# [R-sig-ME] LMER - Plotting of a quadratic effect interacting with time

Fox, John j|ox @end|ng |rom mcm@@ter@c@
Thu Jan 31 20:56:42 CET 2019

```Dear Mathew,

> -----Original Message-----
> From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces using r-
> project.org] On Behalf Of Boden, Matthew T. via R-sig-mixed-models
> Sent: Wednesday, January 30, 2019 4:27 PM
> To: r-sig-mixed-models using r-project.org
> Subject: [R-sig-ME] LMER - Plotting of a quadratic effect interacting with time
>
> Hello,
>
> I have a question related to fitting and plotting a longitudinal linear mixed
> model that includes an interaction between a quadratic effect and time. Data
> attached.
>
> I fit the following:
>
> Q1 <- lmer(Patients ~ Time*FTE + Time*I(FTE^2) +  (FTE  | ID), data = SHARE)
>
> #Yes, the variables are on very different scales - will take care of that later
>
> I find a sizeable quadratic effect.
>
> Fixed effects:
>                 Estimate Std. Error t value
> (Intercept)    6.760e+03  5.347e+02  12.642
> Time           2.033e+01  1.011e+01   2.011
> FTE            9.728e+01  8.583e+00  11.335
> I(FTE^2)      -5.155e-01  4.000e-02 -12.890
> Time:FTE      -5.560e-01  2.254e-01  -2.467
> Time:I(FTE^2)  7.371e-03  1.052e-03   7.006
>
> To plot the quadratic interaction, I attempt to use the effects package.
> However, effects are displayed for Time x FTE, not time by FTE^2. Time x FTE
> is clearly not the plot that I want (I think...).
>
> e1 <- effect(term="Time:I(FTE^2)", mod=Q1)
> ed1<-as.data.frame(e1)
> ed1
>    Time FTE       fit        se     lower     upper
> 1     1  17  8277.635  464.3995  7366.770  9188.500
> 2     4  17  8316.650  463.3763  7407.792  9225.508
> ......
>
> I tried a workaround, by fitting a model that included FTE^2 as a second,
> calculated variable in the data set. Using the effects package, I do indeed
> obtain Time * FTE_sq.
>
> Q2 <- lmer(Patients ~ Time*FTE + Time*FTE_sq +  (FTE  | ID), data = SHARE)
>
> e2 <- effect(term="Time*FTE_sq", mod=Q2)
> ed2<-as.data.frame(e2)
> ed2
>
>    Time FTE_sq        fit        se      lower      upper
> 1     1    300 14678.1413  564.5423 13570.8582 15785.4243
> 2     4    300 14606.9253  563.3827 13501.9166 15711.9340
> ......
>
> But the plot does not at all look like what I would expect. All lines
> representing FTE_sq over time are straight.

Try, plot(Effect(c("Time", "FTE"), Q1)) .

More generally, why not fit the model as  Q1 <- lmer(Patients ~ Time*poly(FTE, 2) +  (FTE  | ID), data = SHARE)  or Q1 <- lmer(Patients ~ Time*poly(FTE, 2, raw=TRUE) +  (FTE  | ID), data = SHARE) ? Also, do you really want the linear term in FTE to be random and the quadratic term only fixed?

I hope this helps,
John

>
> ggplot(ed2, aes(x=Time, y=fit, color=FTE_sq,group=FTE_sq)) +
>    geom_point() +
>    geom_line(size=1.2) +
>    labs(title = "Time x FTE^2", x= "Time",
>         y="Patients", color="FTE^2", fill="FTE^2") + theme_classic() +
>         theme(text=element_text(size=10))
>
> Does my problem (obtaining effects for FTE^2*Time and accurately plotting
> them) relate to my use of the effects package, ggplot, both?
>
> Thank you for the feedback.
>
> Matthew Boden, Ph.D.
> Senior Evaluator
> Program Evaluation & Resource Center
> Office of Mental Health & Suicide Prevention Veterans Health Administration
>
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```