[R-sig-ME] repeated measures: lme(r) vs manova

[Martin Schmettow]

Hi Nathan,

Here is a nice simulation study comparing LME to MANOVA and several other
traditional methods (I hope you don't mind the interdisciplinary transfer):
Gueorguieva, R., & Krystal, J. H. (2004). Move Over ANOVA. Archives of
General Psychiatry, 61, 310-317.

The bottom line: In longitudinal designs, LME has better power in presence
of missing values.

CU, Martin



> -----Original Message-----
> From: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-
> models-bounces at r-project.org] On Behalf Of Nathan Lemoine
> Sent: Monday, March 19, 2012 10:32 PM
> To: r-sig-mixed-models at r-project.org
> Subject: [R-sig-ME] repeated measures: lme(r) vs manova
> 
> Hi all,
> Sorry in advance for the length of this post, but I've searched around and
> couldn't find anything that addressed this issue:
> 
> I recently ran into the issue of deciding on the appropriate way to
analyze a
> repeated measures design. We enriched quadrats to measure productivity
> and we monitored them for three years. Four quadrats were nested within
> plots. Here are the data:
> 
> "plot" "quad" "nut" "t1" "t3" "t4"
> "1" 1 "A" "nut" 17.69130435 70.4 57.8
> "2" 1 "A" "no nut" 65.4173913 125.8 109.9 "3" 1 "B" "nut" 19.56521739
103.2
> 100.8 "4" 1 "B" "no nut" 89.03636364 131.3 99.1 "5" 1 "C" "nut"
29.88723404
> 25.7 29.9 "6" 1 "C" "no nut" 45.45454545 113.1 110.6 "7" 1 "D" "nut"
> 18.28181818 60.9 67.7 "8" 1 "D" "no nut" 68.88888889 136 95 "9" 2 "A"
"nut"
> 35.41666667 61.6 16 "10" 2 "A" "no nut" 40.90909091 59.4 64.7 "11" 2 "B"
"nut"
> 34.14255319 26.7 23.1 "12" 2 "B" "no nut" 36.27021277 71.6 47.2 "13" 2 "C"
> "nut" 13.33333333 20.9 26.4 "14" 2 "C" "no nut" 7.118181818 31.2 19.1 "15"
2
> "D" "nut" 20 30.9 27.8 "16" 2 "D" "no nut" 19.34893617 31.3 16.7 "17" 3
"A"
> "nut" 22.22222222 130.7 163.6 "18" 3 "A" "no nut" 32.90869565 83.8 86.2
"19" 3
> "B" "nut" 38.29787234 99 110.1 "20" 3 "B" "no nut" 38.83636364 127.1 115.2
> "21" 3 "C" "nut" 38.88888889 81.7 193.7 "22" 3 "C" "no nut" 28.98888889
72.1
> 103.8 "23" 3 "D" "nut" 50 111.3 117.7 "24" 3 "D" "no nut" 26.86666667 94.2
113
> "25" 4 "A" "nut" 63.63636364 128.4 114.8 "26" 4 "A" "no nut" 108.8956522
121
> 80.7 "27" 4 "B" "nut" 104.4444444 146.5 102.2 "28" 4 "B" "no nut"
84.74444444
> 111.5 109.9 "29" 4 "C" "nut" 71.31111111 86.2 118.4 "30" 4 "C" "no nut"
> 115.9555556 131.4 141.9 "31" 4 "D" "nut" 75.65555556 141.5 92.5 "32" 4 "D"
> "no nut" 108.9888889 146.6 122.2 "33" 5 "A" "nut" 20.2 57.4 14.6 "34" 5
"A" "no
> nut" 12.34489796 55.4 13.4 "35" 5 "B" "nut" 48.98888889 56.3 28.7 "36" 5
"B"
> "no nut" 35.65555556 55.8 17.6 "37" 5 "C" "nut" 22.22222222 45.9 7.3 "38"
5
> "C" "no nut" 9.088888889 55.6 20.5 "39" 5 "D" "nut" 64.44444444 86.1 61.7
"40"
> 5 "D" "no nut" 15.65555556 75.7 41.8 "41" 6 "A" "nut" 22.22222222 101.1
69.8
> "42" 6 "A" "no nut" 53.33333333 171.2 113.5 "43" 6 "B" "nut" 37.87777778
> 111.1 66.8 "44" 6 "B" "no nut" 46.96666667 120.8 83.8 "45" 6 "C" "nut"
> 17.87777778 120.7 84 "46" 6 "C" "no nut" 21.21212121 116.3 76.8 "47" 6 "D"
> "nut" 24.01304348 86.1 64.6 "48" 6 "D" "no nut" 29.51034483 112.5 51.9
> 
> The basic question is: When is it appropriate to use a MANOVA-based
> repeated measures design over a mixed effects model?
> 
> For example, the MANOVA approach:
> library(car)
> repeated.manova <- lm(cbind(t1,t3,t4)~nut+plot+quad, data=manova.data)
> Manova(repeated.manova)
> 
> nut is not significant and there are 40 denominator df.
> 
> If I set up the data and run lme:
> 
> mixed.dat <- melt(manova.data, id=c("plot","quad","nut"))
> colnames(mixed.dat)[4:5] <- c("time","prod") mixed.dat$time <-
> as.numeric(mixed.dat$time))
> 
> library(nlme)
> lme.repeated <- lme(prod~nut, random=~nut|time, data=mixed.dat)
> anova(lme.repeated)
> 
> Gives 140 denominator df. I'm also not sure this is the appropriate set up
for
> a repeated measures design. Running the following code seems more in line
> with what I've read to take into account the correlation in observations
> within the same plot:
> 
> lme.repeated2 <- lme(prod~nut*time, random=~time|plot,
> data=mixed.dat)
> anova(lme.repeated2)
> 
> This model seems much more appropriate, as observations within plots are
> now allowed to be correlated, but there is still a huge difference between
> the MANOVA-based approach and the mixed-effects-based approach, as
> the mixed-effects model gives me a significant result. The MANOVA assumes
> that I have three (correlated) observations on 48 independent units,
> whereas the lme approach assumes that I have 144 observations on
> correlated units. Also not sure if that interpretation is correct.
> 
> Alternatively, I used lmer() for non-nested, multilevel models allowing
> observations to be correlated in space and time:
> 
> repeated.mixed3 <- lmer(prod~nut + (1|plot) + (1|time), data=mixed.dat)
> repeated.mixed4 <- lmer(prod~ (1|plot) + (1|time), data=mixed.dat)
> anova(repeated.mixed3, repeated.mixed4)
> 
> This approach also gives me a significant result. Which of these is the
most
> appropriate? The differences between lme and lmer are trivial (in this
case),
> but the difference between the MANOVA approach and mixed-effects is
> substantial. I figure the MANOVA approach is probably in correct on
account
> of the nested design, but my question extends to situations when the
design
> is not nested.
> 
> Thanks in advance for your help,
> 
> Nathan
> 
> 
> 
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