z-standardizing and centering...are they the same?

#1
It would seem that peforming these preparatory measures to transform the data are the same. However, I have received differing opinions. I have been told that z transformations are optional and primarily useful for interpretation. While I understand the function, I cannot understand how utilizing standard deviation units which would be around the mean...which would then be 0 is any different than compunting new variables based on centering techniques. Does anyone have any thoughts on this? The ultimate and final goal is to compute regression interactions.

Daniel
 
#2
They are similar, but not the same.

In centering, you are changing the values, but not the scale. So a predictor that is centered at the mean has a new value of 0, but one unit is still one unit. The intercept will change, but the regression coefficient will not change for that variable. Since the regression coefficient is interpreted as the effect on the mean of Y for each one unit difference in X, it doesn't change when X is centered.

And incidentally, despite the name, you don't have to center at the mean. It is often convenient, but there can be advantages of choosing a more meaningful value that is also toward the center of the scale.

But a z score also changes the scale. A one-unit difference now means a one-standard deviation difference. You will interpret the coefficient differently. This is usually done so you can compare coefficients for predictors that were measured on different scales. I can't think of an advantage for doing this for an interaction.

Karen
 
#3
Why aren't my means = 0

That is what i was told by the 1 of the 2 i spoke with. The one that stated (nearly verbatim i might add) what you said is the higher level statistician.

So, Here's my next question. Why is it, having center all variables, that my Means in my descriptions (when conducting my regressions) are not '0'? Should not the 'new' mean be '0'? Thanks by the way for your help.
 
#4
Oh good. Always nice to have concurrence.

Which means are you getting in descriptives? I would think you'd have something like LSMeans, which are means of the DV, not the predictors.

Karen
 
#5
I'm running SPSS and I get my means in the descriptives in the beginning of/prior to the following analyses. It displays the means for all variables input into the model both predictors and outcomes. But, seeing how I centered all of them I wonder if i incorrectly centered them since they are not = 0.

Without "giving away the farm" (crossed out my variables) so to speak i have attached a paint file to give you an idea. Does this clarify?
 
#6
Daniel,

I'd have to look up how SPSS does it, but some of those could be rounding, but some seem a little far.

More likely is some observations got dropped due to missing data, so not everyone who was centered is in the analysis. I would check that.

And you shouldn't center categorical variables like Gender. Doesn't make sense and is not necessary.

Now I'm off to jury duty, so won't be here for a while....

Karen
 
#7
Daniel,

And you shouldn't center categorical variables like Gender. Doesn't make sense and is not necessary.


Karen
Well this is what I thought. But the way it was explained to me is that when a variable is categorical it is not centered around 0 but rather a +1, or +2 (i.e. Males/Females) However, when centered that turns the center to 0 with 1 above and 1 below. Interpretations are meaningless or are of little difference but I got the impression that changing the plot points affect the outcome. This notion of centering is a bit new to me. I was told to center all variables regardless if they were categorical or continuous. Thoughts?
 
#8
Well this is what I thought. But the way it was explained to me is that when a variable is categorical it is not centered around 0 but rather a +1, or +2 (i.e. Males/Females) However, when centered that turns the center to 0 with 1 above and 1 below. Interpretations are meaningless or are of little difference but I got the impression that changing the plot points affect the outcome. This notion of centering is a bit new to me. I was told to center all variables regardless if they were categorical or continuous. Thoughts?
If you mean that you are coding your two categories as +1 and -1, that makes sense. I'm not sure what you mean by centering around +1 or +2.

But if it makes sense to you and you're able to interpret your parameters, then it's probably just a coding scheme I haven't heard of. Dummy coding (0,1) and Effect coding (1, -1) are the most common, but others are certainly legitimate.

Karen
 
#9
Well, actually no. The purpose as explained to me by our department statistician indicated (or at least i interpreted it this way) that when categorical variables such as male and female are centered it moves the dummy coding from a 0/1 or 1/2 to -1 (male) o (nothing) and +1 (females). It makes no sense to me that this would affect the final variance accounted for or in my case being held constant. Maybe i misunderstood but i feel pretty sure he indicated all variables should be centered not just continuous ones. Again, seemed useless. However, I am going to run the analyses with the *** centered and without them centered to see if there is any difference. In theory, there should be no difference, right? Because the mean is only being shifted and no additional variance can/cannot be held constant or removed.
 
#10
Daniel,

I'd have to look up how SPSS does it, but some of those could be rounding, but some seem a little far.

More likely is some observations got dropped due to missing data, so not everyone who was centered is in the analysis. I would check that.
After thorough investigation you are right! Again! Interestingly, the center was different than 0 if data is missing. Not sure I want to try to understand that tonight. But, fact is that one response was not recorded and I had not replaced the value or excluded that case from the analyses. Back to the drawing board to rerun my analyses. At least I enjoy statistics and I am not pulling my hair out in anguish :D
 
#11
After thorough investigation you are right! Again!
LOL. It's amazing, isn't it? :) Just kidding.

Interestingly, the center was different than 0 if data is missing. Not sure I want to try to understand that tonight. But, fact is that one response was not recorded and I had not replaced the value or excluded that case from the analyses. Back to the drawing board to rerun my analyses. At least I enjoy statistics and I am not pulling my hair out in anguish :D
It really is fun when you're not staring at a brick wall, isn't it? I always thought of statistics as one big puzzle.

Here's the basic idea of why the mean isn't 0 if the data are missing. You calculate the mean, and it's 0. Now you take a few observations out and recalculate the mean. Now it's close to 0, but not exactly. That's all.

Karen