Plotting 3-way interaction of factor variables using `lme4`

I'm looking for an elaboration on the amazing answer already provided about creating an interaction plot with a continuous and categorical variable using the predict function of the (development version) of the lme4 package.

I have run a model with an interaction between three categorical variables: discount_i (0/1), rank_i (0/1), and msg ("No norm","Provincial",and "Norm") including subject random effects (id). My outcome variable (choice) is dichotomous. Specifically, my command is:

```m1 <- glmer(choice ~ msg*discount_i*rank_i + (1|id), data=df, family="binomial")
```

I then create a prediction frame:

```predframe <- with(df,expand.grid(rank_i=levels(rank_i),msg=levels(msg),discount_i=levels(discount_i)))
```

And use the predict function (EDITED):

```predframe\$pred.logit <- predict(m1,newdata=predframe,REform=NA)
```

However, this is the point where I part ways with @mnel's instructions. How would I go about graphing the three way interaction between factor variables, rather than a two way interaction between a factor variable and a continuous variable?

Sample data below:

```> dput(df[1:700,2:6])
structure(list(time = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1), choice = c(1, 1,
1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0,
1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1,
1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0,
0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0,
0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1,
1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1,
1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1,
1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1,
1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,
1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1,
1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1,
1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0,
1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0,
1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1,
0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0,
0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1,
1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0,
1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1,
0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1,
1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1,
1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,
1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0,
0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1,
1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1,
1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0,
1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0,
1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0,
1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1,
1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1,
0, 1, 0, 1, 0), msg = structure(c(3L, 1L, 1L, 2L, 3L, 1L, 3L,
3L, 3L, 2L, 2L, 3L, 2L, 3L, 2L, 3L, 1L, 3L, 2L, 3L, 1L, 1L, 3L,
1L, 2L, 3L, 3L, 2L, 2L, 1L, 1L, 1L, 1L, 3L, 2L, 3L, 3L, 2L, 3L,
3L, 1L, 3L, 1L, 2L, 2L, 3L, 2L, 3L, 3L, 2L, 3L, 3L, 1L, 2L, 3L,
3L, 1L, 2L, 3L, 2L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 2L,
3L, 3L, 2L, 2L, 1L, 2L, 2L, 2L, 3L, 3L, 2L, 2L, 2L, 2L, 2L, 1L,
3L, 2L, 3L, 2L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 2L, 2L, 3L, 2L, 3L,
3L, 2L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 2L, 2L, 1L, 3L, 3L, 2L, 3L,
3L, 3L, 2L, 2L, 1L, 2L, 3L, 2L, 2L, 2L, 3L, 3L, 3L, 1L, 2L, 2L,
1L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L,
2L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 3L,
3L, 1L, 2L, 3L, 1L, 1L, 3L, 2L, 2L, 3L, 3L, 1L, 1L, 1L, 2L, 1L,
2L, 3L, 3L, 2L, 1L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 3L, 1L, 1L, 1L,
3L, 2L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 3L, 1L, 2L, 2L, 3L, 3L, 2L,
1L, 3L, 3L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 3L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 1L, 1L, 2L, 3L, 2L, 3L, 3L,
3L, 3L, 1L, 3L, 2L, 1L, 2L, 3L, 1L, 1L, 2L, 3L, 3L, 2L, 1L, 1L,
2L, 1L, 2L, 3L, 3L, 3L, 1L, 2L, 2L, 3L, 1L, 3L, 1L, 3L, 3L, 1L,
1L, 3L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 2L, 2L, 3L, 2L, 3L, 2L, 3L,
1L, 2L, 2L, 1L, 2L, 3L, 3L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 3L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 3L, 3L,
3L, 1L, 3L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 1L, 1L, 2L, 2L, 3L,
1L, 3L, 3L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 2L, 1L, 1L, 2L, 3L, 3L,
3L, 3L, 3L, 2L, 2L, 3L, 2L, 1L, 1L, 2L, 1L, 2L, 3L, 3L, 1L, 1L,
1L, 3L, 3L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 1L, 3L, 2L, 1L, 3L, 3L,
3L, 1L, 3L, 1L, 3L, 1L, 3L, 2L, 3L, 2L, 2L, 1L, 2L, 1L, 3L, 2L,
2L, 3L, 1L, 2L, 1L, 3L, 3L, 3L, 3L, 2L, 2L, 3L, 3L, 3L, 1L, 1L,
1L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 1L, 2L, 3L, 2L, 3L,
2L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 3L, 2L, 1L, 1L,
1L, 2L, 2L, 1L, 2L, 1L, 3L, 1L, 2L, 2L, 2L, 1L, 1L, 3L, 3L, 1L,
1L, 3L, 1L, 3L, 3L, 3L, 3L, 2L, 1L, 1L, 3L, 2L, 1L, 3L, 2L, 2L,
1L, 1L, 3L, 3L, 3L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 2L, 2L, 3L, 1L,
2L, 2L, 3L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 3L, 1L, 3L,
1L, 1L, 3L, 3L, 3L, 2L, 3L, 2L, 2L, 3L, 1L, 2L, 3L, 3L, 2L, 2L,
1L, 2L, 3L, 2L, 1L, 2L, 3L, 3L, 2L, 2L, 2L, 3L, 1L, 2L, 3L, 2L,
3L, 3L, 3L, 3L, 1L, 2L, 3L, 2L, 3L, 3L, 3L, 2L, 3L, 1L, 1L, 2L,
2L, 3L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 2L, 3L,
2L, 2L, 3L, 3L, 3L, 1L, 3L, 2L, 2L, 1L, 2L, 3L, 1L, 3L, 2L, 3L,
1L, 2L, 3L, 2L, 1L, 2L, 3L, 3L, 3L, 3L, 2L, 3L, 2L, 3L, 3L, 2L,
1L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 3L, 1L,
2L, 2L, 3L, 2L, 2L, 3L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 1L, 2L,
1L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 3L, 2L, 3L, 3L, 3L, 1L, 3L, 3L,
2L, 2L, 1L, 2L, 2L, 2L, 2L, 3L, 1L, 1L, 1L, 2L, 3L, 2L, 3L, 1L,
3L, 3L, 3L, 1L, 3L, 3L, 2L, 2L, 3L, 2L, 2L, 3L, 2L, 1L, 2L, 3L,
2L, 2L, 1L, 3L, 2L), .Label = c("No norm", "Norm", "Provincial"
), class = "factor"), discount_i = structure(c(1L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L,
2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L,
2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L,
1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L,
1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L,
1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L,
2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L,
1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L,
1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L,
2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L,
1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L,
2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L,
1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L,
1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L,
2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L,
1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L,
2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L), .Label = c("0", "1"), class = "factor"),
rank_i = structure(c(1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L,
2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L,
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```

Caveat: Have not added the ylab="" to the second overlaid plot call and you probably want to use a non-default ylab for the first one, too. Since the details of this analysis are still opaque to me, I am not standing behind its validity. (Just turning the crank on the machinery.) And there would need to be some further work on the legend. Furthermore, teh ylims were different so would probably want to set them to min and max for c(newpred0, newpred1).

```newpred0 <- predict(m1, newdata = predframe[predframe\$discount_i=="0", ] ,
REform = NA)
interaction.plot(droplevels(predframe[predframe\$discount_i=="0", ])\$rank_i,
droplevels(predframe[predframe\$discount_i=="0", ])\$msg,
newpred0)
newpred1 <- predict(m1, newdata = predframe[predframe\$discount_i=="1", ] ,
REform = NA)
par(new=TRUE);   # This is the way to overlay base graphics on top of each other
interaction.plot(droplevels(predframe[predframe\$discount_i=="1", ])\$rank_i,
droplevels(predframe[predframe\$discount_i=="1", ])\$msg, newpred1,
col="red")
```