Posted by
parisec on
URL: http://spssx-discussion.165.s1.nabble.com/Follow-up-to-piecewise-regression-question-tp5668949p5681234.html
Bruce,
The correlation between age and time is negative up to around age 38, from age 38-50 it is slightly positive, then at age 51+ it is highly positive. I think this makes the function continuous. would you agree?
thanks
Carol
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
[hidden email]] On Behalf Of Bruce Weaver
Sent: Wednesday, May 02, 2012 4:54 AM
To:
[hidden email]
Subject: Re: Follow-up to piecewise regression question
Let me begin by echoing Ryan's disclaimer: I have no particular expertise in piece-wise regression. Having said that, it looks to me as if Ryan's model
allows for discontinuities at the cut-points between age groups. Does that
make sense in the context of your problem, Carol? Or do you want the function to be continuous at the cut-points? (I've not taken time to look at the website the example came from, so I don't know which way those folks specified their model.)
Re interpretation of the coefficients, I always find it helpful to make a plot of fitted values as a function of the main explanatory variables. In your case, this will show graphically the slopes (and intercepts if you
extrapolate) for Age within the various age groups, and help you map back to the coefficients.
HTH.
R B wrote
>
> Carol,
>
> It looks like you set up the model correctly, and that your
> interpretation of the slopes is correct. However, I don't see why you
> centered age at the grand mean. In addition to assessing for shifts in
> slopes from one age group to the next, isn't the purpose of piecewise
> regression to see if there is a shift in intercepts at the cutpoints?
> With that in mind, I would suggest that you NOT center age at any
> value before running the analysis.
> I
> repeat...I think you should enter age into the model in its original form.
> Then you can easily estimate and compare the intercepts at the
> appropriate age cutpoint for adjacent age groups using TEST statements. Concretely...
>
> According to your post, your cutpoints are 38 and 51. Therefore, I
> think you would want to estimate the intercepts at age=38 for age
> groups 1 and 2, and test whether they are significantly different from
> each other. How do you do this? Simple! Add the following TEST
> statements:
>
> /TEST = "int for grp 1 at age 38" group 1 0 0 group*age 38 0 0 /TEST =
> "int for grp 2 at age 38" group 0 1 0 group*age 0 38 0 /TEST = "diff
> in ints between grps 1 and 2 at age 38" group 1 -1 0 group*age 38 -38
> 0
>
> If you want to do the same for age groups 2 and 3, then you'd write
> the following TEST statements:
>
> /TEST = "int for grp 2 at age 51" group 0 1 0 group*age 0 51 0 /TEST =
> "int for grp 3 at age 51" group 0 0 1 group*age 0 0 51 /TEST = "diff
> in ints between grps 2 and 3 at age 51" group 0 1 -1 group*age 0 51
> -51
>
> The full MIXED code, including the above intercept TEST statements
> **AND** slope TEST statements would look like this:
>
> MIXED y BY group WITH age
> /FIXED=group group*age | NOINT SSTYPE(3) /METHOD=REML
> /PRINT=SOLUTION /TEST = "int for grp 1 at age 38" group 1 0 0
> group*age 38 0 0 /TEST = "int for grp 2 at age 38" group 0 1 0
> group*age 0 38 0 /TEST = "diff in ints between grps 1 and 2 at age
> 38" group 1 -1 0 group*age 38 -38 0 /TEST = "int for grp 2 at age 51"
> group 0 1 0 group*age 0 51 0 /TEST = "int for grp 3 at age 51" group
> 0 0 1 group*age 0 0 51 /TEST = "diff in ints between grps 2 and 3 at
> age 51" group 0 1 -1 group*age 0 51 -51 /TEST = "grp 1 slope"
> group*age 1 0 0 /TEST = "grp 2 slope" group*age 0 1 0 /TEST = "grp 3
> slope" group*age 0 0 1 /TEST = "diff in slopes between grp 1 and grp
> 2" group*age 1 -1 0 /TEST = "diff in slopes between grp 2 and grp 3"
> group*age 0 1 -1.
>
> A few points:
>
> (1) The group-specific slopes estimated from the TEST statements
> should equal the group*age interaction coefficients reported in the
> "Estimates of Fixed Effects" Table.
> (2) The code above is UNTESTED. I'm too busy right now to test the
> code above.
> (3) I am no expert in piecewise regression. I'm simply extrapolating
> from the two-category example provided on that website.
>
> HTH,
>
> Ryan
> On Tue, May 1, 2012 at 7:48 PM, Parise, Carol A.
> <PariseC@>wrote:
>
>> **
>> Ryan,
>>
>> This nailed it. When Bruce stated....
>>
>> ****************************************
>> If I followed, however, Ryan's model (see syntax below) included age
>> as
>> *both* a categorical variable (called Group) and a continuous
>> variable (age). The interaction of those two variables (group*age) is
>> what allows the slope for continuous age to vary by age group. That's
>> more or less the same thing you're trying to accomplish by using
>> piece-wise regression, right?
>>
>> MIXED y BY group WITH age
>>
>> /FIXED=group group*age | NOINT SSTYPE(3)
>>
>> /METHOD=REML
>>
>> /PRINT=SOLUTION.
>> ***************************************************
>> The lightbulb went on and i figured out why this made sense.
>
> --- snip ---
>
-----
--
Bruce Weaver
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