      Christoph and others:

      I did succeed, but it was not straightforward.  I ended up using the formula:

      mod<-aov(Lag~Ov*Pr*He*Sp + Error(Bl/Ov/Pr:He),data=dat,na.action=na.omit)

      and repartioning the sums of squares into the proper factors.  I am still not entirely sure I did it correctly or why R split the sums of squares up the way it did, but I know I am very close.  I suspect that the contrasts need to be set differently.

      I should also note that the R output is rather strange in that I had to do a lot of searching to find which terms were actually error terms and which ones were model terms.  An example of the output from R shows this:

      summary(mod)

      Error: Bl
         Df  Sum Sq Mean Sq
      Ov  1   8.466   8.466
      Pr  1  10.845  10.845
      He  1  72.015  72.015
      Sp  2 310.009 155.005

      Error: Bl:Ov
         Df  Sum Sq Mean Sq
      Ov  1 1783.17 1783.17
      Pr  1    9.70    9.70
      He  1  194.48  194.48
      Sp  3   66.80   22.27

      Error: Bl:Ov:Pr:He
                Df  Sum Sq Mean Sq F value Pr(>F)
      Pr         1  303.01  303.01  2.8526 0.1119
      He         1  253.35  253.35  2.3851 0.1433
      Sp         6 1119.67  186.61  1.7568 0.1759
      Ov:Pr      1  307.52  307.52  2.8952 0.1095
      Ov:He      1   88.39   88.39  0.8321 0.3761
      Pr:He      1    7.64    7.64  0.0719 0.7922
      Ov:Sp      6  285.01   47.50  0.4472 0.8359
      Pr:Sp      2  102.27   51.14  0.4814 0.6271
      He:Sp      1   43.78   43.78  0.4121 0.5306
      Ov:Pr:He   1   60.07   60.07  0.5656 0.4637
      Residuals 15 1593.30  106.22               

      Error: Within
                   Df  Sum Sq Mean Sq F value Pr(>F)    
      Sp            6 23448.5  3908.1 54.1807 <2e-16 ***
      Ov:Sp         6   466.6    77.8  1.0781 0.3766    
      Pr:Sp         6   183.3    30.6  0.4236 0.8628    
      He:Sp         6   571.2    95.2  1.3199 0.2494    
      Ov:Pr:Sp      6   360.4    60.1  0.8328 0.5457    
      Ov:He:Sp      6    47.6     7.9  0.1100 0.9952    
      Pr:He:Sp      6   384.4    64.1  0.8881 0.5044    
      Ov:Pr:He:Sp   6   291.2    48.5  0.6727 0.6718    
      Residuals   215 15508.1    72.1                   
      ---
      Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1


      It was relatively straightforward to do the repartioning most of the time; occasionally I couldn't figure it out, however.  Those crossed factors at the split-plot level really give me fits sometimes.

      Anyway, thanks everyone for the help.

      Mike

      -----------------------


      Dear Mike, 

      Have you succeeded with your split-plot ANOVA? 

      Best wishes, 
      Christoph 

      Mike Saunders wrote: 


                Christoph, 

            Thanks for the help.  I think the place where I am having the most problems is the crossed factors at the split-plot level.  A synopsis of the design follows: 

            Blocks:  There are 6 blocks of treatments spread across a site.  Each block is complete in design (Block = 1-6). 

            Whole plot:  Each block has two plots, one of which has the residual tree overstory removed and the other intact (Overstory = yes or no). 

            Split plot:  In each whole plot, there are 4 planting grids for the seeds. A 2 x 2 factorial, at this level, of seed predator control (Caging = yes or no) and herbaceous competition, i.e., grass seed (Herb = yes or no). Spatial placement of grids in the whole plot was random and assignment of caging and herbaceous competition treatments to each grid were random, with the restriction that each of the four treatment combinations appeared only once.  [Note the two factors are crossed at this level and this has been giving me the most problems when setting up the model statement]. 

            Split-split plot:  Each planting grid is a 3 x 3 array of planting areas (individual planting areas are about 15 cm x 15 cm).  Nine different tree species (Species = 1 - 9) were randomly assigned to each planting area and 25 seeds planted in each area. 

            Time to germination, total germination (proportion of the 25) and rate of germination are response variables of interest. 

            I am interested in the main effects Overstory, Caging, Herb, and Species as well as all interactions (although I might throw out 3- and 4-way interactions later). 

            A drawing is attached as a pdf. 

            Thanks in advance for any help you can provide. 

            Mike 


            Mike Saunders 
            Research Assistant 
            Forest Ecosystem Research Program 
            Department of Forest Ecosystem Sciences 
            University of Maine 
            Orono, ME  04469 
            207-581-2763 (O) 
            207-581-4257 (F) 

            ----- Original Message ----- From: "Christoph Scherber" <Christoph.Scherber@uni-jena.de> 
            To: <mike_saunders@umenfa.maine.edu> 
            Cc: <r-help@hypatia.math.ethz.ch> 
            Sent: Thursday, February 03, 2005 5:40 AM 
            Subject: Re: [R] Split-split plot ANOVA 


            Hi Mike, 

            Do you have a schematic drawing of how exactly your treatments were 
            applied? In split-plot experiments, it is generally very important to 
            clearly define the sequence of plot sizes, because if you don´t do this 
            properly, then the output will be confusing. Checking if your degrees of 
            freedom at each level are correct should give you a good idea about 
            whether you´ve specified the model in the right way. 

            Generally, I see some problem with your model specification as you seem 
            to have two (not one) treatments in some of your subplots. 

            If I got it right, the sequence of terms should be something like 
            Block/Whole.plot/Caging/Competition/Species 

            at least if it´s a full split-plot. 

            Can you send me some more details on the design? 


            Regards, 
            Christoph 



            Lorenz.Gygax@fat.admin.ch wrote: 

                          I have been going over and over the examples in MASS and the Pinheiro and Bates example, but cannot get my model to run correctly with either aov or lme. 

                        Could someone give me a hand with the correct model statement? 

                       

                  It would help to see some of the things you have tried already ... 


                            First a description of the design.  We are studying germination rates for various species under a variety of treaments.  This is a blocked split-split plot design.  The levels and treatments are: 

                        Blocks:  1-6 

                        Whole plot treatment: 
                          Overstory:  Yes or No 

                        Split plot treatments: 
                          Caging (to protect against seed predators):  Yes or No 
                          Herbaceous competition (i.e., grass):  Yes or No 

                        Split-split plot treatment: 
                          Tree species:  7 kinds 

                        The response variable is Lag, which is a indication of when the seeds first germinated. 

                       

                  I would try somthing like 

                  lme (fixed= Lag ~ Caging + herbaceous + tree, 
                      data= your.data, 
                      random= ~ 1 | Overstory/split/splitsplit) 

                  Perhaps you want/need to add some interactions as well. Overstory, split and 
                  splitsplit would be factors with specific levels for each of the plots, 
                  split plots and split-split plots, respectively. 

                  Thus what I attempted here is to separate the variables of the hierarchical 
                  design of data gathering (which go into the random effects) and the 
                  treatments (which go into the fixed effects). 

                  The degrees of freedom for the fixed effects are automatically adjusted to 
                  the correct level in the hierarchy. 

                  Did you try that? What did not work out with it? 


                            Lastly, I have unbalanced data since some treatment combinations never had any germination. 

                       

                  In principle, the REML estimates in lme are not effected by unbalanced data. 

                  BUT I do not think that the missing germinations by themselves lead to an 
                  unbalanced data set: I assume it is informative that in some treatment 
                  combinations there was no germination. Thus, your lag there is something 
                  close to infinity (or at least longer than you cared to wait ;-). Thus, I 
                  would argue you have to somehow include these data points as well, otherwise 
                  you can only make a very restricted statement of the kind: if there was 
                  germination, this depended on such and such. 


                            Since the data are highly nonnormal, I hope to do a permutations test on the F-values for each main effect and interaction in order to get my p-values. 

                       

                  As these are durations a log transformation of your response might be 
                  enough. 

                  Regards, Lorenz 
                  - Lorenz Gygax, Dr. sc. nat. 
                  Centre for proper housing of ruminants and pigs 
                  Swiss Federal Veterinary Office 
                  agroscope FAT Tänikon, CH-8356 Ettenhausen / Switzerland 

                  ______________________________________________ 
                  R-help@stat.math.ethz.ch mailing list 
                  https://stat.ethz.ch/mailman/listinfo/r-help 
                  PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html  
           
     

Mike Saunders
Research Assistant
Forest Ecosystem Research Program
Department of Forest Ecosystem Sciences
University of Maine
Orono, ME  04469
207-581-2763 (O)
207-581-4257 (F)

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