# Interpret contradicting output of lmer model with categorical interaction in R

I am struggling to interpret my output in R. It does not make sense to me.

I first regressed participants' ratings (= value) on manipulations (= variable: H high, AI high, H low, AI low, and control). I then checked whether this effect is moderated by the participants' experience (= Frequency :7 groups, the higher, the less experience). Frequency was added as an interaction factor in my model:

H4_mod <- lmer(value ~ variable * Frequency + (1|subject), data =
ANALYSIS_long, REML = FALSE)


Then, in order to find out whether the interaction effect is statistically significant, I compared the H4_mod with a reduced model:

red_H4_mod <- lmer(value ~ variable + Frequency + (1|subject), data =
ANALYSIS_long, REML = FALSE)


An ANOVA and a look at cAICs revealed that the interaction is statistically significant. So far, so good.

Now, I want to find out what the effect looks like. I predicted that the higher the experience, the lower the effect of the prediction (value ~ variable).

I get confused with the output I get from

summary(H4_mod)

Fixed effects:
Estimate Std. Error         df t value Pr(>|t|)
(Intercept)               6.846e+00  2.872e-01  8.334e+02  23.839  < 2e-16 ***
variable[T.2]             9.542e-01  3.223e-01  1.032e+03   2.960 0.003145 **
variable[T.3]            -8.000e-01  3.223e-01  1.032e+03  -2.482 0.013226 *
variable[T.4]             1.104e+00  3.223e-01  1.032e+03   3.426 0.000638 ***
variable[T.5]            -1.154e+00  3.223e-01  1.032e+03  -3.581 0.000359 ***
Frequency2                3.310e-01  3.739e-01  8.334e+02   0.885 0.376362
Frequency3                5.490e-01  3.650e-01  8.334e+02   1.504 0.132893
Frequency4               -5.164e-01  5.615e-01  8.334e+02  -0.920 0.358013
Frequency5                2.875e-01  6.421e-01  8.334e+02   0.448 0.654468
Frequency6                5.417e-02  6.043e-01  8.334e+02   0.090 0.928602
Frequency7               -1.156e+00  5.295e-01  8.334e+02  -2.183 0.029329 *
variable[T.2]:Frequency2 -3.397e-01  4.197e-01  1.032e+03  -0.809 0.418551
variable[T.3]:Frequency2 -4.087e-01  4.197e-01  1.032e+03  -0.974 0.330432
variable[T.4]:Frequency2 -5.592e-01  4.197e-01  1.032e+03  -1.332 0.183033
variable[T.5]:Frequency2 -2.545e-01  4.197e-01  1.032e+03  -0.606 0.544378
variable[T.2]:Frequency3 -5.901e-01  4.097e-01  1.032e+03  -1.440 0.150082
variable[T.3]:Frequency3  5.128e-03  4.097e-01  1.032e+03   0.013 0.990015
variable[T.4]:Frequency3 -4.837e-01  4.097e-01  1.032e+03  -1.181 0.238045
variable[T.5]:Frequency3  2.875e-01  4.097e-01  1.032e+03   0.702 0.482980
variable[T.2]:Frequency4  3.407e-02  6.303e-01  1.032e+03   0.054 0.956904
variable[T.3]:Frequency4  2.471e-01  6.303e-01  1.032e+03   0.392 0.695154
variable[T.4]:Frequency4  2.841e-01  6.303e-01  1.032e+03   0.451 0.652301
variable[T.5]:Frequency4  1.025e+00  6.303e-01  1.032e+03   1.626 0.104285
variable[T.2]:Frequency5 -5.708e-01  7.208e-01  1.032e+03  -0.792 0.428548
variable[T.3]:Frequency5 -2.250e+00  7.208e-01  1.032e+03  -3.122 0.001848 **
variable[T.4]:Frequency5 -1.288e+00  7.208e-01  1.032e+03  -1.786 0.074342 .
variable[T.5]:Frequency5 -1.413e+00  7.208e-01  1.032e+03  -1.960 0.050295 .
variable[T.2]:Frequency6 -1.970e-01  6.783e-01  1.032e+03  -0.290 0.771525
variable[T.3]:Frequency6 -9.714e-01  6.783e-01  1.032e+03  -1.432 0.152417
variable[T.4]:Frequency6 -3.327e-01  6.783e-01  1.032e+03  -0.491 0.623863
variable[T.5]:Frequency6 -1.203e+00  6.783e-01  1.032e+03  -1.773 0.076448 .
variable[T.2]:Frequency7  3.658e-01  5.944e-01  1.032e+03   0.616 0.538350
variable[T.3]:Frequency7 -6.000e-02  5.944e-01  1.032e+03  -0.101 0.919610
variable[T.4]:Frequency7  2.583e-02  5.944e-01  1.032e+03   0.043 0.965340
variable[T.5]:Frequency7  4.742e-01  5.944e-01  1.032e+03   0.798 0.425178
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Can someone explain it to me? The intercept is my control manipulation ("variable"), but what happened to Frequency 1? I read that only the Frequency 7 group has a significant impact on the relationship (value ~ variable). When I look further down at the (what I think) actual interaction effects, these are only significant for Frequency 5.

Furthermore, I tried to figure out the relationships by looking at an effects plot

e <- allEffects(H4_mod)
plot(e, multiline = TRUE, confint = TRUE, ci.style = "bars")


Unfortunately, this confuses me even more... Can someone help me interpreting the results? So far, I can only say that Frequency significantly interacts with the value ~ variable relationship. But I would love (and have) to make a statement about the direction.

THANK YOU!

• You have used the effects tag which refers to a specific R package (not to effects in general). If the tag does not belong here, I suggest to remove it. – Richard Hardy May 14 at 10:04
• Hej, thank you! For the effects plot, I used the effects package :) – Theresa May 14 at 10:14
• OK, then my comment is irrelevant. – Richard Hardy May 14 at 10:30