LMER - Plotting of a quadratic effect interacting with time

Thu, Jan 31, 2019 3:05 PM

Worked like a charm!  Thanks, John.  

-----Original Message-----
From: Fox, John [mailto:jfox at mcmaster.ca] 
Sent: Thursday, January 31, 2019 11:57 AM
To: Boden, Matthew T. <Matthew.Boden at va.gov>
Cc: r-sig-mixed-models <r-sig-mixed-models at r-project.org>
Subject: [EXTERNAL] RE: LMER - Plotting of a quadratic effect interacting with time

Dear Mathew,

-----Original Message-----
From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at 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 at 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

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LMER - Plotting of a quadratic effect interacting with time

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