典型相关分析Canonical Correlation Analysis.pptx

From Problem to AnalysisJacques Tacq;Exercise : We consider the analysis of the associations between indicators of economic inequality and indicators of political instability of countries. Economic inequality is measured as the GINI index (X1), the % of the labour force employed in agriculture (X2) and other indicators, such as the distribution of land, the % of farm households that rent their land and GNP per capita. The second political set of Y-variables could be represented by stability of leadership (Y1), the total number of violent incidents (Y2) and further also the number of people killed during the period and the stability of democracy. In this mini-exercise we consider the first two indicators of each set. For a random sample of n=12 countries the data matrix is as follows : GINI index % of farmers leadership violence Yugoslavia 43.7 67 0 0 Poland 45.0 57 8.5 5 Japan 47.0 40 15.7 0.1 India 52.2 71 3.0 14.0 Philippines 56.4 59 14.0 292.0 Sweden 57.7 13 8.5 0 New Zealand 77.3 16 12.8 0 Spain 78.0 50 0 0.2 Italy 80.3 29 15.5 0.2 Iraq 88.1 81 16.2 344.0 Venezuela 90.9 42 14.9 111.0 Bolivia 93.8 72 15.3 663.0 Perform a canonical correlation analysis.;X1;The investigation in which the relationship between the economic and political set is examined shows a structure like in a piece of vocal music for two voices in which the voices join in one after the other, singing the same theme. This is called the canonical structure. The canonical variables (X* and Y*) are indicated with an asterisk and are linear combinations of variables of a set, which are all measured at the quantitative measurement level. The linear combinations will be calculated in such a way that the correlation between the canonical (latent) variables – i.e. the correlation between the sets - is maximized. As linear combinations and are weighted sums, the coefficients ai and bi are