binary variables.

Any variables that effectively measure the same concept are likely to have high collinearity.

For example, let’s say that we have a variable measuring memory where respondents are able to choose very good, average, or poor as a response.

One way to use this data in a regression model would be to convert the data into three dichotomous (yes/no) variables indicating a person’s response.

However, if you then include all of these dichotomous variables in your model, you will have a big problem because they will become perfectly multicollinear. This is because anyone who indicated that they had a very good memory, by default, also indicated that they do not have a poor memory. The two variables measure the same thing: a person’s memory.

Another common example can be found in the use of height and weight variables. Although the two variables measure different things, broadly speaking they can both be said to measure a person’s body size, and they will almost always be highly correlated.

As a result, if both variables are included as predictors in a model, it can be difficult to discern the effect that each variable has individually on the outcome (measured by the coefficient).

Thus, as you build your model, you need to be aware of the potentially confounding impact of using highly similar predictor variables. In an ideal model, all independent variables will have no or very low correlation to each other, but a high correlation with the dependent variable.

### Conclusion: Use Regression Effectively by Keeping it Simple

Regression analysis can be a powerful explanatory tool and a highly persuasive way of demonstrating relationships between complex phenomena, but it is also easy to misuse if you are not an expert statistician.

If you decide to use regression analysis, you shouldn’t ask it to do too much: don’t force your data to explain something that you otherwise can’t explain!

Moreover, regression should only be used where it is appropriate and when their is sufficient quantity and quality of data to give the analysis meaning beyond your sample. If you can’t generalize beyond your sample, you really haven’t explained anything at all.

Lastly, always keep in mind that the best regression model is based on a strong theoretical foundation that demonstrates not just that A and B are related, but why A and B are related.

If you keep all of these things in mind, you will be on your way to crafting a powerful and persuasive argument.

March 10th, 2015

### Finding Balance in Graduate School

In the darkest days of the graduate school “doldrums,” as you wade through readings and midterms and papers, it can be hard to recall why exactly you decided to go to grad school in the first place. Even though you might feel like you can hardly find time to breathe, the truth is you can make time for relaxing, catching a movie, spending time with your partner, or whatever else you enjoy — if you try.

How can you balance graduate school with enjoying your personal life? Here are five things you can try:

1. Schedule School Like A 9-to-5

Grad school can often feel like a 24/7 job where you need to be thinking about your research, coursework, and teaching all the time in order to compete in the academic job market. Not so!

If you discipline yourself, you can work a semi-regular “shift” and still make time for dating, relaxing, and hobbies. Figure out when your most productive daytime hours are, and schedule 8-10 working hours during that time. If you stay on task during these hours, you can feel good about shutting it down to enjoy some personal time.  Of course there will always be emergencies and last-minute deadlines, but by scheduling working shifts you can actually minimize their occurrence and lead a more ‘normal’ day-to-day life.

1. Make Working Time Productive

Procrastination during your scheduled hours will drag work into your personal time, so you need to find strategies to stay productive and on task. Download an app that blocks time-wasting websites; write from a computer with internet disabled; meditate or go for a walk – whatever you have to do to stay on task.

Schedule short breaks every 60 to 90-minutes so that you stay energized and give your brain some relief.

1. Set Goals & Reward Yourself

If you’ve ever had a pet, you know how effective small rewards can be. But you are trainable, too! Set realistic goals for yourself and then reward yourself when you meet them. Small rewards for finishing tasks or meeting goals can go a long way toward keeping you motivated. Figure out what you respond to – a Starbucks coffee? A homemade cookie? A night out dancing? – and reward yourself when you meet set goals. The more that you give yourself rewards, the more you will be willing to meet your own goals when you set them.

1. Schedule Personal Time

Some people dislike the idea of penciling in their partners or setting aside a block of time for pleasure reading – but given how graduate school work tends to expand to fill all of your time, scheduling off chunks of time to take care of your personal needs might be the smartest way to make sure they don’t get constantly sidelined. So schedule yourself some free time, put your school work away, and indulge.  You’ll find that the more you allow yourself to refresh your brain, the more you will actually get done when it’s time to work – because your mind will be focused on work, and not how tired of working you are.

1. Banish the Guilt

It’s easy to envision yourself working productively around the clock to finish academic obligations or publish one more paper. The flip side is that you often guilt yourself when you aren’t working – you think that any minute you spend relaxing could be spent working! But the truth is, even if you love your research area, it’s easy to get “burned out” in academia.

If you work around the clock, you can get disillusioned and discouraged. The more exhausted you are mentally and spiritually with your work, the harder it is over the long-term for you to produce high-quality scholarship. You have to take breaks in order to produce your best work.

Divest yourself from the guilt that graduate school can bring. Whenever you feel guilty for spending time on non-work things, mentally change the subject and remind yourself that it’s OK to spend time relaxing and recharging – even more, it’s healthy.

So divest yourself from the guilt that graduate school can bring. Whenever you feel guilty for spending time on non-work things, mentally change the subject and remind yourself that it’s OK to spend time relaxing and recharging – even more, it’s healthy.  This is a “fake it ’til you make it” kind of thing – you will have to actively pretend you don’t feel guilty at first. Spend more time focused on producing the highest quality work and less time on berating yourself. Beating yourself up is never productive anyway! So stay positive and learn to focus on a positive reinforcement-based schedule. The more you do this, the less guilt you will eventually learn to feel during time off.