[R-sig-ME] Mean Centering Data in Linear Mixed Models

[Chris Howden]

As others have said which centring you use, if any, is based on how
you want to interpret the parameters and the results you are after.

A good example of when to do respondent centring is when you do
segmentations on survey data. Some people naturally rate high while
others rate low. If we don't do resp centring we almost always get a
segmentation with high vs low rates. Which is of little interest.

So in your example I suppose the question is what you want the grand
mean ie intercept to represent if the predictor is

1) zero (no centring)
2) at its average (overall centring)
3) at that resp's average (resp centring)
4) at the group average (group averaging),... Although I'm a little
unsure exactly how this would work and if there may be some unforeseen
consequences.


Chris Howden
Founding Partner
Tricky Solutions
Tricky Solutions 4 Tricky Problems
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On 24/08/2013, at 12:12, Joshua Wiley <jwiley.psych at gmail.com> wrote:

> Hi,
>
> Mean centering only changes the interpretation of the intercept; group mean
> centering changes the interpretation of the intercept and the slope
> coefficient.
>
> Which is appropriate, if either, is more of a substantive and
> interpretational issue.  To discuss issues like these, I would suggest
> seeking the advice of a local statistician or a statistical consultant.
>
> Cheers,
>
> Josh
>
>
>
>
>
> On Fri, Aug 23, 2013 at 6:43 PM, AvianResearchDivision <segerfan83 at gmail.com
>> wrote:
>
>> Hi,
>>
>> Thank you for the response.  I guess my question still is unanswered to a
>> certain degree.  I can see now that mean centering changes the
>> interpretation of the intercept and doing this is probably up to whomever
>> is performing the analysis.  In my situation, interpreting an intercept at
>> 0 dB ambient noise doesn't make much sense because that value probably
>> doesn't exist anywhere.  However, with my particular situation where I have
>> a fixed effect that has 12 levels with all 59 individuals divided up
>> unevenly within those levels, is grand mean centering the way to go or is
>> group mean centering?  I suppose I can't decide because I can't imagine a
>> scenario where group mean centering would be warranted.  With either group
>> mean or grand mean, all that is being done is subtracting a mean from a
>> value, correct?  I've read some papers (Kontiainen et al. 2009) where they
>> did this and then divided the result by the overall standard deviation of
>> that variable.
>>
>> Thank you!
>>
>>
>> On Fri, Aug 23, 2013 at 9:13 PM, Joshua Wiley <jwiley.psych at gmail.com>wrote:
>>
>>> Hi,
>>>
>>> Mean centering will only change the interpretation of the intercept, and
>>> could be done easily using (for example):
>>>
>>> scale(mtcars$mpg, scale=FALSE)
>>>
>>> Group mean centering, so that each individual has mean 0 changes things
>>> as this is no longer just adding a constant.  A higher score then is
>>> relative to each individuals' mean, not to an absolute value.
>>>
>>> This can be accomplished using:
>>>
>>> mtcars <- within(mtcars, {
>>>  gmmpg <- ave(mpg, cyl, FUN = function(x) x - mean(x))
>>> })
>>>
>>> Cheers,
>>>
>>> Joshua
>>>
>>>
>>>
>>> On Fri, Aug 23, 2013 at 5:43 PM, AvianResearchDivision <
>>> segerfan83 at gmail.com> wrote:
>>>
>>>> Hi all,
>>>>
>>>> I have a data set that includes 1 predictor variable (ambient noise) that
>>>> is continuous and 2 predictor variables that are factors.  One of the
>>>> predictor variables has 12 levels, that has 59 individuals (random
>>>> effect)
>>>> grouped within (unevenly).  The question is, should I consider mean
>>>> centering my continuous predictor variable?  I know that interpretation
>>>> of
>>>> the model results means that the intercept and slope are based on ambient
>>>> noise of 0 dB.  If I do want to mean center my data, is there a specific
>>>> way I should do this because of the predictor variable that has
>>>> individuals
>>>> grouped within?  Thank you for your help.
>>>>
>>>>        [[alternative HTML version deleted]]
>>>>
>>>> _______________________________________________
>>>> R-sig-mixed-models at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>>
>>>
>>> --
>>> Joshua Wiley
>>> Ph.D. Student, Health Psychology
>>> University of California, Los Angeles
>>> http://joshuawiley.com/
>>> Senior Analyst - Elkhart Group Ltd.
>>> http://elkhartgroup.com
>
>
> --
> Joshua Wiley
> Ph.D. Student, Health Psychology
> University of California, Los Angeles
> http://joshuawiley.com/
> Senior Analyst - Elkhart Group Ltd.
> http://elkhartgroup.com
>
>    [[alternative HTML version deleted]]
>
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