R help - Aug 2013 - varpart

Dear R-users

I applied vegan's varpart function to partition the effects of  
explanatory matrices. Adj. R square for the unique fraction [a] is  
0.25. Does anyone know why the decomposition by hand using rda gives  
me a different result for [a] (constrained proportion is 0.32)? I used  
cbind() for the conditional fractions, but it should be similar to  
condition()?

Thanks very much
Sibylle

 > AZ_var<-varpart(AZ, OeAF, Acker, Gruen)
 > plot(AZ_var)
 >
 > AZ_var

Partition of variation in RDA

Call: varpart(Y = AZ, X = OeAF, Acker, Gruen)

Explanatory tables:
X1:  OeAF
X2:  Acker
X3:  Gruen

No. of explanatory tables: 3
Total variation (SS): 239101
             Variance: 1811.4
No. of observations: 133

Partition table:
                       Df R.square Adj.R.square Testable
[a+d+f+g] = X1        29  0.55103      0.42463     TRUE
[b+d+e+g] = X2        11  0.12135      0.04147     TRUE
[c+e+f+g] = X3         9  0.23870      0.18300     TRUE
[a+b+d+e+f+g] = X1+X2 40  0.64676      0.49318     TRUE
[a+c+d+e+f+g] = X1+X3 38  0.59086      0.42546     TRUE
[b+c+d+e+f+g] = X2+X3 20  0.36936      0.25675     TRUE
[a+b+c+d+e+f+g] = All 49  0.69072      0.50813     TRUE
Individual fractions
[a] = X1 | X2+X3      29               0.25139     TRUE
[b] = X2 | X1+X3      11               0.08268     TRUE
[c] = X3 | X1+X2       9               0.01495     TRUE
[d]                    0              -0.00893    FALSE
[e]                    0              -0.01412    FALSE
[f]                    0               0.20033    FALSE
[g]                    0              -0.01816    FALSE
[h] = Residuals                        0.49187    FALSE
Controlling 1 table X
[a+d] = X1 | X3       29               0.24246     TRUE
[a+f] = X1 | X2       29               0.45171     TRUE
[b+d] = X2 | X3       11               0.07375     TRUE
[b+e] = X2 | X1       11               0.06856     TRUE
[c+e] = X3 | X1        9               0.00083     TRUE
[c+f] = X3 | X2        9               0.21528     TRUE
---
Use function 'rda' to test significance of fractions of interest
 > rda(AZ, OeAF, cbind(Acker, Gruen))
Call: rda(X = AZ, Y = OeAF, Z = cbind(Acker, Gruen))

                 Inertia Proportion Rank
Total         1811.3728     1.0000
Conditional    669.0542     0.3694   20
Constrained    582.0993     0.3214    4
Unconstrained  560.2193     0.3093    4
Inertia is variance

Eigenvalues for constrained axes:
    RDA1    RDA2    RDA3    RDA4
570.343   8.310   1.833   1.614

Eigenvalues for unconstrained axes:
     PC1     PC2     PC3     PC4
533.129  12.619  11.618   2.854


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Sibylle St?ckli <sibylle.stoeckli <at> gmx.ch> writes:
>
> I applied vegan's varpart function to partition the effects of  
> explanatory matrices. Adj. R square for the unique fraction [a] is  
> 0.25. Does anyone know why the decomposition by hand using rda gives  
> me a different result for [a] (constrained proportion is 0.32)? I used  
> cbind() for the conditional fractions, but it should be similar to  
> condition()?
...
                        Df R.square Adj.R.square Testable
...
> [a+b+d+e+f+g] = X1+X2 40  0.64676      0.49318     TRUE
> [a+c+d+e+f+g] = X1+X3 38  0.59086      0.42546     TRUE
> [b+c+d+e+f+g] = X2+X3 20  0.36936      0.25675     TRUE
> [a+b+c+d+e+f+g] = All 49  0.69072      0.50813     TRUE
> Individual fractions
> [a] = X1 | X2+X3      29               0.25139     TRUE
...

Sibylle,

When you decompose by hand, you probably calculate

X1 | X2+X3 = All - X2+X3, or

0.32136 = 0.69072 - 0.36936,

whereas varpart function in vegan calculates this as

0.25139 = 0.50813 - 0.49318 (with smaller round-off error).

That is, vegan uses column "Adj.R.square", but you used column
"R.square"
in your hand calculation.

This is documented in ?varpart with a reference to publications where
this is justified (Peres-Neto et al. 2006, Legendre & Legendre 2012).

Sorry for excessive pruning of your original post: I use gmane to 
post and it does not allow appropriate quoting of the original 
message.

Cheers, Jari Oksanen