mfso                   package:fso                   R Documentation

_M_u_l_t_i_d_i_m_e_n_s_i_o_n_a_l _F_u_z_z_y _S_e_t _O_r_d_i_n_a_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     A multidimensional extension of fuzzy set ordination (FSO) that
     constructs a multidimensional ordination by mapping samples from
     fuzzy topological space to Euclidean space for statistical
     analysis.  MFSO can be used in exploratory or testing modes.

_U_s_a_g_e:

     ## S3 method for class 'formula':
     mfso(formula,dis,data,permute=FALSE,lm=TRUE,scaling=1,...)
     ## Default S3 method:
     mfso(x,dis,permute=FALSE,scaling=1,lm=TRUE,notmis=NULL,...)
     ## S3 method for class 'mfso':
     summary(object,...)

_A_r_g_u_m_e_n_t_s:

 formula: Model formula, with no left hand side.  Right hand side gives
          the independent variables to use in fitting the model

     dis: a dist object of class 'dist' returned from 'dist',
          'vegdist', or 'dsvdis'

    data: a data frame containing the variables specified in the
          formula

 permute: a switch to control how the probability of correlations is
          calculated.  permute=FALSE (the default) uses a parametric Z
          distribution approximation; permute=n permutes the
          independent variables (permute-1) times and estimates the
          probability as (m+1)/(permute) where m is the number of
          permuted correlations greater than or equal to the observed
          correlation.

      lm: a switch to control scaling of axes after the first axis.  If
          lm=TRUE (the default) each axis is constructed independently,
          and then subjected to a Gram-Schmidt orthogonalization to all
          previous axes to preserve only the the variability that is
          uncorrelated with all previous axes.  If lm=FALSE, the full
          extent of all axes is preserved without correcting for
          correlation with previous axes.

 scaling: a switch to control how the initial fuzzy set axes are
          scaled: 1 = use raw $mu$ membership values, 2 = relativize
          $mu$ values [0,1], 3 = relativize $mu$ values [0,1] and
          multiply by respective correlation coefficient.  

       x: a quantitative matrix or dataframe.  One axis will be fit for
          each column

  notmis: a vector passed from the formula version of mfso to control
          for missing values in the data

  object: an object of class 'mfso'

     ...: generic arguments for future use

_D_e_t_a_i_l_s:

     mfso performs individual fso calculations on each column of a data
     frame or matrix, and then combines those fso axes into a higher
     dimensional object.  The algorithm of fuzzy set ordination is
     described in the help file for fso.  The key element in mfso is
     the Gram-Schmidt orthogonalization, which ensures that each axis
     is independent of all previous axes.  In practice, each axis is
     regressed against all previous axes, and the residuals are
     retained as the data.

_V_a_l_u_e:

     an object of class 'mfso' with components: 

      mu: a matrix of fuzzy set memberships of samples, analogous to
          the coordinates of the samples along the axes, one column for
          each axis

    data: a dataframe containing the independent variables as columns

       r: a vector of correlation coefficients, one for each axis in
          order

       p: a vector of probabilities of observing correlations as high
          as observed

     var: a vector of variables names used in fitting the model

   gamma: a vector of the fraction of variance for an axis that is
          independent of all previous axes

_N_o_t_e:

     MFSO is an extension of single dimensional fuzzy set ordination
     designed to achieve low dimensional representations of a
     dissimilarity or distance matrix as a function of environmental or
     experimental variables. Although it is not technically a
     ``constrained ordination,'' in practice its use is similar to
     'cca' or 'rda'.

     If you set lm=FALSE, an mfso is equivalent to an fso, but the
     plotting routines differ.  For an mfso, the plotting routine plots
     each axis against all others in turn; for an fso the plotting
     routine plots each axis against the environmental or experimental
     variable it is derived from.

_A_u_t_h_o_r(_s):

     David W. Roberts droberts@montana.edu

_R_e_f_e_r_e_n_c_e_s:

     Roberts, D.W.  2007.  Statistical analysis of multidimensional 
     fuzzy set ordinations.  Ecology in press. 

     <URL: http://ecology.montana.msu.edu/R/labdsv/lab11/lab11.html>

_S_e_e _A_l_s_o:

     'cca','capscale'

_E_x_a_m_p_l_e_s:

         require(labdsv)
         data(bryceveg) # returns a vegetation dataframe
         data(brycesite) # returns a dataframe of environmental variables
         dis.bc <- dsvdis(bryceveg,'bray/curtis')
                       # returns an object of class sQuote{dist}
         demo.mfso <- mfso(~elev+slope+av,dis.bc,data=brycesite) # creates the mfso
         plot(demo.mfso)

