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

Boden, Matthew T. M@tthew@Boden @end|ng |rom v@@gov
Wed Jan 30 22:27:20 CET 2019

```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.

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