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Re: st: positive interaction - negative covariance


From   andrea pedrazzani <andrea.pedrazzani.piter@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: positive interaction - negative covariance
Date   Sat, 23 Feb 2013 11:58:50 +0100

Sorry, I misunderstoond the syntax. If I do as you suggest (using
-x-), I have two straight line, both with almost the same positive
slope. The first one (where the condition Z is absent) has a bit
higher intercept and is slightly steeper than the second (where the
condition is present).

As for the model, I meant a fractional logit. I am using

xi: glm DEPVAR    X  Z  X*Z  other-covariates   i.fixed-effects,
family(binomial) r

where DEPVAR is a fractional response variable.


Best,
Andrea

2013/2/23 Nick Cox <njcoxstata@gmail.com>:
> Correction. The code should end
>
> , ra(1 1764)
>
> On Sat, Feb 23, 2013 at 12:45 AM, Nick Cox <njcoxstata@gmail.com> wrote:
>> This is very confusing.
>>
>> 1. In terms of your previous statement of "a simple regression model"
>> you should have applied code like this, tailored to the special syntax
>> of -twoway function-.
>>
>> local b0 = 1.663478
>> local b1 = .0021067
>> local b2 = -.3692713
>> local b3 = -.0010758
>>
>> twoway function `b0' + `b1'*x, ra(1 1764) || ///
>>         function `b0' + (`b1' + `b3')*x + `b2', x(1 1764)
>>
>> after which the functions would appear as perfect straight lines; no
>> jaggedness is implied. The jaggedness is a consequence of using -dur-
>> when only -x- is allowed and needed. -x- is a generic x axis variable
>> and unrelated to any variable in the dataset.
>>
>> 2. But now you are telling us that it is a flogit model, a term I
>> don't recognise.
>>
>> I think you won't get good help if you don't explain clearly and
>> consistently what you are doing.
>>
>> Nick
>>
>> On Fri, Feb 22, 2013 at 10:50 PM, andrea pedrazzani
>> <andrea.pedrazzani.piter@gmail.com> wrote:
>>> Thank you very much Nick, Jay and David.
>>>
>>>
>>> My -x- is -dur-, whose range is from 1 to 1764.
>>> I plotted the two curves as you suggested me:
>>>
>>>
>>> local b0 = 1.663478
>>> local b1 = .0021067
>>> local b2 = -.3692713
>>> local b3 = -.0010758
>>>
>>> twoway function `b0' + `b1'*dur, ra(1 1764) || ///
>>>        function `b0' + (`b1' + `b3')*dur + `b2', ra(1 1764)
>>>
>>>
>>> The two functions have the same shape and are very close to each
>>> other. Both tend to slightly increase as -x- increases (the functions
>>> are really jagged, because -dur- has many values). The first one
>>> (where the condition Z is absent) is always a bit higher than the
>>> second (where the condition is present). If I am not wrong, this
>>> indicates that the impact of both on my dependent variable goes in the
>>> same (positive) direction.
>>>
>>>
>>> To Jay: my dependent variable is a proportion (I am using flogit)
>>>
>>>
>>> To David:
>>>> Thus, X has a positive impact on Y when Z is present and when Z is
>>>> absent, but those contributions are not significantly different.  That
>>>> is, the interaction is essentially absent.
>>>
>>> Thank you for clarifying the point. Indeed, if I compare the
>>> confidence interval of b1 to the confidence interval of (b1+b3), they
>>> are not statistically different. Is it the same? In a book I read, the
>>> authors make this comparison.
>>>
>>>
>>> 2013/2/22 David Hoaglin <dchoaglin@gmail.com>:
>>>> Dear Andrea,
>>>>
>>>> The basis for a statement about the interaction is the estimate of b3
>>>> and its standard error: After taking into account the contributions of
>>>> X and Z, the interaction is not significant (p = .245).
>>>>
>>>> Thus, X has a positive impact on Y when Z is present and when Z is
>>>> absent, but those contributions are not significantly different.  That
>>>> is, the interaction is essentially absent.
>>>>
>>>> A negative covariance between b1 and b3 is to be expected.
>>>>
>>>> You may want to remove XZ from the model.
>>>>
>>>> Regards,
>>>>
>>>> David Hoaglin
>>>>
>>>> On Fri, Feb 22, 2013 at 12:32 PM, andrea pedrazzani
>>>> <andrea.pedrazzani.piter@gmail.com> wrote:
>>>>> Hello,
>>>>>
>>>>> I have a simple regression model with an interaction: Y = b0 + (b1)X +
>>>>> (b2)Z + (b3)XZ.
>>>>> Z is a dummy (0 or 1).
>>>>>
>>>>> b1 = .0021067  (SE= .0008513 and p=0.013)
>>>>> b2 = -.3692713  (SE= .2329837 and p=0.113)
>>>>> b3 = -.0010758  (SE= .000926 and p=0.245)
>>>>>
>>>>> Hence, the combined coefficient (i.e., the coefficient on X when Z=1)
>>>>> is positive:
>>>>> b1+b3 =  .0021067 + -.0010758 = .0010309
>>>>>
>>>>> with SE = sqrt( var(b1) + var(b3)*(Z^2) + 2Z*cov(b1,b3)  )
>>>>>             = sqrt( .0000007246 + .0000008574*1 + -.0000007079*2 )
>>>>>             = .00040768
>>>>>
>>>>> To get the p-value for the combinet coefficient, I did
>>>>> .0010309/.00040768 = 2.528699.  The corresponding p = 0.0114.
>>>>>
>>>>> Summing up, X has a positive impact on Y when the condition Z is
>>>>> present (.0010309), and a positive impact also when the condition Z is
>>>>> not present (.0021067).
>>>>> So, what can I say about the interaction? What kind of interaction is
>>>>> it when the impact of X is positive both when the condition is present
>>>>> and when it is absent? Moreover, the coefficients b1 and (b1+b3) are
>>>>> very similar to each other.
>>>>> Also, both b1 and the combined coefficient (b1+b3) are positive, but
>>>>> the covariance between b1 and b3 is negative. It sounds strange to
>>>>> me...
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