Advanced statistics for master students Correspondence analysis

zz zzz z Correspondence analysis Literature: Hebák a kol., 3. díl SPSS Categories 8.0 Chicago, SPSS Inc. Introduction to SPSS Optimal Scaling Procedures for Categorical Data, pp. 1-20, Corresponce Analysis pp Jobson, J.D.: Applied Multivariate Data AnalysisVolume II: Categorical and Multivariate Methods, Springer-Verlag, Berlin, 1992 Aplication in Czech: Mareš, P.: Češi: Zaměstnání a práce-jak jsou Češi spokojeni ve své práci, Sociální studia 6: , 2001 Vlachová, K.: Stranická identifikace v České republice, Sociologické texty č.5, 2000, SoÚ AV ČR Matějů, P., Vlachová, K. a kol.: Nerovnost, spravedlnost, politika, Slon, Praha, str , 2000

zz zzz z Corresponce Analysis Historical note: Metod originated in France (70 ties, Jean-Paul Benzérci), from the middle of 80-ties in English Contingency table-base for this technique Well-known facts: Chi-square test and adjusted residuals (sign scheme)

zz zzz z Correspondence analysis The goal – to find deviations from independency in contingency table (resp. in correspondence table) in chart The result –chart with categories of row and column variables Interpretation – distances between categories of row and column variables (electorate, brands) variables-nominal or ordinal

zz zzz z Correspondence analysis characteristics of technique – quite pretty, nice charts, used by academics as well as in business correspondence table – divide absolute frequencies by the number of respondents (sometimes in % as total percentages) Example - correspondence table of accused in EXCEL – file corresp.xls

zz zzz z Correspondence analysis -logic Row and column profiles – looking for departures from independence in correspondence table (we use row and column profiles – simple analogy to row and column percentages) Graphical presentation – see again corresp.xls (interpretation) SPSS – file corresp.sps) Three plots – row profile plot, column profile plot and biplot - Different information in individual plots - Biplot –the most common output

zz zzz z Correspondence analysis Example on data –affiliation of Czech parties electorate Vlachová, K.. Stranická identifikace v České republice. Sociologické texty č Menu SPSS Analyze-Data Reduction-Correspondence Analysis Number of dimensions –selection (2 possibilities) =max. nr. of rows or columns (min of them) minus 1 - 1) According to inertia - „analogy" to explained variance in factor analysis - 2) based on our task Most common is to use 2 dimensions (simple to plot and interpret)

zz zzz z Distance measure Chi-square- for classical contingency table Normalization -symmetrical- for relations between categories of both variables -row principal – for relations between categories of row variable -column principal - for relations between categories of row variable -principal – combination of row and colum but no possibility to draw biplot -custom – from -1 thru 1 from column (-1) thru row principal (1), 0=symmetrical;

zz zzz z Standardization -remove row and column means – centering of variables – the best for most purposes Outputs (Plots) - Biplot - row points - column points

zz zzz z Outputs –interpretation -inertia and its interpretation - Row and column scores tables, interpretation of dimensions, explanation of individual points - Biplot, row and column plots - Changes of plots with row and column normalization

zz zzz z Outputs in SPSS -Plot in EXCEL use Score in Dimension from tables row and column scores -example !!!the same scaling on x and y axes is necessary!!!! Other possibilities in correspondence analysis - supplemental categories- picture based on categories not including supplementak, supplemental are used for this space- příklad-next party (SPR-RSČ) to common space of 5 parties – menu and command

HW Try to use correspondence analysis on your data (at least two variables with 5 categories)