use natural way of calculationg RsquareAdj for cca: conflicts varpart

varpart adjusts R2 of basic components, and R2-adj for a testable
partial model is the difference of adjusted models. This version
of RsquareAdj.cca directly estimates the R2 of the partial model and
adjusts that, or in other words, adjusts a difference of R2 values
of taking difference of adjusted R2 values (varpart).

R/RsquareAdj.R

@@ -33,30 +33,20 @@
     list(r.squared = R2, adj.r.squared = radj)
 }
 
-## cca result: RsquareAdj is calculated similarly as in
-## varpart(). This is similar "semipartial" model as for rda() and
-## found as a difference of R2-adj values of combined model with
-## constraints + conditions and only conditions.
+## cca result: R2_adj calculation for partial models differs from
+## varpart(), where it is assessed as difference of R2_adj values for
+## conditions and constraints. Here we use difference of unadjusted R2
+## values, and adjust that difference.
 `RsquareAdj.cca` <-
     function (x, permutations = 1000, ...)
 {
     r2 <- x$CCA$tot.chi / x$tot.chi
-    if (is.null(x$pCCA)) {
-        p <- permutest(x, permutations, ...)
-        radj <- 1 - ((1 - r2) / (1 - mean(p$num / x$tot.chi)))
-    } else {
-        p <- getPermuteMatrix(permutations, nobs(x))
-        Y <- ordiYbar(x, "initial")
-        r2tot <- (x$pCCA$tot.chi + x$CCA$tot.chi) / x$tot.chi
-        r2null <- mean(sapply(seq_len(nrow(p)), function(i)
-            sum(qr.fitted(x$CCA$QR, Y[p[i,],])^2)))
-        r2tot <- 1 - ((1-r2tot)/(1-r2null/x$tot.chi))
-        r2p <- x$pCCA$tot.chi / x$tot.chi
-        r2null <- mean(sapply(seq_len(nrow(p)), function(i)
-            sum(qr.fitted(x$pCCA$QR, Y[p[i,],])^2)))
-        r2p <- 1 - ((1-r2p)/(1-r2null/x$tot.chi))
-        radj <- r2tot - r2p
-    }
+    ## model='direct' makes a difference in pCCA: it guarantees that
+    ## dependent data are permuted in the same way in the partial and
+    ## constrained components so that we can take their difference for
+    ## the correction term.
+    p <- permutest(x, permutations, model = "direct")
+    radj <- 1 - ((1 - r2) / (1 - mean(p$num) / x$tot.chi))
     list(r.squared = r2, adj.r.squared = radj)
 }
 

man/RsquareAdj.Rd

@@ -32,8 +32,7 @@ Adjusted R-square
   R-squared for a cca. The permutations can be calculated in parallel by
   specifying the number of cores which is passed to \code{\link{permutest}}}
 
-  \item{\dots}{ Other arguments (ignored) except in the case of cca in 
-  which these arguments are passed to \code{\link{permutest}}.} 
+  \item{\dots}{ Other arguments (ignored).}
 }
 
 \details{ The default method finds the adjusted
@@ -49,9 +48,7 @@ Adjusted R-square
   models in \code{\link{glm}}.
 
   The adjusted, \eqn{R^2}{R-squared} of \code{cca} is computed using a
-  permutation approach developed by Peres-Neto et al. (2006). By
-  default 1000 permutations are used. Adjusted \eqn{R^2}{R-squared} is
-  not calculated for partial CCA.
+  permutation approach developed by Peres-Neto et al. (2006).
 
   The raw \eqn{R^2}{R-squared} of partial \code{rda} gives the
   proportion explained after removing the variation due to conditioning