princomp.rplus         package:compositions         R Documentation

_P_r_i_n_c_i_p_a_l _c_o_m_p_o_n_e_n_t _a_n_a_l_y_s_i_s _f_o_r _r_e_a_l _a_m_o_u_n_t_s

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

     A principal component analysis is done in real geometry (i.e.
     using iit-transform).

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

      ## S3 method for class 'rplus':
      princomp(x,...,scores=TRUE)
      ## S3 method for class 'princomp.rplus':
      print(x,...)
      ## S3 method for class 'princomp.rplus':
      plot(x,y=NULL,...,npcs=min(10,length(x$sdev)),
               type=c("screeplot","variance","biplot","loadings","relative"),
               main=NULL,scale.sdev=1)
      ## S3 method for class 'princomp.rplus':
      predict(object,newdata,...)

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

       x: an rplus-dataset (for princomp) or a result from
          princomp.rplus

       y: not used

  scores: a logical indicating whether scores should be computed or not

    npcs: the number of components to be drawn in the scree plot

    type: type of the plot: '"screeplot"' is a lined screeplot,
          '"variance"' is a boxplot-like screeplot, '"biplot"' is a
          biplot, '"loadings"' displays the loadings as a  'barplot'

scale.sdev: the multiple of sigma to use when plotting the loadings

    main: title of the plot

  object: a fitted princomp.rplus object

 newdata: another amount dataset of class rcomp

     ...: further arguments to pass to internally-called functions

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

     Mainly a 'princomp(iit(x))' is performed. Note all parts in a
     composition  or in an amount vector share a natural scaling.
     Therefore, they do not need any  preliminary standardization
     (which in fact would produce a loss of important information). 
     For this reason, 'princomp.rplus' works on the covariance matrix. 
      The plot routine provides screeplots ('type = "s"','type= "v"'),
     biplots ('type = "b"'), plots of the effect of loadings ('type =
     "b"') in 'scale.sdev*sdev'-spread, and loadings of pairwise
     differences ('type = "r"'). 
      The interpretation of a screeplot does not differ from ordinary
     screeplots. It shows the eigenvalues of the covariance matrix,
     which represent the portions of variance explained by the
     principal components.  
      The interpretation of the biplot uses, additionally to the
     classical interperation, a compositional concept: the differences
     between two arrowheads can be interpreted as the shift of mass 
     between the two components represented by the arrows.  
      The amount loading plot is more or less a standard loadings plot.
     The loadings are displayed by a barplot as positive and negative
     changes of amounts. 
      The loadings plot can work in two different modes: If
     'scale.sdev' is set to 'NA' it displays the amount vector being
     represented by the unit vector of loadings in the iit-transformed
     space. If 'scale.sdev' is numeric we use this amount vector scaled
     by the standard deviation of the respective component.  
      The relative plot displays the 'relativeLoadings' as a barplot.
     The deviation from a unit bar shows the effect of  each principal
     component on the respective differences.

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

     'princomp' gives an object of type
     'c("princomp.rcomp","princomp")' with the following content: 

    sdev: the standard deviation of the principal components

loadings: the matrix of variable loadings (i.e., a matrix which columns
          contain the eigenvectors). This is of class '"loadings"'

Loadings: the loadings as an '"rmult"'-object

  center: the iit-transformed vector of means used to center the
          dataset

  Center: the 'rplus' vector of means used to center the dataset 
          ('center' and 'Center' have no difference, except that the
          second has a class)

   scale: the scaling applied to each variable

   n.obs: number of observations

  scores: if 'scores = TRUE', the scores of the supplied data on the
          principal components. Scores are coordinates in a basis given
          by the principal components and thus not compositions

    call: the matched call

na.action: not clearly understood

     'predict' returns a matrix of scores of the observations in the
     'newdata' dataset. 
      The other routines are mainly called for their side effect of
     plotting or printing and return the object 'x'.

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

     'iit','rplus', 'relativeLoadings'  'princomp.rcomp',
     'princomp.aplus',

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

     data(SimulatedAmounts)
     pc <- princomp(rplus(sa.lognormals5))
     pc
     summary(pc)
     plot(pc)           #plot(pc,type="screeplot")
     plot(pc,type="v")
     plot(pc,type="biplot")
     plot(pc,choice=c(1,3),type="biplot")
     plot(pc,type="loadings")
     plot(pc,type="loadings",scale.sdev=-1) # Downward
     plot(pc,type="relative",scale.sdev=NA) # The directions
     plot(pc,type="relative",scale.sdev=1) # one sigma Upward 
     plot(pc,type="relative",scale.sdev=-1) # one sigma Downward
     biplot(pc)
     screeplot(pc)
     loadings(pc)
     relativeLoadings(pc,mult=FALSE)
     relativeLoadings(pc)
     relativeLoadings(pc,scale.sdev=1)
     relativeLoadings(pc,scale.sdev=2)

     pc$sdev^2
     cov(predict(pc,sa.lognormals5))

