In all linear regression models, the intercept has the same definition: the mean of the response, Y, when all predictors, all X = 0.
But “when all X=0” has different implications, depending on the scale on which each X is measured and on which terms are included in the model.
So let’s specifically discuss the meaning of the intercept in some common models:
Recently I gave a webinar The Steps to Running Any Statistical Model. A few hundred people were live on the webinar. We held a Q&A session at the end, but as you can imagine, we didn’t have time to get through all the questions.
This is the first in a series of written answers to some of those questions. I’ve tried to sort them by the step each is about.
A written list of the steps is available here.
If you missed the webinar, you can view the video here. It’s free.
Yes. There’s no point in asking research questions that the data you have available can’t answer.
So the order of the steps would have to change—you may have to start with a vague idea of the type of research question you want to ask, but only refine it after doing some descriptive statistics, or even running an initial model.
You want to at least start thinking about them as you’re doing the lit review and formulating your research questions.
Think about how you could measure variables, which ones are likely to be collinear or have a lot of missing data. Think about the kind of model you’d have to do for each research question.
Think of a scenario where the same research question could be operationalized such that the dependent variable is measured either continuous or ordered categories. An easy example is income in dollars measured by actual income or by income categories.
By all means, if people can answer the question with a real and accurate number, your analysis will be much, much easier. In many situations, they can’t. They won’t know, remember, or tell you their exact income. If so, you may have to use categories to prevent missing data. But these are things to think about early.
I would start by putting the literature review before Step 1. You’ll use that to decide on a theoretical research question, as well as ways to operationalize it..
But it will help you other places as well. For example, it helps the sample size calculations to have variance estimates from other studies. Other studies may give you an idea of variables that are likely to have missing data, too little variation to include as predictors. They may change your exploratory factor analysis in Step 7 to a confirmatory one.
In fact, just about every step can benefit from a good literature review.
If you missed the webinar, you can view the video here. It’s free.
One area in statistics where I see conflicting advice is how to analyze pre-post data. I’ve seen this myself in consulting. A few years ago, I received a call from a distressed client. Let’s call her Nancy.
Nancy had asked for advice about how to run a repeated measures analysis. The advisor told Nancy that actually, a repeated measures analysis was inappropriate for her data.
Nancy was sure repeated measures was appropriate. This advice led her to fear that she had grossly misunderstood a very basic tenet in her statistical training.
Nancy had measured a response variable at two time points for two groups. The intervention group received a treatment and a control group did not. Participants were randomly assigned to one of the two groups.
The researcher measured each participant before and after the intervention.
Nancy was sure that this was a classic repeated measures experiment. It has (more…)
I don’t usually get into discussions here about the teaching of statistics, as that’s not really the point of this blog.
Even so, I found this idea fascinating, and since this blog is about learning statistics, I thought you may find it interesting as well.
The following is a TED talk by Arthur Benjamin, who is a math professor at Harvey Mudd College. Let me start by saying he is awesome. I already watched his Mathemagician TED talk with my kids*, so when I found this, I already expected it to be very good.
I wasn’t disappointed.
*if you too are on an active campaign to instill a love of math in your kids, I highly recommend it.
Here are two of my favorite quotes, keeping in mind that I took calculus in high school and I LOVED it. Even so, he’s got some really good points:
“Very few people actually use calculus in a conscious, meaningful way in their day-to-day lives. On the other hand, statistics–that’s a subject that you could, and should, use on a daily basis.”
“If it’s taught properly, it can be a lot of FUN. I mean, probability and statistics–it’s the mathematics of games and gambling, it’s…it’s analyzing trends, it’s predicting the future.”
If you find the video isn’t working, you can watch it directly on the TED site (this is the first time I’ve embedded a video). 🙂
If you’ve ever worked with multilevel models, you know that they are an extension of linear models. For a researcher learning them, this is both good and bad news.
The good side is that many of the concepts, calculations, and results are familiar. The down side of the extension is that everything is more complicated in multilevel models.
This includes power and sample size calculations. (more…)
Standardized regression coefficients remove the unit of measurement of predictor and outcome variables. They are sometimes called betas, but I don’t like to use that term because there are too many other, and too many related, concepts that are also called beta.
There are many good reasons to report them: