Repeated measurements of lettuce growth — pederson.lettuce.repeated • agridat

Repeated measurements of lettuce growth for 3 treatments.

data("pederson.lettuce.repeated")

Format

A data frame with 594 observations on the following 4 variables.

plant: plant number
day: day of observation
trt: treatment
weight: weight

Details

Experiment conducted in a greenhouse in Silver Bay, Minnesota. Plants were grown hydroponically. Treatment 1 had 9 plants per raft. Treatment 2 had 18 plants, treatment 3 had 36 plants. The response variable is weight of plant, roots, soil, cup, and water. The plants were measured repeatedly beginning Dec 1, and ending Jan 9, when the plants were harvested.

Source

Levi Dawson Pederson (2015). Mixed Model Analysis for Repeated Measures of Lettuce Growth Thesis at University of Minnesota. Appendix C. https://scse.d.umn.edu/sites/scse.d.umn.edu/files/pedersonprojectthesis.pdf

References

None

Examples


library(agridat)
data(pederson.lettuce.repeated)
dat <- pederson.lettuce.repeated

libs(lattice)
dat <- dat[order(dat$day),]
xyplot(weight ~ day|trt, dat, type='l', group=plant, layout=c(3,1),
main="pederson.lettuce.repeated")

# \dontrun{
# Pederson used this SAS MIXED model for unstructured covariance
# proc mixed data=Project.Spacingdata; 
# class trt plant day; 
# model weight=trt day trt*day; 
# repeated day / subject=plant type=un r rcorr;   

# This should give the same results as SAS, but does not.
libs(nlme)
dat <- transform(dat, plant=factor(plant), day=factor(day))
datg <- groupedData(weight ~ day|plant, data=dat)
un1 <- gls(weight ~ trt * day, data=datg,
           correlation=corSymm(value=rep(.6,55), form = ~ 1 | plant),
           control=lmeControl(opt="optim", msVerbose=TRUE,
                              maxIter=500, msMaxIter=500))
#> initial  value 2429.796794 
#> iter  10 value 2043.265582
#> iter  20 value 2026.878345
#> iter  30 value 1991.844910
#> iter  40 value 1974.144855
#> iter  50 value 1962.086595
#> iter  60 value 1957.390081
#> final  value 1957.093673 
#> converged
logLik(un1)*2 # nlme has 1955, SAS had 1898.6
#> 'log Lik.' -1955.263 (df=89)

# Comparing the SAS results in Pederson (page 16) and the nlme results, we notice
# the SAS correlations in table 5.2 are unusually low for the first
# column. The nlme results have a higher correlation in the first column
# and just "look" better
un1
#> Generalized least squares fit by REML
#>   Model: weight ~ trt * day 
#>   Data: datg 
#>   Log-restricted-likelihood: -977.6315
#> 
#> Coefficients:
#> (Intercept)       trtT2       trtT3        day5        day8       day12 
#> 49.26666667 -0.46111111  0.69444444  0.73888889  2.57222222  4.42777778 
#>       day15       day18       day21       day26       day33       day36 
#>  5.66666667  7.05555556 11.14444444 19.70555556 26.26111111 32.78888889 
#>       day40  trtT2:day5  trtT3:day5  trtT2:day8  trtT3:day8 trtT2:day12 
#> 38.73333333  0.75555556  1.56111111  0.56111111  0.76111111  0.06111111 
#> trtT3:day12 trtT2:day15 trtT3:day15 trtT2:day18 trtT3:day18 trtT2:day21 
#>  0.51666667 -0.05555556  0.69444444 -0.27777778  0.96666667 -0.66666667 
#> trtT3:day21 trtT2:day26 trtT3:day26 trtT2:day33 trtT3:day33 trtT2:day36 
#> -0.86666667 -1.72222222 -3.48333333 -2.55000000 -0.43888889 -2.55000000 
#> trtT3:day36 trtT2:day40 trtT3:day40 
#> -1.89444444 -3.07222222 -6.53888889 
#> 
#> Correlation Structure: General
#>  Formula: ~1 | plant 
#>  Parameter estimate(s):
#>  Correlation: 
#>    1     2     3     4     5     6     7     8     9     10   
#> 2  0.945                                                      
#> 3  0.942 0.980                                                
#> 4  0.938 0.962 0.986                                          
#> 5  0.919 0.944 0.973 0.990                                    
#> 6  0.901 0.922 0.951 0.974 0.994                              
#> 7  0.883 0.900 0.929 0.956 0.971 0.979                        
#> 8  0.803 0.803 0.845 0.879 0.895 0.909 0.955                  
#> 9  0.706 0.701 0.741 0.777 0.799 0.821 0.882 0.954            
#> 10 0.504 0.515 0.555 0.602 0.629 0.656 0.743 0.866 0.944      
#> 11 0.537 0.551 0.587 0.633 0.657 0.683 0.763 0.864 0.929 0.963
#> Degrees of freedom: 594 total; 561 residual
#> Residual standard error: 5.564987 

# }