Why centered variables

That question has a very complicated answer. Most of the time, though, binary variables are dummy coded. If they are, then they have a specific meaning that works well in interactions. So you can change that coding to something that resembles centering for very specific reasons.

But most of the time they are left as is. Your email address will not be published. Skip to primary navigation Skip to main content Skip to primary sidebar There are two reasons to center predictor variables in any type of regression analysis—linear, logistic, multilevel, etc. To make interpretation of parameter estimates easier. I was recently asked when is centering NOT a good idea?

For reason 2, centering especially helps interpretation of parameter estimates coefficients when: a you have an interaction in the model b particularly if that interaction includes a continuous and a dummy coded categorical variable and c if the continuous variable does not contain a meaningful value of 0 d even if 0 is a real value, if there is another more meaningful value such as a threshold point. So when NOT to center: 1. If all continuous predictors have a meaningful value of 0.

If you have no interaction terms involving that predictor. And if there are no values that are particularly meaningful. Learn the approach for understanding coefficients in that regression as we walk through output of a model that includes numerical and categorical predictors and an interaction.

Take Me to The Video! Thank you. Dear Karen, Is it necessary to create centered-mean variables for the dummy variables when you are creating interactions between two dummy variables? Kind regards, Michiel. Hi Steve, Similar to you, I also had some multilevel models in which Level 2 predictors became non-significant once these predictors were grand-mean centered.

Hello Karen, Good explanation, it was helpful to me. It can also change other coefficients if the centered variable is involved in an interaction.

Hi Lauren, Sure. Hi Yan, That question has a very complicated answer. Leave a Reply Cancel reply Your email address will not be published. In particular, it does not change the coefficients of any terms that involve the centered variable. In the example given above, centering x1 would change b0, b2, b3, and b As used here, "centering a variable at " means subtracting from all the scores on the variable, converting the original scores to deviations from.

So why not always center at the means, routinely? Three reasons. First, the main-effect coefficients of the uncentered variables may themselves be of interest. Centering in such cases would be counter-productive, since it changes the main-effect coefficients of other variables. Second, centering will make all the M[. Third, centering at a value such as the mean, that is defined by the distribution of the predictors as opposed to being chosen rationally, means that all coefficients that are affected by centering will be specific to your particular sample.

If you center at the mean then someone attempting to replicate your study must center at your mean, not their own mean, if they want to get the same coefficients that you got. The solution to this problem is to center each variable at a rationally chosen central value of that variable that depends on the meaning of the scores and does not depend on the distribution of the scores.

The significance of the overall effects may be tested by the usual procedures for testing linear combinations of regression coefficients. However, the results must be interpreted with care because the overall effects are not structural parameters but are design-dependent.

The structural parameters -- the regression coefficients uncentered, or with rational centering and the error variance -- may be expected to remain invariant under changes in the distribution of the predictors, but the overall effects will generally change.

The overall effects are specific to the particular sample and should not be expected to carry over to other samples with different distributions on the predictors. If an overall effect is significant in one study and not in another, it may reflect nothing more than a difference in the distribution of the predictors. In particular, it should not be taken as evidence that the relation of the dependent variable to the predictors is different in the two studies.

I have been going crazy with the same question, but i finally found the solution to your and my problem. Two options are available: 1. I want to see how muscle strength, affects bone mass and I want to take into account gender to see if it affects differently in girls and boys. The idea is that the higher the muscle strength the higher the bone mass. I therefore have:. My coefficients were. Constant: 0. Looking at this you might think that muscle is affecting bone negatively, but you have to think of your centred variables, not your original variables.

Applying these values to the equation:. Therefore the final results will be exactly the same. Sign up to join this community.

The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why could centering independent variables change the main effects with moderation? Ask Question. Asked 8 years, 3 months ago. Active 4 years, 3 months ago. The data set outputted from the proc means is shown below. As you can see, it has only one observation. The other thing to notice about this data set is that it has no variables in common with the original data set.

This makes merging it with the original data set somewhat more difficult. The steps needed to overcome this problem are explained just above the data set that performs the merge. If you try to merge the grand1 data set and the original test data set as you normally would, you will find that you have the values of m1 and m2 only for the first case, and missing values for the remaining 14 cases.

Hence, we need to use a do loop to assign the values of m1 and m2 to new variables, which we have called mean1 and mean2. Also, we need to use the retain statement to retain the values of mean1 and mean2 so that their values are not set to missing when the data step iterates the second time. We cannot just retain m1 and m2 , because that would be altering their values as we read them into the grand1merged data set, which is not allowed.

Finally, we calculate the grand mean centered variables that we want, grmscore1 and grmscore2. In the code below, four new variables are created: mean1 is the mean of score1 , mean2 is the mean of score2 , grandmc1 is the grand mean centered variable for score1 and grandmc2 is the grand mean centered variable for score2.

There may be times when you want to create an aggregate variable. An aggregate variable is one that aggregates data from a "lower level" to a "higher level". Hence, a new variable is created that is the mean of the test scores for each class.