http://spssx-discussion.165.s1.nabble.com/Follow-up-to-piecewise-regression-question-tp5668949p5680368.html
They specified it the way I did. See "try 3":
> 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
> 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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>
http://sites.google.com/a/lakeheadu.ca/bweaver/>
> "When all else fails, RTFM."
>
> NOTE: My Hotmail account is not monitored regularly.
> To send me an e-mail, please use the address shown above.
>
> --
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