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# RE: st: centred mean age

 From Thomas Norris To "statalist@hsphsun2.harvard.edu" Subject RE: st: centred mean age Date Thu, 31 Jan 2013 09:13:20 +0000

```Dear Nick, Rich and David and statalisters,

Thank you very much for your advice. If I may clarify just so I can progress without doubt. I found that the best fitting multilevel model for my prenatal weight dataset was a cubic polynomial (tried fracpolys and spline). I then decided to centre the age term as it is not intuitive to have an intercept at 0 as, in prenatal life,  there should be nothing at zero.

I have created a dummy variable for ethnicity, to see if there are differences between two ethnic groups, and interacted this with age (pakage, pakage2,pakeage3) and centred age (in the centred model).

The coefficients in the uncentred model were:
Age: 0.256372
Age2: -0.0009669
Age3= -0.0000291
Pak= -0.5843112
Pakage= 0.0617149
Pakage2= -0.0021505
Pakage3= 0.0000234

In the uncentred model:
Age: 0.1062287
Age2: -0.0037464
Age3= -0.0000291
Pak= -0.0427686
Pakage= -0.0039254
Pakage2= 0.0000899
Pakage3= 0.0000234

As people have since told me, it is fine that the coefficients change value after the centreing, but the interactions between age and age2 and ethnicity have switched from positive to negative and vice versa, after centreing. Is this what one would expect?

Many thanks,

Tom

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
Sent: 30 January 2013 20:38
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: centred mean age

Please show us what is troubling you. (See the Statalist FAQ for advice on giving detailed, precise information.)

Nick

On Wed, Jan 30, 2013 at 8:32 PM,  <t.norris2@lboro.ac.uk> wrote:
> Hi Nick,
>
> Thank you for you reply.
>
> I was under the impression that the age coefficients in a centred model shouldn't be different to an uncentred model though, and mine change.
>
> Is this change therefore ok?
>
> Thank you,
>
> Tom
>
>
> Sent using BlackBerry® from Orange
>
> -----Original Message-----
> From: Nick Cox <njcoxstata@gmail.com>
> Sender: <owner-statalist@hsphsun2.harvard.edu>
> Date: Wed, 30 Jan 2013 20:20:48
> To: <statalist@hsphsun2.harvard.edu>
> Subject: Re: st: centred mean age
>
> Whether or not it helps in your model, I see no problem in what you
> describe. It's the way that linear, quadratic and cubic terms work
> together in a model that's important.
>
> All that said, there are quite possibly better ways of doing what you
> want, such as cubic splines or fractional polynomials, which are well
> supported in Stata.
>
> Nick
>
> On Wed, Jan 30, 2013 at 7:08 PM, Thomas Norris <T.Norris2@lboro.ac.uk> wrote:
>
>> I am having trouble with centering my independent variable (age) in a cubic polynomial.
>>
>> I have generated the centred age by using gen centrage= age-r(mean)
>> and then to get the centred quadratic and cubic I simple raise
>> centrage to ^2 and ^3 respectively (gen centrage2= centrage^2)(gen
>> gentrage3=centrage^3)
>>
>> However, the negative centred age terms (ie those smaller than the mean) become positive when squaring them, which is what is mathematically correct, but it doesn't help my models.
>>
>> If for example the mean was 30 weeks and I had 2 separate obs, one at 25 weeks and one at 35 weeks, the centred age would be -5 and 5, but the centred age^2 are both 25.

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