determine the minimum ratio for two subsequent eigenvalues to be considered different
determine the minimum ratio for two subsequent eigenvalues to be considered different
getPCtol(n, expect = 2)
n |
sample size |
expect |
expectation value for chi-square distribution of df=2 |
returns the minimum ratio between two subsequent subsequent eigenvalues to be considered different.
Bookstein, F. L. Measuring and reasoning: numerical inference in the sciences. Cambridge University Press, 2014
## reproduce the graph from Bookstein (2014, p. 324) ## and then compare it to ratios for values to be considered ## statistically significant myseq <- seq(from=10,to = 50, by = 2) myseq <- c(myseq,seq(from=50,to=1000, by =20)) ratios <- getPCtol(myseq) plot(log(myseq),ratios,cex=0,xaxt = "n",ylim=c(1,5.2)) ticks <- c(10,20,50,100,200,300,400,500,600,700,800,900,1000) axis(1,at=log(ticks),labels=ticks) lines(log(myseq),ratios) abline(v=log(ticks), col="lightgray", lty="dotted") abline(h=seq(from=1.2,to=5, by = 0.2), col="lightgray", lty="dotted") ## now we raise the bar and compute the ratios for values ## to be beyond the 95th percentile of ## the corresponding chi-square distribution: ratiosSig <- getPCtol(myseq,expect=qchisq(0.95,df=2)) lines(log(myseq),ratiosSig,col=2)
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