Linear Regression Analysis - 3 Common Causes of Multicollinearity and What Do to About Them

Multicollinearity in regression is one of those issues that strikes fear into the hearts of researchers. You've heard about its dangers in statistics classes, and colleagues and journal reviews question your results because of it.

Multicollinearity is simply redundancy in the information contained in predictor variables. If the redundancy is moderate, it usually only affects the interpretation of regression coefficients. But if it is severe-at or near perfect redundancy, it causes the model to "blow up." (And yes, that's a technical term).

But the reality is that there are only five situations where it commonly occurs. And three of them have very simple solutions. These are:

1. Improper dummy coding.

When you change a categorical variable into dummy variables, you will have one fewer dummy variable than you had categories. That's because the last category is already indicated by having a 0 on all other dummy variables. Including the last category just adds redundant information, resulting in multicollinearity. So always check your dummy coding if it seems you've got a multicollinearity problem.

2. Including a predictor that is computed from other predictors.

For example, I once had a client who was trying to test if larger birds had higher probability of finding a mate. This bird had a special tail, and he wondered if the size of the whole bird or the tail was more helpful to the bird in finding a mate. To compare them, he put three measures of size into the model: Body length, tail length, and total length of bird. Total length was the sum of the first two. The model blew up. Include two, but not all three.

3. Using the same or nearly the same variable twice.

A similar situation occurs when two measures of the same concept are included in a model. Sometimes researchers want to see which predicts an outcome better. For example, does personal income or household income predict stress level better? If they are both just measuring income, combine them into a single income variable using Principal Components Analysis.

And to get to the bottom of detecting and correcting for multicollinearity, I invite you to a free download of a 75-minute training audio when you go to The Analysis Factor website. Visit http://www.analysisfactor.com to get started today.

© 2008 Karen Grace-Martin - Statistical Consultant and founder of The Analysis Factor

Karen Grace-Martin has helped social science researchers practice statistics for 9 years, as a statistical consultant at Cornell University and in her own business. She knows the kinds of resources and support that researchers need to practice statistics confidently, accurately, and efficiently, no matter what their statistical background. To answer your questions, receive advice, and view a list of resources to help you learn and apply appropriate statistics to your data, visit http://www.analysisfactor.com

The Top 4 Things You Won't Miss - If You Do Your Degree Online

Time at university is an important rite of passage, and one that many consider to be 'the most fun years of your life'. Today, however, the temptation to do your degree online seems to get stronger for young people and mature students alike - whether it's for the sake of convenience, saving money, or simply because more subjects become available to study each year. Whilst reflecting on my time at university, there were certainly many great times, but I realised quickly that it wasn't for everybody...and to be honest, it wasn't all tequila slammin' and Monopoly tournaments. Here are four things you probably won't miss.

4. Halls. Yes, the social aspect of halls can be great, but these places are strange. Typically, there will be several students to one kitchen/living area...and that is usually a very small area which can cause some strain amongst comradeship if certain people aren't pulling their weight in regards to washing up etc. Most modern halls are fairly nice aesthetically, unlike the breeze-block monsters of the past, but if they have been lived in for more than a few years it will surely be hard to ignore the wear and tear. The two worst things about halls: 1. It's impossible to make your room homely. 2. There's a warden ...and he loves his authority.

3. Shared Housing. Surprisingly, shared housing has its own drawbacks. Firstly, it is far more likely that you'll have a nightmare landlord, and you may soon realise that your excellent rent deal might not be so excellent. For instance, electricity key metres are the most infuriating thing when you live in a house with several other people. Some housemates will pay at the right time, others won't...and there is nothing worse than waking up on a dark winter's morn in a house with no electricity. Actually there is, just think about how fun an electric shower can be when your metre's continually running on empty.

2. Transport. Transport problems certainly don't affect everybody (especially not if you're lucky enough to have your own car), but in certain areas they can be a nightmare. In my first year we had little reason to complain because bus travel was free for students. But by the second year, and with an increased influx of students, being packed into a First Great Western like a sardine whilst trying to finish your recommended reading is incredibly frustrating. But not as frustrating as not being picked up at all, which was also a regular occurrence.

1. Morning Lectures. I know what you're thinking, laziness, and yes you'd be right. But the fact of the matter is student life and being expected to be on top learning form at nine o'clock the next morning just doesn't make sense, especially after spending all night trying to make your room homely, then waking up in an electricity-less house, and then being left at the bus stop for an hour. Frankly, the option of being able to take your lecture at any time via online learning seems like the greatest advancement in higher education in recent years. In fact, I'll be surprised if, in the future, recorded lectures aren't made available for normal students who simply can't be bothered to attend early lectures.

Sarah Maple writes about adult education and education online.

Professors - Using Instructor-Directed Learning Methods - Whole Group Discussions Early in the Term

Students retain information most effectively when discussions are frequent, nonthreatening, lively, and mentally challenging. Leading discussions with all of these qualities is a significant challenge in contemporary classrooms, populated as they are by diverse students with varied experiences. Large classes are probably the major obstacle to orchestrating effective discussions. Some likely culprits that slow down discussions include:

• fear of embarrassment,
• lack of knowledge,
• low self-esteem,
• cultural issues that indicate you should be 'seen and not heard,' and the like
• the desire not to stick out from the crowd

You will want to work toward minimizing some of these concerns so that you have wider participation among those students who in the past may have been reluctant to participate actively in large-group discussions. You can probably relate to those reasons from your own experience, so be sensitive to your students' feelings. To achieve an atmosphere in which classroom discussions achieve their fullest potential, employ the following common sense practices:

• Break the class into groups of no more than five students (sometimes called buzz groups) to discuss a critical question. If you establish this type of grouping right from the beginning of your class, this is a comfortable format for them. You can have them pull chairs together, turn around in their seats (especially for fixed seating arrangements), or gather around their table.
• Decide what the purpose is for the small group. You want students to know what the outcome is supposed to be for their discussion. Often, many members of a class may be tuned out when you are establishing the purpose, so use words and written cues.
• Establish ground rules for discussion groups, such as "value all opinions" and "each member must participate." Many students know how to 'behave' in groups, but a few outspoken and socially inept students can shut down other members of their group in a hurry.
• Before discussion begins, have students introduce themselves to each other and select a spokesperson for reporting their collective conclusions. One of the reasons that I asked students to wear name tags throughout the semester in large classes was to help facilitate the use of names.
• Monitor the discussion within groups to ensure that students understand and follow the ground rules. You are constantly walking around among the different groups so that you know what is happening, where there might be questions, or which groups could use some additional direction.
• Prompt participation from all students by posing nonthreatening, open-ended questions. If you only ask yes-no questions or questions for which there is one and only one answer, some students will be afraid of being wrong. With more open-ended questions, you are likely to get not only more participation, but also the thinking and discussion you are working to elicit.
• Have each group report their findings in an orderly way, encouraging amplification of key points. Depending on the size of the entire class, you can have ALL groups report out, or just select a certain number.
• Summarize the overall activity, by citing appropriate points you heard within groups and asking for illumination from individuals making those points. It's never wise to assume that the students are summarizing for themselves. It's also smart to reinforce the key learning AND the reason that the learning was enhanced because of their discussions.

These strategies will assist you and your students as you get the semester or quarter off to a good start. Later in the term, you can continue to use these practices, however once they are established, it becomes more natural and effective for everyone.

Strategic professors know that using a variety of teaching and learning methods is critical to students' learning and success. Pay attention to the ideas in this article and others available from Meggin McIntosh. In addition, you can learn much more about teaching and reaching the many different types of students who are in today's college classroom by reading the book *Teaching College in an Age of Accountability* (Allyn & Bacon). The book was written by Richard Lyons & Meggin McIntosh (the author of this article).

To learn more ideas that you can use as a faculty member, be sure to check out http://www.TopTenProductivityTips.com and http://www.meggin.com

(c) 2008 by Meggin McIntosh, Ph.D., "The Ph.D. of Productivity"(tm). Through her company, Emphasis on Excellence, Inc., Meggin McIntosh changes what people know, feel, dream, and do. Sound interesting? It is!