[R-sig-ME] Interpreting the coefficients of a main effect

[Sverre Stausland]

Hi Ted,

thanks for your comment. I understand your point, but let's for the
sake of argument assume that the p-value of the main effect is as
strong as desired.

My questions were about how to interpret the coefficients for the main
effect and its interactions (do you add them up to find the overall
effect of the main effect?) and how to do model comparisons (do you
compare the model with a model where both the main effect and its
interactions are removed?).

Thanks
Sverre

On Mon, Mar 7, 2011 at 6:27 PM, Charles E. (Ted) Wright
<cewright at uci.edu> wrote:
> It seems dicey to try to describe an "overall effect of reaction time" based
> on this analysis, given that p-value, which may be somewhat suspect, is only
> marginally significant, and that there are two important interactions with
> reaction time. I would certainly want to explore these interactions
> carefully -- are they ordinal or disordinal for example -- before trying to
> arrive at any summary.
>
> Ted Wright
>
> On Mon, 7 Mar 2011, Sverre Stausland 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.
>>
>> Question 1:
>> Is that the correct way to see the overall effect of ReactionTime?
>>
>> 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?
>>
>> 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?
>>
>> Thank you
>> Sverre
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>>
>
>