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

Sverre Stausland johnsen at fas.harvard.edu
Tue Mar 8 00:00:54 CET 2011

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

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

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