I would like to make an interaction plot to visually display the difference or similarity in slopes of interaction of a categorical variable (4 levels) and a standardized continuous variable from the results of a regression model.
with(GLMModel, interaction.plot(continuous.var, categorical.var, response.var))
Is not what I am looking for. It produces a plot in which the slope changes for each value of the continuous variable. I'm looking to make a plot with constant slopes as in the following plot:
Any ideas?
I fit a model of the form fit<-glmer(resp.var ~ cont.var*cat.var + (1|rand.eff) , data = sample.data , poisson)
Here is some sample data:
structure(list(cat.var = structure(c(4L, 4L, 1L, 4L, 1L, 2L,
1L, 1L, 1L, 1L, 4L, 1L, 1L, 3L, 2L, 4L, 1L, 1L, 1L, 2L, 1L, 2L,
2L, 1L, 3L, 1L, 1L, 2L, 4L, 1L, 2L, 1L, 1L, 4L, 1L, 3L, 1L, 3L,
3L, 4L, 3L, 4L, 1L, 3L, 3L, 1L, 2L, 3L, 4L, 3L, 4L, 2L, 1L, 1L,
4L, 1L, 1L, 1L, 1L, 1L, 1L, 4L, 1L, 4L, 4L, 3L, 3L, 1L, 3L, 3L,
3L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 4L, 1L, 3L, 4L, 1L, 1L, 4L,
1L, 3L, 1L, 1L, 3L, 2L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 2L, 4L,
4L, 1L, 2L, 1L, 4L, 3L, 1L, 1L, 3L, 2L, 4L, 4L, 1L, 4L, 1L, 3L,
2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 4L, 1L,
2L, 2L, 1L, 1L, 2L, 3L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 3L, 2L, 4L,
1L, 3L, 1L, 1L, 4L, 4L, 2L, 4L, 1L, 1L, 3L, 4L, 2L, 1L, 3L, 3L,
4L, 3L, 2L, 3L, 1L, 4L, 2L, 2L, 1L, 4L, 1L, 2L, 3L, 4L, 1L, 4L,
2L, 1L, 3L, 3L, 3L, 4L, 1L, 1L, 1L, 3L, 1L, 3L, 4L, 2L, 1L, 4L,
1L, 1L, 1L, 2L, 1L, 1L, 4L, 1L, 3L, 1L, 2L, 1L, 4L, 1L, 2L, 4L,
1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 4L, 1L, 4L, 3L,
3L, 3L, 4L, 1L, 3L, 1L, 1L, 4L, 4L, 4L, 4L, 2L, 1L, 1L, 3L, 2L,
1L, 4L, 4L, 2L, 4L, 2L, 4L, 1L, 3L, 4L, 1L, 1L, 2L, 3L, 2L, 4L,
1L, 1L, 3L, 4L, 2L, 2L, 3L, 4L, 1L, 2L, 3L, 1L, 2L, 4L, 1L, 4L,
2L, 4L, 3L, 4L, 2L, 1L, 1L, 1L, 1L, 1L, 4L, 4L, 1L, 4L, 4L, 1L,
4L, 2L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 3L, 2L, 2L, 1L, 1L, 4L,
1L, 4L, 3L, 1L, 2L, 1L, 4L, 2L, 4L, 4L, 1L, 2L, 1L, 1L, 1L, 4L,
1L, 4L, 1L, 2L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 4L, 3L, 1L, 4L, 1L,
2L, 4L, 1L, 1L, 3L, 3L, 2L, 4L, 4L, 1L, 1L, 2L, 2L, 1L, 2L, 4L,
3L, 4L, 4L, 4L, 4L, 1L, 3L, 1L, 2L, 2L, 2L, 4L, 2L, 3L, 4L, 1L,
3L, 2L, 2L, 1L, 1L, 1L, 3L, 1L, 2L, 2L, 1L, 1L, 3L, 2L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 4L, 4L, 4L, 3L, 3L, 2L, 1L, 3L, 2L, 1L,
1L, 1L, 4L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 4L, 3L, 2L, 4L, 3L, 2L,
1L, 3L, 1L, 3L, 1L, 4L, 3L, 1L, 4L, 4L, 2L, 4L, 1L, 1L, 2L, 4L,
4L, 2L, 3L, 4L, 4L, 3L, 1L, 4L, 1L, 2L, 4L, 1L, 1L, 4L, 1L, 1L,
1L, 1L, 1L, 3L, 4L, 1L, 4L, 4L, 2L, 2L, 2L, 2L, 3L, 4L, 4L, 1L,
1L, 4L, 2L, 3L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 4L, 2L,
3L, 1L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 1L, 1L, 1L), .Label = c("A",
"B", "C", "D"), class = "factor"), cont.var = c(-0.0682900527296927,
0.546320421837542, -0.273160210918771, -0.887770685486005, 0.136580105459385,
0.75119058002662, 0.546320421837542, -0.273160210918771, -0.682900527296927,
0.136580105459385, 0.75119058002662, 0.75119058002662, 0.75119058002662,
0.341450263648464, 0.75119058002662, 0.546320421837542, 0.546320421837542,
-0.478030369107849, -0.478030369107849, -0.682900527296927, -0.682900527296927,
0.546320421837542, -0.478030369107849, -0.0682900527296927, 0.136580105459385,
0.136580105459385, 0.75119058002662, -0.478030369107849, 0.75119058002662,
-0.887770685486005, 0.136580105459385, -0.478030369107849, 0.341450263648464,
-0.682900527296927, -0.478030369107849, 0.341450263648464, -0.478030369107849,
0.546320421837542, 0.75119058002662, -0.478030369107849, -0.273160210918771,
0.546320421837542, -0.682900527296927, 0.75119058002662, -0.478030369107849,
-0.887770685486005, 0.136580105459385, -0.887770685486005, -0.0682900527296927,
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0.341450263648464, 0.546320421837542, -0.478030369107849, 0.136580105459385,
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0.546320421837542, 0.75119058002662, 0.546320421837542, 0.136580105459385,
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-0.0682900527296927, -0.0682900527296927, 0.546320421837542,
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-0.682900527296927, -0.478030369107849, -0.478030369107849, -0.682900527296927,
0.75119058002662, 0.341450263648464, -0.0682900527296927, 0.341450263648464,
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0.341450263648464, 0.136580105459385, -0.478030369107849, 0.136580105459385,
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-0.0682900527296927, 0.136580105459385, 0.546320421837542, -0.478030369107849,
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0.546320421837542, -0.0682900527296927, 0.75119058002662, -0.273160210918771,
0.546320421837542, 0.341450263648464, -0.0682900527296927, -0.0682900527296927,
-0.0682900527296927, -0.887770685486005, 0.136580105459385, -0.273160210918771,
-0.478030369107849, 0.75119058002662, 0.341450263648464, 0.546320421837542,
-0.273160210918771, 0.546320421837542, 0.75119058002662, -0.273160210918771,
0.75119058002662, 0.546320421837542, -0.273160210918771, -0.273160210918771,
0.75119058002662, -0.273160210918771, -0.0682900527296927, 0.136580105459385,
-0.478030369107849, 0.75119058002662, 0.75119058002662, -0.887770685486005,
-0.887770685486005, 0.546320421837542, -0.682900527296927, -0.887770685486005,
0.136580105459385, 0.75119058002662, 0.75119058002662, -0.478030369107849,
0.136580105459385, 0.75119058002662, -0.273160210918771, -0.682900527296927,
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-0.478030369107849, 0.136580105459385, -0.682900527296927, -0.0682900527296927,
-0.478030369107849, 0.136580105459385, -0.887770685486005, -0.273160210918771,
-0.0682900527296927, -0.273160210918771, -0.887770685486005,
0.546320421837542, 0.546320421837542, -0.478030369107849, -0.273160210918771,
-0.0682900527296927, 0.136580105459385, -0.478030369107849, 0.75119058002662,
0.341450263648464, 0.136580105459385, 0.136580105459385, 0.75119058002662,
0.136580105459385, -0.0682900527296927, 0.546320421837542, -0.0682900527296927,
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0.136580105459385, 0.136580105459385, -0.682900527296927, 0.341450263648464,
0.341450263648464, -0.273160210918771, -0.682900527296927, -0.0682900527296927,
0.75119058002662, -0.887770685486005, -0.478030369107849, -0.273160210918771,
-0.478030369107849, -0.478030369107849, 0.136580105459385, -0.478030369107849,
0.136580105459385, -0.478030369107849, 0.136580105459385, -0.0682900527296927,
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0.75119058002662, -0.682900527296927, 0.75119058002662, 0.75119058002662,
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0.136580105459385, 0.136580105459385, 0.136580105459385, 0.136580105459385,
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-0.887770685486005, -0.887770685486005, -0.0682900527296927,
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0.136580105459385, -0.478030369107849, -0.273160210918771, 0.136580105459385,
0.75119058002662, 0.546320421837542, -0.478030369107849, -0.273160210918771,
-0.273160210918771, 0.136580105459385, -0.273160210918771, -0.0682900527296927,
0.75119058002662, 0.136580105459385), resp.var = c(2L, 1L, 0L,
1L, 0L, 0L, 0L, 0L, 0L, 1L, 3L, 1L, 0L, 1L, 0L, 1L, 2L, 0L, 1L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 2L,
1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 2L,
0L, 3L, 2L, 0L, 2L, 2L, 0L, 0L, 0L, 1L, 1L, 3L, 1L, 2L, 0L, 1L,
0L, 0L, 1L, 0L, 2L, 0L, 2L, 4L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 2L,
3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 2L,
0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 2L, 0L, 1L, 0L, 4L, 1L, 0L,
1L, 1L, 0L, 0L, 0L, 1L, 3L, 0L, 2L, 0L, 0L, 2L, 1L, 0L, 0L, 2L,
0L, 0L, 0L, 2L, 0L, 0L, 3L, 0L, 0L, 2L, 1L, 1L, 0L, 0L, 3L, 1L,
1L, 2L, 0L, 2L, 0L, 2L, 2L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 2L, 2L, 1L, 0L, 0L, 1L,
0L, 0L, 0L, 0L, 6L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L,
1L, 0L, 0L, 1L, 3L, 1L, 0L, 2L, 3L, 0L, 0L, 1L, 0L, 0L, 1L, 1L,
0L, 0L, 0L, 0L, 1L, 2L, 1L, 1L, 0L, 0L, 2L, 0L, 2L, 0L, 0L, 1L,
1L, 0L, 0L, 2L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L,
0L, 1L, 0L, 2L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L,
0L, 3L, 0L, 0L, 3L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 2L, 1L, 1L, 0L, 2L, 2L, 0L, 2L, 1L, 0L, 2L, 0L, 0L, 0L, 0L,
3L, 0L, 2L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 2L, 0L, 1L, 1L, 0L, 1L,
0L, 3L, 1L, 3L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 2L, 0L,
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0L, 1L, 0L, 0L, 3L, 1L, 1L, 2L, 0L, 0L, 3L, 0L, 0L, 0L, 1L, 1L,
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1L, 2L, 0L, 2L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L,
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1L, 1L, 0L, 0L, 0L, 2L, 0L, 1L, 0L, 3L, 0L, 2L, 0L, 0L, 0L, 2L,
0L), rand.eff = c(37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L,
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43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L,
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L,
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L,
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43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L)), .Names = c("cat.var",
"cont.var", "resp.var", "rand.eff"), row.names = c(NA, 500L), class = "data.frame")
Here's an answer of sorts (by the way, you had some missing quotation marks in your data frame above, which had to be fixed manually ...)
Fit the model:
library(lme4)
fit <- glmer(resp.var ~ cont.var:cat.var + (1|rand.eff) ,
data = sample.data , poisson)
(Note that this is a slightly weird model specification -- forces all categories to have the same value at cont.var==0
. Did you mean cont.var*cat.var
?
library(ggplot2)
theme_update(theme_bw()) ## set white rather than gray background
Quick and dirty linear regressions:
ggplot(sample.data,aes(cont.var,resp.var,linetype=cat.var))+
geom_smooth(method="lm",se=FALSE)
Now with a Poisson GLM (but not incorporating the random effect), and showing the data points:
ggplot(sample.data,aes(cont.var,resp.var,colour=cat.var))+
stat_sum(aes(size=..n..),alpha=0.5)+
geom_smooth(method="glm",family="poisson")
The next bit requires the development (r-forge) version of lme4
, which has a predict
method:
Set up data frame for prediction:
predframe <- with(sample.data,
expand.grid(cat.var=levels(cat.var),
cont.var=seq(min(cont.var),
max(cont.var),length=51)))
Predict at population level (REform=NA
), on the linear predictor (logit) scale (this is the only way you will get straight lines on the plot)
predframe$pred.logit <- predict(fit,newdata=predframe,REform=NA)
minmaxvals <- range(sample.data$cont.var)
ggplot(predframe,aes(cont.var,pred.logit,linetype=cat.var))+geom_line()+
geom_point(data=subset(predframe,cont.var %in% minmaxvals),
aes(shape=cat.var))
Now on the response scale:
predframe$pred <- predict(fit,newdata=predframe,REform=NA,type="response")
ggplot(predframe,aes(cont.var,pred,linetype=cat.var))+geom_line()+
geom_point(data=subset(predframe,cont.var %in% minmaxvals),
aes(shape=cat.var))