# Functions for performing and displaying a spatial partitioning of cca or rda results The function `mso` adds an attribute `vario` to an object of class `"cca"` that describes the spatial partitioning of the `cca` object and performs an optional permutation test for the spatial independence of residuals. The function `plot.mso` creates a diagnostic plot of the spatial partitioning of the `"cca"` object. ```r mso(object.cca, object.xy, grain = 1, round.up = FALSE, permutations = 0) msoplot(x, alpha = 0.05, explained = FALSE, ylim = NULL, legend = "topleft", ...) ``` ## Arguments - `object.cca`: An object of class cca, created by the `cca` or `rda` function. - `object.xy`: A vector, matrix or data frame with the spatial coordinates of the data represented by `object.cca`. The number of rows must match the number of observations (as given by `nobs`) in `cca.object`. Alternatively, interpoint distances can be supplied as a `dist` object. - `grain`: Interval size for distance classes. - `round.up`: Determines the choice of breaks. If false, distances are rounded to the nearest multiple of grain. If true, distances are rounded to the upper multiple of grain. - `permutations`: a list of control values for the permutations as returned by the function `how`, or the number of permutations required, or a permutation matrix where each row gives the permuted indices. - `x`: A result object of `mso`. - `alpha`: Significance level for the two-sided permutation test of the Mantel statistic for spatial independence of residual inertia and for the point-wise envelope of the variogram of the total variance. A Bonferroni-type correction can be achieved by dividing the overall significance value (e.g. 0.05) by the number of distance classes. - `explained`: If false, suppresses the plotting of the variogram of explained variance. - `ylim`: Limits for y-axis. - `legend`: The x and y co-ordinates to be used to position the legend. They can be specified by keyword or in any way which is accepted by `legend`. - ``...``: Other arguments passed to functions. ## Details The Mantel test is an adaptation of the function `mantel` to the parallel testing of several distance classes and similar to multivariate `mantel.correlog`. It compares the mean inertia in each distance class to the pooled mean inertia of all other distance classes. If there are explanatory variables (RDA, CCA, pRDA, pCCA) and a significance test for residual autocorrelation was performed when running the function `mso`, the function `plot.mso` will print an estimate of how much the autocorrelation (based on significant distance classes) causes the global error variance of the regression analysis to be underestimated ## Returns The function `mso` returns an amended `cca` or `rda` object with the additional attributes `grain`, `H`, `H.test` and `vario`. - **grain**: The grain attribute defines the interval size of the distance classes . - **H**: H is an object of class 'dist' and contains the geographic distances between observations. - **H.test**: H.test contains a set of dummy variables that describe which pairs of observations (rows = elements of `object$H`) fall in which distance class (columns). - **vario**: The vario attribute is a data frame that contains some or all of the following components for the rda case (cca case in brackets): - **`H`**: Distance class as multiples of grain. - **`Dist`**: Average distance of pairs of observations in distance class H. - **n**: Number of unique pairs of observations in distance class H. - **`All`**: Empirical (chi-square) variogram of total variance (inertia). - **`Sum`**: Sum of empirical (chi-square) variograms of explained and residual variance (inertia). - **`CA`**: Empirical (chi-square) variogram of residual variance (inertia). - **`CCA`**: Empirical (chi-square) variogram of explained variance (inertia). - **`pCCA`**: Empirical (chi-square) variogram of conditioned variance (inertia). - **`se`**: Standard error of the empirical (chi-square) variogram of total variance (inertia). - **`CA.signif`**: P-value of permutation test for spatial independence of residual variance (inertia). ## References Wagner, H.H. 2004. Direct multi-scale ordination with canonical correspondence analysis. **Ecology** 85: 342--351. ## Author(s) The responsible author was Helene Wagner. ## Note The function is based on the code published in the Ecological Archives E085-006 (tools:::Rd_expr_doi("10.1890/02-0738") ). ## See Also `mantel.correlog`. ## Examples ```r ## Reconstruct worked example of Wagner (submitted): X <- matrix(c(1, 2, 3, 2, 1, 0), 3, 2) Y <- c(3, -1, -2) tmat <- c(1:3) ## Canonical correspondence analysis (cca): Example.cca <- cca(X, Y) Example.cca <- mso(Example.cca, tmat) msoplot(Example.cca) Example.cca$vario ## Correspondence analysis (ca): Example.ca <- mso(cca(X), tmat) msoplot(Example.ca) ## Unconstrained ordination with test for autocorrelation ## using oribatid mite data set as in Wagner (2004) data(mite) data(mite.env) data(mite.xy) mite.cca <- cca(log(mite + 1)) mite.cca <- mso(mite.cca, mite.xy, grain = 1, permutations = 99) msoplot(mite.cca) mite.cca ## Constrained ordination with test for residual autocorrelation ## and scale-invariance of species-environment relationships mite.cca <- cca(log(mite + 1) ~ SubsDens + WatrCont + Substrate + Shrub + Topo, mite.env) mite.cca <- mso(mite.cca, mite.xy, permutations = 99) msoplot(mite.cca) mite.cca ```

mso function