[R] Homogeneity of regression slopes

[Doug Adams]

That's good insight, and gives me some good ideas for what direction
to this.  Thanks everyone !

Doug

P.S. - I guess if you have a significant interaction, that implies the
slopes of the individual regression lines are significantly different
anyway, doesn't it...



On Tue, Sep 14, 2010 at 11:33 AM, Thomas Stewart <tgstewart at gmail.com> wrote:
> If you are interested in exploring the "homogeneity of variance" assumption,
> I would suggest you model the variance explicitly.  Doing so allows you to
> compare the homogeneous variance model to the heterogeneous variance model
> within a nested model framework.  In that framework, you'll have likelihood
> ratio tests, etc.
> This is why I suggested the nlme package and the gls function.  The gls
> function allows you to model the variance.
> -tgs
> P.S. WLS is a type of GLS.
> P.P.S It isn't clear to me how a variance stabilizing transformation would
> help in this case.
>
> On Tue, Sep 14, 2010 at 6:53 AM, Clifford Long <gnolffilc at gmail.com> wrote:
>>
>> Hi Thomas,
>>
>> Thanks for the additional information.
>>
>> Just wondering, and hoping to learn ... would any lack of homogeneity of
>> variance (which is what I believe you mean by different stddev estimates) be
>> found when performing standard regression diagnostics, such as residual
>> plots, Levene's test (or equivalent), etc.?  If so, then would a WLS routine
>> or some type of variance stabilizing transformation be useful?
>>
>> Again, hoping to learn.  I'll check out the gls() routine in the nlme
>> package, as you mentioned.
>>
>> Thanks.
>>
>> Cliff
>>
>>
>> On Mon, Sep 13, 2010 at 10:02 PM, Thomas Stewart <tgstewart at gmail.com>
>> wrote:
>>>
>>> Allow me to add to Michael's and Clifford's responses.
>>>
>>> If you fit the same regression model for each group, then you are also
>>> fitting a standard deviation parameter for each model.  The solution
>>> proposed by Michael and Clifford is a good one, but the solution assumes
>>> that the standard deviation parameter is the same for all three models.
>>>
>>> You may want to consider the degree by which the standard deviation
>>> estimates differ for the three separate models.  If they differ wildly,
>>> the
>>> method described by Michael and Clifford may not be the best.  Rather,
>>> you
>>> may want to consider gls() in the nlme package to explicitly allow the
>>> variance parameters to vary.
>>>
>>> -tgs
>>>
>>> On Mon, Sep 13, 2010 at 4:52 PM, Doug Adams <fog0 at gmx.com> wrote:
>>>
>>> > Hello,
>>> >
>>> > We've got a dataset with several variables, one of which we're using
>>> > to split the data into 3 smaller subsets.  (as the variable takes 1 of
>>> > 3 possible values).
>>> >
>>> > There are several more variables too, many of which we're using to fit
>>> > regression models using lm.  So I have 3 models fitted (one for each
>>> > subset of course), each having slope estimates for the predictor
>>> > variables.
>>> >
>>> > What we want to find out, though, is whether or not the overall slopes
>>> > for the 3 regression lines are significantly different from each
>>> > other.  Is there a way, in R, to calculate the overall slope of each
>>> > line, and test whether there's homogeneity of regression slopes?  (Am
>>> > I using that phrase in the right context -- comparing the slopes of
>>> > more than one regression line rather than the slopes of the predictors
>>> > within the same fit.)
>>> >
>>> > I hope that makes sense.  We really wanted to see if the predicted
>>> > values at the ends of the 3 regression lines are significantly
>>> > different... But I'm not sure how to do the Johnson-Neyman procedure
>>> > in R, so I think testing for slope differences will suffice!
>>> >
>>> > Thanks to any who may be able to help!
>>> >
>>> > Doug Adams
>>> >
>>> > ______________________________________________
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>>>
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>>>
>>> ______________________________________________
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>>
>
>