multispati               package:ade4               R Documentation

_M_u_l_t_i_v_a_r_i_a_t_e _s_p_a_t_i_a_l _a_n_a_l_y_s_i_s

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

     This function ensures a multivariate extension of the univariate
     method of spatial autocorrelation analysis. By accounting for the
     spatial dependence of data observations and their multivariate
     covariance simultaneously,  complex interactions among many
     variables are analysed. Using a methodological scheme borrowed
     from duality diagram  analysis, a strategy for the exploratory
     analysis of spatial pattern in the multivariate is developped.

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

     multispati(dudi, listw, scannf = TRUE, nfposi = 2, nfnega = 0)
     plot.multispati(x, xax = 1, yax = 2, ...) 
     summary.multispati(object, ...) 
     print.multispati(x, ...)

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

    dudi: an object of class 'dudi' for the duality diagram analysis

   listw: an object of class 'listw' for the spatial dependence of data
          observations

  scannf: a logical value indicating whether the eigenvalues bar plot
          should be displayed

  nfposi: an integer indicating the number of kept positive axes

  nfnega: an integer indicating the number of kept negative axes

x, object: an object of class 'multispati'

xax, yax: the numbers of the x-axis and the y-axis

     ...: further arguments passed to or from other methods

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

     This analysis generalizes the Wartenberg's multivariate spatial
     correlation analysis to various duality diagrams created by the
     functions ('dudi.pca', 'dudi.coa', 'dudi.acm', 'dudi.mix'...) If
     _dudi_ is a duality diagram created by the function 'dudi.pca' 
     and _listw_ gives spatial weights created by a row normalized
     coding scheme, the analysis is equivalent to Wartenberg's
     analysis. 

     We note X the data frame with the variables, Q the column weights
     matrix  and D the row weights matrix associated to the duality
     diagram _dudi_. We note L the neighbouring weights matrix
     associated to  _listw_. Then, the ''multispati'' analysis gives
     principal axes v that maximize the spatial autocorrelation : 

            I(XQv) = t(v)t(Q)t(X)DLXQv / t(v)t(Q)t(X)DXQv

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

     Returns an object of class 'multispati'.

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

     Daniel Chessel chessel@biomserv.univ-lyon1.fr 
      Sbastien Ollier ollier@biomserv.univ-lyon1.fr

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

     Grunsky, E. C. and Agterberg, F. P. (1988) Spatial and
     multivariate analysis of geochemical data from metavolcanic rocks
     in the Ben Nevis area, Ontario. _Mathematical Geology_, *20*,
     825-861.

     Switzer, P. and Green, A.A. (1984) Min/max autocorrelation factors
     for multivariate spatial imagery. Tech. rep. 6, Stanford
     University.

     Thioulouse, J., Chessel, D. and Champely, S. (1995) Multivariate
     analysis of spatial patterns: a unified approach to local and
     global structures. _Environmental and Ecological Statistics_, *2*,
     1-14.

     Wartenberg, D. E. (1985) Multivariate spatial correlation: a
     method for exploratory geographical analysis. _Geographical
     Analysis_, *17*, 263-283.

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

     'dudi','listw'

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

     ## Not run: 
     if (require(maptools, quiet = TRUE) & require(spdep, quiet = TRUE)) {
         data(mafragh)
         maf.xy <- mafragh$xy
         maf.flo <- mafragh$flo
         maf.listw <- nb2listw(neig2nb(mafragh$neig))
         s.label(maf.xy, neig = mafragh$neig, clab = 0.75)
         maf.coa <- dudi.coa(maf.flo,scannf = FALSE)
         multispati.randtest(maf.coa, maf.listw)
         maf.coa.ms <- multispati(maf.coa, maf.listw, scannf = FALSE, nfposi = 2, nfnega = 2)
         summary(maf.coa.ms)
         par(mfrow = c(1,3))
         barplot(maf.coa$eig)
         barplot(maf.coa.ms$eig) 
         s.corcircle(maf.coa.ms$as)
      
         par(mfrow = c(2,2))
         s.value(maf.xy, -maf.coa$li[,1])
         s.value(maf.xy, -maf.coa$li[,2])
         s.value(maf.xy, maf.coa.ms$li[,1])
         s.value(maf.xy, maf.coa.ms$li[,2])
         par(mfrow = c(1,1))

         par(mfrow = c(1,2))
         w1 <- -maf.coa$li[,1:2]
         w1m <- apply(w1, 2, lag.listw, x = maf.listw)
         s.match(w1, w1m, clab = 0.75)
         w1.ms <- maf.coa.ms$li[,1:2]
         w1.msm <- apply(w1.ms, 2, lag.listw, x = maf.listw)
         s.match(w1.ms, w1.msm, clab = 0.75)
         par(mfrow = c(1,1))

         maf.pca <- dudi.pca(mafragh$mil, scannf = FALSE)
         multispati.randtest(maf.pca, maf.listw)
         maf.pca.ms <- multispati(maf.pca, maf.listw, scannf=FALSE)
         plot(maf.pca.ms)
     }
     ## End(Not run)

