[R] MANOVA: how do I read off within and between Sum-of-Squares info from the manova result?

[Spencer Graves]

	  1.  You did NOT provide an example, so I don't know if the following 
example will help.  I got it by following ?manova to "?summary.manova".

      tear <- c(6.5, 6.2, 5.8, 6.5, 6.5, 6.9, 7.2, 6.9, 6.1, 6.3,
                6.7, 6.6, 7.2, 7.1, 6.8, 7.1, 7.0, 7.2, 7.5, 7.6)
      gloss <- c(9.5, 9.9, 9.6, 9.6, 9.2, 9.1, 10.0, 9.9, 9.5, 9.4,
                 9.1, 9.3, 8.3, 8.4, 8.5, 9.2, 8.8, 9.7, 10.1, 9.2)
      opacity <- c(4.4, 6.4, 3.0, 4.1, 0.8, 5.7, 2.0, 3.9, 1.9, 5.7,
                   2.8, 4.1, 3.8, 1.6, 3.4, 8.4, 5.2, 6.9, 2.7, 1.9)
      Y <- cbind(tear, gloss, opacity)
      rate <- factor(gl(2,10), labels=c("Low", "High"))
      additive <- factor(gl(2, 5, len=20), labels=c("Low", "High"))

      fit <- manova(Y ~ rate * additive)
      summary.aov(fit)           # univariate ANOVA tables
      summary(fit, test="Wilks") # ANOVA table of Wilks' lambda

	  2.  To proceed further, I tried the following:

 > class(fit)
[1] "manova" "maov"   "aov"    "mlm"    "lm"

	  Inspired by this, I then tried the following:

 > ?methods
 > methods(class="manova")
[1] summary.manova
 > methods(class="maov")
no methods were found
 > methods(class="mlm")
  [1] add1.mlm*         anova.mlm         deviance.mlm*     drop1.mlm* 

  [5] estVar.mlm*       mauchly.test.mlm* plot.mlm          predict.mlm 

  [9] SSD.mlm*          summary.mlm       vcov.mlm*

    Non-visible functions are asterisked

	  This led me further:

 > fit
Call:
    manova(Y ~ rate * additive)

Terms:
                    rate additive rate:additive Residuals
tear             1.7405   0.7605        0.0005    1.7640
gloss            1.3005   0.6125        0.5445    2.6280
opacity          0.4205   4.9005        3.9605   64.9240
Deg. of Freedom       1        1             1        16

Residual standard error: 0.3320392 0.4052777 2.014386
Estimated effects may be unbalanced
 > estVar(fit)
              tear    gloss   opacity
tear     0.110250  0.00125 -0.191875
gloss    0.001250  0.16425 -0.034500
opacity -0.191875 -0.03450  4.057750
 > SSD(fit)
$SSD
           tear  gloss opacity
tear     1.764  0.020  -3.070
gloss    0.020  2.628  -0.552
opacity -3.070 -0.552  64.924

$call
manova(Y ~ rate * additive)

$df
[1] 16

	  If this does NOT answer your question, PLEASE do read the posting 
guide! (www.R-project.org/posting-guide.html) and send us another post. 
  Realize, however, that in r-help as in just about any other aspect of 
human existence, people who are more clear about what they want are 
generally more successful.

	  3.  I used MANOVA on a project 30 years ago.  From that and 
subsequent experience, it seem to me that MANOVA is a highly specialized 
tool for which the required assumptions are rarely met.  Most people are 
much better off making lots of plots to possible models and then 
residuals from model fits, etc.  In rare cases, MANOVA doubtless can 
find effects that can not be seen in the component univariate analyses. 
  However, I have yet to encounter such a case.  If I had time to pursue 
a modeling effort beyond simple univeriate analyses, I thing I would 
move to "structural equation modeling" (package sem) or "partial least 
squares".  "RSiteSearch" can lead you to R capabilities for these.  (See 
also "http://finzi.psych.upenn.edu/R/Rhelp02a/archive/29119.html").

	  hope this helps.
	  spencer graves	

Michael wrote:

> Hi all,
> 
> I am experimenting the function "manova" in R.
> 
> I tried it on a few data sets, but I did not understand the result:
> 
> I used "summary(manova_result)"
> 
> and "summary(manova_result, test='Wilks')"
> 
> and they gave a bunch of numbers...
> 
> But I need the Sum-of-Squares of BETWEEN and WITHIN matrices...
> 
> How do I read off from the R's manova results?
> 
> Any good example code and results?
> 
> Also, I am looking for tutorials/notes on how to compute those BETWEEN and
> WITHIN Sum-of-Squares myself...
> 
> I did not find any good discussion about MANOVA on the quite a few books I
> have on my hand currently...
> 
> Any books/referecnes/notes/tutorials give clear formulas on how to compute
> the MANOVAs?
> 
> Thanks a lot!
> 
> 	[[alternative HTML version deleted]]
> 
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