I know that I could use lm(a ~ (b + c + d)^2) in order to get all possible two-way interactions in a model, but I need only the interactions with a single predictor. Let's say I want the possible interaction of B + C + D with predictor E.
I've tried:
lmer(MyVar ~ (1|ID) + (B + C + D)^E, data = data, REML = F)
Error in terms.formula(formula, data = data) :
invalid power in formula
I know that I could hard code each interaction with either * or :, but I suppose there's a simple way to do that all at once, isn't there? Thanks in advance.
Peter already provided an answer in the comments, but just so there is a worked example here, I have used the carrots dataset from the lmerTest package to fit this kind of model.
#### Load Library ####
library(lmerTest)
#### Fit 3 Interactions with Predictor ####
fit <- lmer(Preference
~ (Work + Homesize + Age) * sens2
+ (1 + sens2 | Consumer),
data=carrots)
summary(fit)
This specific model has more than 12 parameters, so it gives a warning at the that it can't show the entire correlation matrix at the end:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula:
Preference ~ (Work + Homesize + Age) * sens2 + (1 + sens2 | Consumer)
Data: carrots
REML criterion at convergence: 3793
Scaled residuals:
Min 1Q Median 3Q Max
-3.5393 -0.5531 0.0221 0.6129 3.0304
Random effects:
Groups Name Variance Std.Dev. Corr
Consumer (Intercept) 0.194588 0.44112
sens2 0.002667 0.05164 0.30
Residual 1.070431 1.03462
Number of obs: 1233, groups: Consumer, 103
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 4.599943 0.269675 92.130730 17.057 <2e-16 ***
Work2 0.252784 0.215224 92.355377 1.175 0.2432
Work3 0.049107 0.202453 92.620270 0.243 0.8089
Work4 0.350115 0.241920 92.357943 1.447 0.1512
Work5 -0.172296 0.251901 92.336511 -0.684 0.4957
Work6 0.142940 0.306935 92.245988 0.466 0.6425
Work7 0.284870 0.222300 92.466369 1.281 0.2032
Homesize3 -0.210541 0.117745 92.054098 -1.788 0.0770 .
Age2 0.147557 0.258083 91.931134 0.572 0.5689
Age3 0.175345 0.244237 91.940161 0.718 0.4746
Age4 0.143185 0.286984 91.891878 0.499 0.6190
sens2 -0.005156 0.048716 92.036870 -0.106 0.9159
Work2:sens2 -0.026848 0.038861 92.096571 -0.691 0.4914
Work3:sens2 0.025743 0.036536 92.167106 0.705 0.4828
Work4:sens2 0.020395 0.043681 92.097263 0.467 0.6417
Work5:sens2 0.041402 0.045486 92.091579 0.910 0.3651
Work6:sens2 0.041545 0.055435 92.076468 0.749 0.4555
Work7:sens2 -0.026257 0.040130 92.126134 -0.654 0.5145
Homesize3:sens2 0.034216 0.021273 92.017206 1.608 0.1112
Age2:sens2 0.050271 0.046641 91.984618 1.078 0.2839
Age3:sens2 0.049982 0.044137 91.986480 1.132 0.2604
Age4:sens2 0.098257 0.051868 91.973468 1.894 0.0613 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation matrix not shown by default, as p = 22 > 12.
Use print(x, correlation=TRUE) or
vcov(x) if you need it
Since this may be common for models that have a lot of interaction terms, you can simply follow the advice given with the warning and just run vcov(fit) to see the rest:
22 x 22 Matrix of class "dpoMatrix"
(Intercept) Work2 Work3 Work4
(Intercept) 0.0727247177 -2.460271e-02 -2.159223e-02 -2.485573e-02
Work2 -0.0246027147 4.632157e-02 2.731653e-02 2.605219e-02
Work3 -0.0215922283 2.731653e-02 4.098720e-02 2.751607e-02
Work4 -0.0248557275 2.605219e-02 2.751607e-02 5.852536e-02
Work5 -0.0188462642 2.535069e-02 2.746376e-02 2.638325e-02
Work6 -0.0590599021 2.577976e-02 2.074795e-02 2.352827e-02
Work7 -0.0196165301 2.525230e-02 2.745152e-02 2.594625e-02
Homesize3 -0.0109607544 -3.400679e-04 3.870252e-03 2.706524e-03
Age2 -0.0407749626 -6.515489e-03 -1.335698e-02 -4.201862e-03
Age3 -0.0494575617 -7.385083e-04 -7.919796e-03 -3.694373e-03
Age4 -0.0511840024 -5.047503e-04 -6.213891e-03 -8.488546e-04
sens2 0.0017103436 -5.694673e-04 -4.960309e-04 -5.737888e-04
Work2:sens2 -0.0005694673 1.082713e-03 6.301142e-04 6.007327e-04
Work3:sens2 -0.0004960308 6.301141e-04 9.510769e-04 6.326784e-04
Work4:sens2 -0.0005737887 6.007327e-04 6.326785e-04 1.367865e-03
Work5:sens2 -0.0004311883 5.838187e-04 6.310805e-04 6.061557e-04
Work6:sens2 -0.0013903112 5.995643e-04 4.776545e-04 5.446369e-04
Work7:sens2 -0.0004495020 5.815462e-04 6.308496e-04 5.958678e-04
Homesize3:sens2 -0.0002555305 -1.271474e-05 8.614862e-05 5.884019e-05
Age2:sens2 -0.0009699655 -1.494199e-04 -3.104255e-04 -9.394093e-05
Age3:sens2 -0.0011767009 -1.158708e-05 -1.805710e-04 -8.082443e-05
Age4:sens2 -0.0012155754 -8.270833e-06 -1.427594e-04 -1.592515e-05
Work5 Work6 Work7 Homesize3
(Intercept) -1.884626e-02 -5.905990e-02 -1.961653e-02 -1.096075e-02
Work2 2.535069e-02 2.577976e-02 2.525230e-02 -3.400679e-04
Work3 2.746376e-02 2.074795e-02 2.745152e-02 3.870252e-03
Work4 2.638325e-02 2.352827e-02 2.594625e-02 2.706524e-03
Work5 6.345422e-02 1.792640e-02 3.446007e-02 2.839939e-03
Work6 1.792640e-02 9.420917e-02 1.785281e-02 1.291156e-03
Work7 3.446007e-02 1.785281e-02 4.941720e-02 4.034687e-03
Homesize3 2.839939e-03 1.291156e-03 4.034687e-03 1.386395e-02
Age2 -7.707013e-03 3.230279e-02 -7.764027e-03 -1.515922e-03
Age3 -1.021223e-02 4.033104e-02 -9.334598e-03 2.906882e-03
Age4 -1.878498e-02 4.116822e-02 -2.475574e-02 4.240265e-03
sens2 -4.311884e-04 -1.390312e-03 -4.495020e-04 -2.555306e-04
Work2:sens2 5.838188e-04 5.995648e-04 5.815462e-04 -1.271468e-05
Work3:sens2 6.310805e-04 4.776551e-04 6.308496e-04 8.614867e-05
Work4:sens2 6.061557e-04 5.446375e-04 5.958678e-04 5.884025e-05
Work5:sens2 1.483935e-03 4.114916e-04 7.971930e-04 6.188087e-05
Work6:sens2 4.114910e-04 2.207829e-03 4.096409e-04 2.535023e-05
Work7:sens2 7.971929e-04 4.096415e-04 1.151554e-03 9.018370e-05
Homesize3:sens2 6.188081e-05 2.535036e-05 9.018363e-05 3.267278e-04
Age2:sens2 -1.768088e-04 7.730782e-04 -1.781380e-04 -3.387819e-05
Age3:sens2 -2.350601e-04 9.623697e-04 -2.142697e-04 7.102571e-05
Age4:sens2 -4.406804e-04 9.803703e-04 -5.821051e-04 1.018839e-04
Age2 Age3 Age4 sens2
(Intercept) -4.077496e-02 -4.945756e-02 -5.118400e-02 0.0017103436
Work2 -6.515489e-03 -7.385083e-04 -5.047503e-04 -0.0005694673
Work3 -1.335698e-02 -7.919796e-03 -6.213891e-03 -0.0004960309
Work4 -4.201862e-03 -3.694373e-03 -8.488546e-04 -0.0005737888
Work5 -7.707013e-03 -1.021223e-02 -1.878498e-02 -0.0004311884
Work6 3.230279e-02 4.033104e-02 4.116822e-02 -0.0013903117
Work7 -7.764027e-03 -9.334598e-03 -2.475574e-02 -0.0004495020
Homesize3 -1.515922e-03 2.906882e-03 4.240265e-03 -0.0002555306
Age2 6.660707e-02 4.917829e-02 4.874852e-02 -0.0009699654
Age3 4.917829e-02 5.965166e-02 5.751230e-02 -0.0011767008
Age4 4.874852e-02 5.751230e-02 8.235963e-02 -0.0012155754
sens2 -9.699654e-04 -1.176701e-03 -1.215575e-03 0.0023732002
Work2:sens2 -1.494201e-04 -1.158717e-05 -8.270915e-06 -0.0008009534
Work3:sens2 -3.104256e-04 -1.805711e-04 -1.427594e-04 -0.0007021649
Work4:sens2 -9.394109e-05 -8.082452e-05 -1.592525e-05 -0.0008088714
Work5:sens2 -1.768090e-04 -2.350602e-04 -4.406805e-04 -0.0006125030
Work6:sens2 7.730783e-04 9.623699e-04 9.803704e-04 -0.0019275339
Work7:sens2 -1.781381e-04 -2.142698e-04 -5.821052e-04 -0.0006376798
Homesize3:sens2 -3.387822e-05 7.102570e-05 1.018839e-04 -0.0003572095
Age2:sens2 1.574981e-03 1.162241e-03 1.152849e-03 -0.0013328873
Age3:sens2 1.162241e-03 1.410198e-03 1.360446e-03 -0.0016167476
Age4:sens2 1.152849e-03 1.360446e-03 1.949606e-03 -0.0016727270
Work2:sens2 Work3:sens2 Work4:sens2 Work5:sens2
(Intercept) -5.694673e-04 -4.960308e-04 -5.737887e-04 -4.311883e-04
Work2 1.082713e-03 6.301141e-04 6.007327e-04 5.838187e-04
Work3 6.301142e-04 9.510769e-04 6.326785e-04 6.310805e-04
Work4 6.007327e-04 6.326784e-04 1.367865e-03 6.061557e-04
Work5 5.838188e-04 6.310805e-04 6.061557e-04 1.483935e-03
Work6 5.995648e-04 4.776551e-04 5.446375e-04 4.114916e-04
Work7 5.815462e-04 6.308496e-04 5.958678e-04 7.971930e-04
Homesize3 -1.271468e-05 8.614867e-05 5.884025e-05 6.188087e-05
Age2 -1.494201e-04 -3.104256e-04 -9.394109e-05 -1.768090e-04
Age3 -1.158717e-05 -1.805711e-04 -8.082452e-05 -2.350602e-04
Age4 -8.270915e-06 -1.427594e-04 -1.592525e-05 -4.406805e-04
sens2 -8.009534e-04 -7.021649e-04 -8.088714e-04 -6.125030e-04
Work2:sens2 1.510208e-03 8.888542e-04 8.476685e-04 8.246902e-04
Work3:sens2 8.888542e-04 1.334852e-03 8.949241e-04 8.931412e-04
Work4:sens2 8.476685e-04 8.949241e-04 1.908065e-03 8.579816e-04
Work5:sens2 8.246902e-04 8.931412e-04 8.579816e-04 2.068938e-03
Work6:sens2 8.398725e-04 6.749491e-04 7.659950e-04 5.829051e-04
Work7:sens2 8.214882e-04 8.927538e-04 8.437191e-04 1.121775e-03
Homesize3:sens2 -1.207554e-05 1.252882e-04 8.732358e-05 9.165766e-05
Age2:sens2 -2.118283e-04 -4.351115e-04 -1.361084e-04 -2.505820e-04
Age3:sens2 -2.290075e-05 -2.572678e-04 -1.193013e-04 -3.321938e-04
Age4:sens2 -1.572527e-05 -2.020783e-04 -2.686406e-05 -6.127763e-04
Work6:sens2 Work7:sens2 Homesize3:sens2
(Intercept) -1.390311e-03 -0.0004495020 -2.555305e-04
Work2 5.995643e-04 0.0005815462 -1.271474e-05
Work3 4.776545e-04 0.0006308496 8.614862e-05
Work4 5.446369e-04 0.0005958678 5.884019e-05
Work5 4.114910e-04 0.0007971929 6.188081e-05
Work6 2.207829e-03 0.0004096415 2.535036e-05
Work7 4.096409e-04 0.0011515535 9.018363e-05
Homesize3 2.535023e-05 0.0000901837 3.267278e-04
Age2 7.730783e-04 -0.0001781381 -3.387822e-05
Age3 9.623699e-04 -0.0002142698 7.102570e-05
Age4 9.803704e-04 -0.0005821052 1.018839e-04
sens2 -1.927534e-03 -0.0006376798 -3.572095e-04
Work2:sens2 8.398725e-04 0.0008214882 -1.207554e-05
Work3:sens2 6.749491e-04 0.0008927538 1.252882e-04
Work4:sens2 7.659950e-04 0.0008437191 8.732358e-05
Work5:sens2 5.829051e-04 0.0011217754 9.165766e-05
Work6:sens2 3.072991e-03 0.0005804819 4.112908e-05
Work7:sens2 5.804819e-04 0.0016104051 1.306882e-04
Homesize3:sens2 4.112908e-05 0.0001306882 4.525614e-04
Age2:sens2 1.056816e-03 -0.0002524409 -4.911036e-05
Age3:sens2 1.318931e-03 -0.0003035236 9.540544e-05
Age4:sens2 1.345904e-03 -0.0008078267 1.388138e-04
Age2:sens2 Age3:sens2 Age4:sens2
(Intercept) -9.699655e-04 -1.176701e-03 -1.215575e-03
Work2 -1.494199e-04 -1.158708e-05 -8.270833e-06
Work3 -3.104255e-04 -1.805710e-04 -1.427594e-04
Work4 -9.394093e-05 -8.082443e-05 -1.592515e-05
Work5 -1.768088e-04 -2.350601e-04 -4.406804e-04
Work6 7.730782e-04 9.623697e-04 9.803703e-04
Work7 -1.781380e-04 -2.142697e-04 -5.821051e-04
Homesize3 -3.387819e-05 7.102571e-05 1.018839e-04
Age2 1.574981e-03 1.162241e-03 1.152849e-03
Age3 1.162241e-03 1.410198e-03 1.360446e-03
Age4 1.152849e-03 1.360446e-03 1.949606e-03
sens2 -1.332887e-03 -1.616748e-03 -1.672727e-03
Work2:sens2 -2.118283e-04 -2.290075e-05 -1.572527e-05
Work3:sens2 -4.351115e-04 -2.572678e-04 -2.020783e-04
Work4:sens2 -1.361084e-04 -1.193013e-04 -2.686406e-05
Work5:sens2 -2.505820e-04 -3.321938e-04 -6.127763e-04
Work6:sens2 1.056816e-03 1.318931e-03 1.345904e-03
Work7:sens2 -2.524409e-04 -3.035236e-04 -8.078267e-04
Homesize3:sens2 -4.911036e-05 9.540544e-05 1.388138e-04
Age2:sens2 2.175354e-03 1.606007e-03 1.592130e-03
Age3:sens2 1.606007e-03 1.948116e-03 1.878419e-03
Age4:sens2 1.592130e-03 1.878419e-03 2.690248e-03