# Mixed Models and other new stuff

“I’m XX years old and I’ve never used (insert any statistical technique here). Why do I need to know this?”

I’ve heard some version of the above on every topic from linear regression to structural equation models, and at every age from teenagers to executives in their sixties. I’ve even made comments like that myself. All of those people, especially me, were wrong. Not in the “I’ve never used this”. I believe that. It is the implication that you wouldn’t use it if you knew it. I’ve never used my non-existent knowledge of Chinese and I got by when I was in Hongkong and Beijing and with the various Chinese people I have met, but if I had known Chinese I am sure I would have used it and probably learned a lot more interesting things about the places I went and people I met.

The same is true of statistics. Wednesday, I’m going to San Diego to a workshop for professors on mixed models using SAS. Now, I have used mixed models in the past and even gave a presentation it you can find on the presentations page on this site.Still, it’s probably been over a year since I did a mixed model. Survival analysis, plain vanilla ANOVA and regression and some flat out descriptive studies have been the order of the day, not to mention a lot of javascript.

Now that I’m going to San Diego, I’m seeing mixed models everywhere. For example, I am planning a study where we present students with instructional choices for a topic, say frequency distributions. The choices could be a web page, video, applet that lets you create distributions. Choices would vary in difficulty and quality (as rated in advance by me & some other people). My dependent variable in this case would be how much time the student spends reading, watching or playing with this resource. Student is going to be a repeated random effect here. Difficulty is a fixed effect, as is quality.

So … that is a mixed model.

I’m also looking at improvement in students who play our math game we’ve developed. There is a pretest and posttest, so that is the repeated factor. There is the group – intervention or comparison – so that’s a fixed factor. Other variables I could include are grade (fixed) or teacher (random). What if I included, though, how involved their teacher was with the students using the game, either (high- providing hints, made up a cheat sheet, taught the same material in class if she noticed students were having difficulty) , low (sat and read the newspaper) or moderate? Anyway you look at it, this could be a mixed model.

Then I got to thinking of something else where  I could have the type of instructional resource a student chose as a dependent variable, say a video, web page or some active option like a game or applet. Then I would do a multinomial logistic regression and have things like difficulty and quality as variables. However, the same student would be making lots of choices. Instead of 6,000 independent records, I might have 100 students each making an average of 60 choices during the game. In this case, I could use the generalized estimating equations (GEE) method to control for correlated observations. I definitely would not use PROC MIXED.

My point is that once I started thinking about mixed models, I started seeing where I could and couldn’t use them. Not only did this get me thinking about mixed models it also started me looking at other ways to work with repeated and random effects. I think the same would be true of almost any statistical technique.

Speaking of going to class … I try to do that whenever I can. I’ve been so swamped writing two grant proposals that it’s been impossible to get away for very long. So much so, that when the Joint Mathematical Meetings were in San Diego last week, I skipped the conference and just took a class.

A couple of years ago, I was at the Western Users of SAS Software conference and went to a class on survival analysis given by Gerry Hobbs. It was very good. A much younger colleague saw me and asked why I would be going to a class. He said,

“I’ve heard you give talks on survival analysis. Why would you go to a class by someone else?”

I thought the answer was obvious,

“Because I’m sure he knows some things I don’t, either details about the technique, about programming or about how to present it . And I want to learn.”

It reminded me years ago of when I was an assistant professor at Minot State University. I happened to be taking a class in microbiology because my friend, Nina Parker, was teaching it and I heard she was a great professor (she was). Another professor, in the chemistry department, was taking a French course at the same time. We both got the same startled reactions from other students. He said to me,

“One of them actually asked me, ‘You have a PhD, why are you taking an introductory French class?’ and I told her, To learn French!”

Learn new stuff. It’s not a strange concept. Really.