ANALISI DELLE CORRISPONDENZE IN R

Transcription

1 ANALISI DELLE CORRISPONDENZE IN R Un esempio I dati sono tratti da un'indagine ISTAT Aspetti della vita quotidiana condotta a febbraio 2010; sono reperibili sul sito Riguardano la frequenza in cui incontrano gli amici a seconda delle fasce d'età. Alcune classi sono state raggruppate. > amici= read.delim("d:/c-rogantin/diduniv/sd2/ /calcolatore/ancorr/amici.txt", + header =T, row.names=1); amici tuttig piu_v_sett una_v_sett qual_v_mese qual_v_anno mai_noamici >= Profili riga e colonna e distribuzioni marginali > profili_riga=prop.table(as.matrix(amici), 1) > profili_colonna=prop.table(as.matrix(amici), 2) > round(profili_riga*100,1) tuttig piu_v_sett una_v_sett qual_v_mese qual_v_anno mai_noamici >= > margine_riga=margin.table(as.matrix(amici), 1) > margine_colonna=margin.table(as.matrix(amici),2) > tot=sum(margine_riga) > media_riga=margine_riga/tot > media_colonna=margine_colonna/tot > round(media_riga*100,1) >= round(media_colonna*100,1) tuttig piu_v_sett una_v_sett qual_v_mese qual_v_anno mai_noamici Diagrammi a barre dei profili e delle deviazioni dalla media > par(mfrow=c(4,3)) > for (i in 1:dim(profili_riga)[1]) > {barplot(profili_riga[i,],main=row.names(profili_riga)[i])} [omissis]

2 > for (i in 1:dim(profili_riga)[1]) > {barplot(profili_riga[i,]-media_colonna,main=row.names(profili_riga)[i])} > par(mfrow=c(1,1)) Analisi delle corrispondenze Per effettuare l analisi delle corispondenze bisogna installare un modulo di R, chiamato ca 1. Dal menu Packages selezionare Set CRAN mirror... e scegliere un sito da cui prendere il modulo, ad esempio Italy(Padua). Sulla finestra Console appare > choosecranmirror() 2. Dal menu Packages selezionare Install package(s)... e scegliere ca Sulla finestra Console appare > utils:::menuinstallpkgs() trying URL ' Content type 'application/zip' length bytes (87 Kb) opened URL downloaded 87 Kb package ca successfully unpacked and MD5 sums checked The downloaded binary packages are in C:\Users\rogantin\AppData\Local\Temp\RtmpaYj8ht\downloaded_packages 3. Nel programma richiamare il modulo nel seguente modo > library(ca) ## richiama il modulo ca > ca_amici=ca(amici) La chiamata generale della funzione ca è la seguente: obj nd ca(obj, nd = NA, suprow = NA, supcol = NA, subsetrow = NA, subsetcol = NA) A two-way table of non-negative data, usually frequencies. Number of dimensions to be included in the output; if NA the maximum possible dimensions are included. Indices of supplementary rows. Indices of supplementary columns. suprow supcol subsetrow Row indices of subset. subsetcol Column indices of subset.

3 > summary(ca_amici) Principal inertias (eigenvalues): dim value % cum% scree plot ************************* ********* * Total: Rows: name mass qlt inr k=1 cor ctr k=2 cor ctr Columns: name mass qlt inr k=1 cor ctr k=2 cor ctr 1 tttg p_v_ un ql_v_m ql_v_n m_nm La struttura costruita con la funzione ca contiene varie informazioni. 1. sv Singular values (square roots of eigenvalues) 2. nd Dimenson of the solution 3. rownames Row names 4. rowmass Row masses 5. rowdist Row chi-square distances to centroid 6. rowinertia Row inertias 7. rowcoord Row standard coordinates 8. rowsup Indices of row supplementary points 9. colnames Column names 10. colmass Column masses 11. coldist Column chi-square distances to centroid 12. colinertia Column inertias 13. colcoord Column standard coordinates 14. colsup Indices of column supplementary points > ca_amici[1:15] $sv [1] $nd [1] NA

4 $rownames [1] "6-10" "11-14" "15-17" "18-19" "20-24" "25-34" "35-44" "45-54" "55-59" [10] "60-64" "65-74" ">=75" $rowmass [1] [7] $rowdist [1] [8] $rowinertia [1] [7] $rowcoord [,1] [,2] [,3] [,4] [,5] [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,] [9,] [10,] [11,] [12,] $rowsup logical(0) $colnames [1] "tuttig" "piu_v_sett" "una_v_sett" "qual_v_mese" "qual_v_anno" [6] "mai_noamici" $colmass [1] $coldist [1] $colinertia [1] $colcoord [,1] [,2] [,3] [,4] [,5] [1,] [2,] [3,] [4,] [5,] [6,] $colsup logical(0) $call ca(obj = amici)

5 Grafici dell analisi delle corrispondenze > plot(ca_amici) ## Il grafico di default è il Symmetric plot La chiamata generale della funzione plot applciata a una struttura ca è la seguente plot(x, dim = c(1,2), map = "symmetric", what = c("all", "all"), mass = c(false, FALSE), contrib = c("none", "none"), col = c("#0000ff", "#FF0000"), pch = c(16, 1, 17, 24), labels = c(2, 2), arrows = c(false, FALSE),...) x dim map what mass Simple correspondence analysis object returned by ca Numerical vector of length 2 indicating the dimensions to plot on horizontal and vertical axes respectively; default is first dimension horizontal and second dimension vertical. Character string specifying the map type. Allowed options include "symmetric" (default) "rowprincipal" "colprincipal" "symbiplot" "rowgab" "colgab" "rowgreen" "colgreen" Vector of two character strings specifying the contents of the plot. First entry sets the rows and the second entry the columns. Allowed values are "all" (all available points, default) "active" (only active points are displayed) "passive" (only supplementary points are displayed) "none" (no points are displayed) The status (active or supplementary) of rows and columns is set in ca using the options suprow and supcol. Vector of two logicals specifying if the mass should be represented by the area of the point symbols (first entry for rows, second one for columns) contrib Vector of two character strings specifying if contributions (relative or absolute) should be represented by different colour intensities. Available options are "none" (contributions are not indicated in the plot). "absolute" (absolute contributions are indicated by colour intensities). "relative" (relative contributions are indicated by colour intensities). If set to "absolute" or "relative", points with zero contribution are displayed in white. The higher the contribution of a point, the closer the corresponding colour to the one specified by the col option. col pch Vector of length 2 specifying the colours of row and column point symbols, by default blue for rows and red for columns. Colours can be entered in hexadecimal (e.g. "\#FF0000"), rgb (e.g. rgb(1,0,0)) values or by R-name (e.g. "red"). Vector of length 4 giving the type of points to be used for row active and supplementary, column active and supplementary points. See pchlist for a list of symbols.

6 labels arrows Vector of length two specifying if the plot should contain symbols only (0), labels only (1) or both symbols and labels (2). Setting labels to 2 results in the symbols being plotted at the coordinates and the labels with an offset. Vector of two logicals specifying if the plot should contain points (FALSE, default) or arrows (TRUE). First value sets the rows and the second value sets the columns.... Further arguments passed to plot and points. Details The function plot.ca makes a two-dimensional map of the object created by ca with respect to two selected dimensions. By default the scaling option of the map is "symmetric", that is the so-called symmetric map. In this map both the row and column points are scaled to have inertias (weighted variances) equal to the principal inertia (eigenvalue or squared singular value) along the principal axes, that is both rows and columns are in pricipal coordinates. Other options are as follows: -"rowprincipal" or "colprincipal" - these are the so-called asymmetric maps, with either rows in principal coordinates and columns in standard coordinates, or vice versa (also known as row-metricpreserving or column-metric-preserving respectively). These maps are biplots; -"symbiplot" - this scales both rows and columns to have variances equal to the singular values (square roots of eigenvalues), which gives a symmetric biplot but does not preserve row or column metrics; -"rowgab" or "colgab" - these are asymmetric maps (see above) with rows (respectively, columns) in principal coordinates and columns (respectively, rows) in standard coordinates multiplied by the mass of the corresponding point. These are also biplots and were proposed by Gabriel & Odoroff (1990); -"rowgreen" or "colgreen" - these are similar to "rowgab" and "colgab" except that the points in standard coordinates are multiplied by the square root of the corresponding masses, giving reconstructions of the standardized residuals. This function has options for sizing and shading the points. If the option mass is TRUE for a set of points, the size of the point symbol is proportional to the relative frequency (mass) of each point. If the option contrib is "absolute" or "relative" for a set of points, the colour intensity of the point symbol is proportional to the absolute contribution of the points to the planar display or, respectively, the quality of representation of the points in the display. I tre seguenti grafici sono ottenuti con le opzioni "colprincipal", "symbiplot", "symmetric" > plot(ca_amici, dim=c(1,2), mass = TRUE, contrib = "absolute", + map = "colprincipal", arrows = c(false, FALSE), col=c("red","blue"))

7 > plot(ca_amici, dim=c(1,2), mass = TRUE, # contrib = "absolute", + map = "symbiplot", arrows = c(false,true), col=c("red","blue")) > plot(ca_amici, dim=c(1,2), mass = TRUE, contrib = "absolute", + map = "symmetric", arrows = c(false,true), col=c("red","blue"))