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# Re: st: Question about interactions

 From David Hoaglin To statalist@hsphsun2.harvard.edu Subject Re: st: Question about interactions Date Mon, 4 Mar 2013 11:55:07 -0500

```Karin,

Together, the two 4-point scales would yield a total of 16 predictors
(each of which is an indicator variable for a combination of a
category of variable1 and a category of variable2).

In your model the combination of variable1=1 and variable2=1
corresponds to the constant term.

The combination of variable1=1 and variable2=2 corresponds to the
"main effect" for variable2=2 (and similarly for variable2=3 and
variable2=4).

The combination of variable1=2 and variable2=1 corresponds to the
"main effect" for variable1=2 (and similarly for variable1=3 and
variable1=4).

The coefficients for the other 9 combinations of a category of
variable1 and a category of variable2 appear under variable1#variable2
in the sketch of output that you included.

I hope this is helpful.

David Hoaglin

On Mon, Mar 4, 2013 at 11:30 AM, K Jensen <k.x.jensen@gmail.com> wrote:
> Sorry to try your patience but can I test my understanding here?
>
> The results for 1-2 (say) are calculated from the main effect betas
> for variable1=1 and variable2=2?
>
> Thankyou
> Karin
>
> On 4 March 2013 15:37, Maarten Buis <maartenlbuis@gmail.com> wrote:
>> On Mon, Mar 4, 2013 at 3:48 PM, K Jensen wrote:
>>> I am fitting two four-point scales as predictors in a logistic
>>> regression and am interested in looking at the interaction between the
>>> two.
>>>
>>> If I fit variable1##variable2 I get odds ratios for the following:
>>> variable1
>>>         2
>>>         3
>>>         4
>>> variable2
>>>         2
>>>         3
>>>         4
>>> variable1#
>>> variable2
>>> 2       2
>>> 2       3
>>> 2       4
>>> 3       2
>>> 3       3
>>> 3       4
>>> 4       2
>>> 4       3
>>> 4       4
>>>
>>> I obviously don't understand this because it doesn't include cells
>>> 1-2, 1-3, 1-4, 2-1, 3-1 or 4-1. Can someone explain this?
>>
>> For both variables the category 1 is the reference category and is
>> thus, together with its interaction terms, excluded. More on this, and
>> alternatives, can be seen here: M.L. Buis (2012) "Stata tip 106: With
>> or without reference", The Stata Journal, 12(1), pp. 162-164.
>> <http://www.maartenbuis.nl/publications/ref_cat.html>.
>>
>> -- Maarten
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