[R-sig-ME] Interpreting the coefficients of a main effect
Ista Zahn
izahn at psych.rochester.edu
Tue Mar 8 14:05:03 CET 2011
Hi Sverre,
I hope you'll forgive me if I get this wrong, but I don't think the
interpretation of the fixed effects differs much from regular
regression. See below.
On Mon, Mar 7, 2011 at 11:00 PM, Sverre Stausland
<johnsen at fas.harvard.edu> wrote:
> Hi mixed-models users,
>
> I am trying to interpret the coefficients I get from lmer models. In
> model A, I have these variables:
>
> Dependent variable:
> Correct response (0=incorrect, 1=correct)
>
> Independent variables:
> Trial (continuous)
> ReactionTime (continuous)
> Stimulus (binary: 'same' or 'different')
>
> Here is the output:
>
> Fixed effects:
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) 3.756272 1.344013 2.795 0.00519 **
> Trial 0.019962 0.007494 2.664 0.00773 **
> ReactionTime -2.354231 1.236785 -1.904 0.05697 .
> Stimulussame -5.364448 1.203831 -4.456 8.34e-06 ***
> Trial:ReactionTime -0.014469 0.006982 -2.072 0.03822 *
> Trial:Stimulussame -0.010312 0.002525 -4.085 4.41e-05 ***
> ReactionTime:Stimulussame 4.838763 1.105341 4.378 1.20e-05 ***
>
> I am curious about the overall effect of ReactionTime. If I understand
> it correctly, I should add the all the coefficients with ReactionTime
> in it to see that, i.e. (-2.25)+(-0.02)+4.84 = 2.57. In other words,
> slower responses give more accurate responses.
Describing an "overall" effect is bound to be misleading in the
presence of such a strong interaction. Your data are telling you that
the effect of ReactiontTime differs depending on the Stimulus. Why do
you insist that there must be a single number for an effect that is
clearly variable?
>
> Question 1:
> Is that the correct way to see the overall effect of ReactionTime?
No I don't think so. If you _really_ want average effects (and again,
I'm hard pressed to imagine why) then center your continuous
predictors and contrast-code (not dummy code!) your factors and re-run
the model including the interactions or interpret the value from model
B below.
>
> In model B, I do the same as above, but I leave out interactions with
> ReactionTime. Now I get this:
>
> Fixed effects:
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) 1.992515 0.598379 3.330 0.000869 ***
> Trial 0.006496 0.002061 3.152 0.001622 **
> ReactionTime -0.739240 0.452896 -1.632 0.102626
> Stimulussame -0.331084 0.353614 -0.936 0.349126
> Trial:Stimulussame -0.011652 0.002440 -4.776 1.79e-06 ***
>
> Question 2:
> How do I interpret the fact that the overall effect of ReactionTime in
> model A with interactions is positive, whereas the overall effect in
> model B without interactions is negative? Is the coefficient in model
> B simply not trustworthy as a result of leaving out significant
> interactions?
The ReactionTime coefficient is not a trustworthy estimate of the
"overall" effect in either model, given the strong interaction.
>
> Question 3:
> Normally I do model comparisons with anova to determine the effect of
> a variable. In model A, where I am curious about the significance of
> ReactionTime in predicting the dependent variable, should I compare
> model A (= the superset model) with a subset model where I remove the
> main effect ReactionTime _as well as_ all the interactions it is a
> part of?
I think that's a reasonable test.
>
> Thank you
> Sverre
>
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>
--
Ista Zahn
Graduate student
University of Rochester
Department of Clinical and Social Psychology
http://yourpsyche.org
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