Regression models

Concepts in Linear Regression to know before learning Multilevel Models

November 21st, 2023 by

Are you learning Multilevel Models? Do you feel ready? Or in over your head?

It’s a very common analysis to need to use. I have to say, learning it is not so easy on your own. The concepts of random effects are hard to wrap your head around and there is a ton of new vocabulary and notation. Sadly, this vocabulary and notation is not consistent across articles, books, and software, so you end up having to do a lot of translating.

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Member Training: Linear Model Assumption Violations: What’s Next?

June 30th, 2023 by

What do you do if the assumptions of linear models are violated?
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Member Training: Interactions in Poisson and Logistic Regression

May 1st, 2023 by

Interactions in statistical models are never especially easy to interpret. Throw in non-normal outcome variables and non-linear prediction functions and they become even more difficult to understand. (more…)


Dummy Coding in SPSS GLM–More on Fixed Factors, Covariates, and Reference Groups

March 22nd, 2023 by

Stage 2If you have a categorical predictor variable that you plan to use in a regression analysis in SPSS, there are a couple ways to do it.

You can use the SPSS Regression procedure.  Or you can use SPSS General Linear Model–>Univariate, which I discuss here. If you use Syntax, it’s the UNIANOVA command.

The big question in SPSS GLM is what goes where.  As I’ve detailed in another post, any continuous independent variable goes into covariates.  And don’t use random factors at all unless you really know what you’re doing.

 

So the question is what to do with your categorical variables.  You have two choices, and each has advantages and disadvantages.

The easiest is to put categorical variables in Fixed Factors.  SPSS GLM will dummy code those variables for you, which is quite convenient if your categorical variable has more than two categories.

However, there are some defaults you need to be aware of that may or may not make this a good choice.

The dummy coding reference group default

SPSS GLM always makes the reference group the one that comes last alphabetically.

So if the values you input are strings, it will be the one that comes last.  If those values are numbers, it will be the highest one.

Not all procedures in SPSS use this default so double check the default if you’re using something else. Some procedures in SPSS let you change the default, but GLM doesn’t.

In some studies it really doesn’t matter which is the reference group.

But in others, interpreting regression coefficients will be a whole lot easier if you choose a group that makes a good comparison such as a control group or the most common group in the data.

If you want that to be the reference group in SPSS GLM, make it come last alphabetically.  I’ve been known to do things like change my data so that the control group becomes something like ZControl.  (But create a new variable–never overwrite original data).

It really can get confusing, though, if the variable was already dummy coded–if it already had values of 0 and 1.  Because 1 comes last alphabetically, SPSS GLM will make that group the reference group and internally code it as 0.

This can really lead to confusion when interpreting coefficients.  It’s not impossible if you’re paying attention, but you do have to pay attention. It’s generally better to recode the variable so that you don’t confuse yourself. And while you may believe you’re up for overcoming the confusion, why make things harder on yourself or with any other colleague you’re sharing results with?

Interactions among fixed factors default

There is another key default to keep in mind. GLM will automatically create interactions between any and all variables you specify as Fixed Factors.

If you put 5 variables in Fixed Factors, you’ll get a lot of interactions. SPSS will automatically create all 2-way, 3-way, 4-way, and even a 5-way interaction among those 5 variables.

That’s a lot of interactions.

In contrast, GLM doesn’t create by default any interactions between Covariates or between Covariates and Fixed Factors.

So you may find you have more interactions than you wanted among your categorical predictors. And fewer interactions than you wanted among numerical predictors.

There is no reason to use the default. You can override it quite easily.

Just click on the Model button. Then choose “Custom Model.”  You can then choose which interactions you do, or don’t, want in the model.

If you’re using SPSS syntax, simply add the interactions you want to the /Design subcommand.

So think about which interactions you want in the model. And take a look at whether your variables are already dummy coded.

 


Interpreting the Intercept in a Regression Model

February 21st, 2023 by

Interpreting the Intercept in a regression model isn’t always as straightforward as it looks.

Here’s the definition: the intercept (often labeled the constant) is the expected value of Y when all X=0. But that definition isn’t always helpful. So what does it really mean?

Regression with One Predictor X

Start with a very simple regression equation, with one predictor, X.

If X sometimes equals 0, the intercept is simply the expected value of Y at that value. In other words, it’s the mean of Y at one value of X. That’s meaningful.

If X never equals 0, then the intercept has no intrinsic meaning. You literally can’t interpret it. That’s actually fine, though. You still need that intercept to give you unbiased estimates of the slope and to calculate accurate predicted values. So while the intercept has a purpose, it’s not meaningful.

Both these scenarios are common in real data. (more…)


Member Training: The Link Between ANOVA and Regression

January 31st, 2023 by

Stage 2If you’ve used much analysis of variance (ANOVA), you’ve probably heard that ANOVA is a special case of linear regression. Unless you’ve seen why, though, that may not make a lot of sense. After all, ANOVA compares means between categories, while regression predicts outcomes with numeric variables.ANOVA chart (more…)