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RE: st: RE: GLLAMM: logitic regression interaction non signficant but lincom gives signficant result


From   Kieran McCaul <kieran.mccaul@uwa.edu.au>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: GLLAMM: logitic regression interaction non signficant but lincom gives signficant result
Date   Sun, 20 May 2012 10:24:14 +0800

...

There is nothing confusing here.

Suppose I have some data and I run a series of regressions

(1) regress Y X
(2) regress Y X if G==0
(3) regress Y X if G==1
(4) regress Y G*X

In the first three regressions, the coefficient for X is the same - the slope of X is the same. 

Suppose my sample size is large enough that the X coefficient is statistically significant in all three regressions.
Regardless of this, however, the coefficient for the interaction term in (4) will be zero and not significant.

Alternatively, suppose I run the first regression and the coefficient of X is significant with p=0.05 exactly.
Suppose for half my sample G=0 and for the remainder, G=1, then the coefficients of X in (2) and (3), while still the same as in (1), will not be significant.  The coefficient for the interaction term in (4), however, will still be zero and not significant.

Statistical significance has nothing to do with the importance or otherwise of an effect nor does it have anything to do with whether or not an effect exists or not. 

As others have suggested, Andrew Gelman's paper deals with this.



-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Abdelouahid Tajar
Sent: Saturday, 19 May 2012 8:07 PM
To: statalist
Subject: RE: st: RE: GLLAMM: logitic regression interaction non signficant but lincom gives signficant result


Thanks Kieran,

I agree with your interpretation about the interaction term in general, this is exactly how I interpret results of an interaction, but there is a confusion in the results of my interaction term hence my email to the list.

If the two groups have different slopes, one significant and the other is non significant (or both both slopes are significant and one is significantly stepper than the other) then the interaction term should be significant otherwise a non significant interaction term means that the other group has a similar slope to the reference group. But my model shows that the interaction is non signficant the slpoe of time for the reference (group 0) is non significant but the time slope for group 1 is significant hence the confusion.

Regards,

Abdelouahid


----------------------------------------
> From: kieran.mccaul@uwa.edu.au
> To: statalist@hsphsun2.harvard.edu
> Date: Sat, 19 May 2012 12:44:07 +0800
> Subject: st: RE: GLLAMM: logitic regression interaction non signficant but lincom gives signficant result
>
> ...
>
> From your model, the effect of time in group=0 is:
>
> 0.0320535 (-.0165658, .0806729)
> and the effect in group=1 is:
> 0.0773718 (.034855, .1198886)
>
> The time effect for group=1 (0.0773718) lies inside the 95%CI of the time effect in group=0 and so difference between the two is not statistically significant.
>
> That's what the test of the interaction term is telling you. The interaction term is the difference between the two time effects. The null hypothesis being tested is that this difference is zero.
>
>
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Abdelouahid Tajar
> Sent: Friday, 18 May 2012 7:27 PM
> To: statalist
> Subject: st: GLLAMM: logitic regression interaction non signficant but lincom gives signficant result
>
>
> Hi,
>
> I run the following random-intercept logistic regression model for an outcome
> with binomial distribution using gllamm with an interaction between the two covariates in the model: group (binary variable:1/0) and time, treated as continuous, (4 8 12 16 20 24)
>
>
> y is the number of success out of the number of trials : total_y
>
>
> I got result from the interaction term to be non significant (beta=.0453183,p= 0.169), time effect for reference group (group=0) non signficant (0.032,p=0.196), while the lincom result gives a significant slope for group=1 (.0773718,p<0.001). Please see results below, data presented on the log scale.
>
> This may not necessary be related to gllamm and could have another explanation,but I can not find a raison for this confusion at the moment, I would be thankful for any comments or suggestions from the list.
>
>
> Abdelouahid
> *-------------------------Gllamm model---------------*
>
>
>
> xi: gllamm y i.group*time,i(id_n) link(logit) family(binomial) denom(total_y) nip(30) adapt
>
>
>
> *--------results for fixed effects---------*
>
>
>
>
>
>
>
> y Coef. Std.Err. z P>z [95% Conf. Interval]
>
> _group_1 .2725252 .8026569 0.34 0.734 -1.300653 1.845704
>
> time .0320535 .0248062 1.29 0.196 -.0165658 .0806729
>
> _IgroupXtime_1 .0453183 .0329514 1.38 0.169 -.0192653 .1099019
>
> _cons -5.649017 .6287469 -8.98 0.000 -6.881338 -4.416696
>
>
> *-------------------lincom to obtian the slpoe of time for group=1---*
>
>
> lincom time + _groupXtime_1
>
>
> y Coef. Std. Err. z P>z [95% Conf. Interval]
>
>
> (1) .0773718 .0216926 3.57 0.000 .034855 .1198886
> *
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