# Binary interaction terms using lmer

I am trying to create a model using the lmer function. The model will contain the continuous response term "Average.profit" and explanatory terms "Type", "OtherType," and "Game" all 3 of which are binary. I also would like to include the two way interaction terms, these should have 4 possible levels {00,01,01,11} all of which I am interested in, As I would like to know if any of the 4 combinations increase or decrease "Average.profit". The model is below.

> m1<-lmer(Average.payoff~Game+Type+Others.Type+Type:Others.Type+Game:Others.Type+
Game:Type+(1|Subjects),REML=FALSE, data=Subjectsm1)

> m1
Linear mixed model fit by maximum likelihood
Formula: Average.payoff ~ Game + Type + Others.Type + Type:Others.Type +
Game:Others.Type + Game:Type + (1 | Subjects)
Data: Subjectsm1
AIC   BIC logLik deviance REMLdev
54.47 69.67 -18.24    36.47   49.83
Random effects:
Groups   Name        Variance Std.Dev.
Subjects (Intercept) 0.025177 0.15867
Residual             0.122703 0.35029
Number of obs: 40, groups: Subjects, 20

Fixed effects:
Estimate Std. Error t value
(Intercept)          0.6545     0.1746   3.749
Game1                0.2492     0.2088   1.193
Type1               -0.1675     0.2088  -0.802
Others.Type1        -0.5242     0.2088  -2.511
**Type1:Others.Type1  -0.2983**     0.2261  -1.319
Game1:Others.Type1   0.4500     0.2685   1.676
Game1:Type1          0.1733     0.2261   0.767

Correlation of Fixed Effects:
(Intr) Game1  Type1  Oth.T1 T1:O.T G1:O.T
Game1       -0.718
Type1       -0.718  0.435
Others.Typ1 -0.718  0.531  0.435
Typ1:Oth.T1  0.389 -0.108 -0.542 -0.542
Gm1:Othr.T1  0.461 -0.643 -0.129 -0.643  0.000
Game1:Type1  0.389 -0.542 -0.542 -0.108  0.000  0.000


From my understanding the boldsection shows that when Type=1 AND OtherType=1 the response variable decreases by -0.2983 compared to any of the other combinations of type and others type ie. 00,01 or 10. How then do I know about the effect of any of the other combinations of Type and OtherType ie. Does 01 result in a higher response variable than 10?

If this can't be shown from this model what information can I infer about the interaction between Type and OthersType?

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If the variable is a factor (you can make it so with as.factor()), it will not multiply them together - it will create a new factor that is the cross-product of the two. –  Macro Aug 16 '12 at 13:03
Thanks, worry over! yes the lmer function automatically coverts them to factor. –  Jonathan Bone Aug 16 '12 at 14:08
Sorry I'd like to ask an additional question to check I understand correctly. When I run the regression the print out gives me information for Type1:Other.Type1. I can therefore see the effect of having Type=1 and Other.Type =1 on the response variable compared to any of the other three combinations. How then can I tell if having the combination 0/0 is different to 1/0 etc? –  Jonathan Bone Aug 16 '12 at 15:11
Hi @Jonathan, I'm a little unclear on your question. I suspect itIt may help if you could edit your post to reflect this new question. Including the regression output would also be helpful. Your new questions sounds like it may be closely related to this recent answer by me, but I'm not quite sure. –  Macro Aug 16 '12 at 15:49
@Macro Thanks I have re-written my question and will look at your recent answer. –  Jonathan Bone Aug 16 '12 at 16:32
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