Presentation on theme: "Xuhua Xia Slide 1 Correlation Simple correlation –between two variables Multiple and Partial correlations –between one variable and a set of other variables."— Presentation transcript:
Xuhua Xia Slide 1 Correlation Simple correlation –between two variables Multiple and Partial correlations –between one variable and a set of other variables Canonical Correlation –between two sets of variables each containing more than one variable. Simple and multiple correlations are special cases of canonical correlation. Multiple: x 1 on x 2 and x 3 Partial: between X and Y with Z being controlled for
Xuhua Xia Slide 2 Review of correlation XZY 1414.0000 1517.9087 1616.3255 2314.4441 2415.2952 2519.1587 2616.0299 2517.0000 3314.7556 3417.6823 3520.5301 3621.6408 4315.0903 4418.1603 4522.2471 5214.4450 5316.5554 5421.0047 5522.0000 6119.0000 6218.0000 6318.1863 6421.0000 Compute Pearson correlation coefficients between X and Z, X and Y and Z and Y. Compute partial correlation coefficient between X and Y, controlling for Z (i.e., the correlation coefficient between X and Y when Z is held constant), by using the equation in the previous slide. Run R to verify your calculation: install.packages("ggm") library(ggm) md<-read.table("XYZ.txt",header=T) cor(md) s<-var(md) parcor(s) install.packages("psych") library(psych) smc(s)
Data for canonical correlation Xuhua Xia Slide 3 # First three variables: physical # Last three variables: exercise # Middle-aged men weightwaistpulsechinssitupsjumps 1913650516260 193385812101101 18935461314558 2113856815138 17631741520040 16934501712038 154346414215105 1933646617031 1763754416025 15633541521573 1893752213060 16235621214537 1823656414142 1673460615540 154305617251250 166335213210115 247465015050 202376212120120 15732521123080 1383368215043
Xuhua Xia Slide 4 Many Possible Correlations With multiple DV’s (say A, B, C) and IV’s (say a, b, c, d, e), there could be many correlation patterns: –Variable A in the DV set could be correlated to variables a, b, c in the IV set –Variable B in the DV set could be correlated to variables c, d in the IV set –Variable C in the DV set could be correlated to variables a, c, e in the IV set With these plethora of possible correlated relationships, what is the best way of summarizing them?
Xuhua Xia Slide 5 Dealing with Two Sets of Variables The simple correlation approach: –For N DV’s and M IV’s, calculate the simple correlation coefficient between each of N DV’s and each of M IV’s, yielding a total of N*M correlation coefficients The multiple correlation approach: –For N DV’s and M IV’s, calculate multiple or partial correlation coefficients between each of N DV’s and the set of M IV’s, yielding a total of N correlation coefficients The canonical correlation Note: All these deal with linear correlations