Hello, are there any good methods in R that will test if two correlation matrices (obtained in different ways) are equal? Something better than the Mantel test would be preferable. Regards, Patrik Waldmann -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
Patrik Waldmann wrote:> > Hello, > > are there any good methods in R that will test if two correlation matrices (obtained in different ways) are equal? Something better than the Mantel test would be preferable. > > Regards, > > Patrik Waldmann >Not that I know of. I include a function I've written for my own use, assuming multivariate Normality. I'm sure the experts could improve on the function. (And please could they or you point out any embarrasing errors!) David. -- David Wooff, Director, Statistics and Mathematics Consultancy Unit, Department of Mathematical Sciences, University of Durham. Science Laboratories, South Road, Durham, DH1 3LE, UK. Tel. 0191 374 4531, Fax 0191 374 7388. sphericity.daw<-function(n,s1,s2=NULL,estsigma=TRUE){ #### Performs a hypothesis test that a covariance matrix is of specified #### form. Test is of the form H0: S1=sigma^2*S2. n is the number of #### observations on which the sample covariance matrix is based. #### If the input parameter estsigma is TRUE: #### Perform test of the hypothesis that S1=sigma^2 S2, for unknown sigma. #### If S2 not specified, assumed that S2=I. Reference is Basilevsky, #### Statistical Factor Analysis and Related Methods, page 191. #### If the input parameter estsigma is FALSE: #### Perform test of the hypothesis that S1=S2. If S2 not specified, #### assumed that S2=I. Reference is Seber, Multivariate Observations, #### sec 3.5.4 #### Only the lower triangle+diagonal is required at entry, and the upper #### triangle is ignored. #### DAW July 2000 p<-nrow(s1) for (i in 1:(p-1)){for (j in ((i+1):p)){ s1[i,j]<-s1[j,i] s2[i,j]<-s2[j,i] }} if (!is.null(s2)){ b<-eigen(s2,symmetric=T,only.values=F) r<-b$vectors %*% diag(1/sqrt(b$values)) s<-t(r) %*% s1 %*% r } else { s<-s1 } d<-eigen(s,symmetric=T,only.values=T)$values ldet<-sum(log(d)) tr<-sum(d) if (estsigma==TRUE){ sighat<-tr/p cc<--(n-(2*p^2+p+2)/(6*p))*(ldet-p*log(tr/p)) statistic <- cc sighat<-sighat names(statistic) <- "Sphericity test statistic" parameter <- 0.5*(p+2)*(p-1) names(parameter) <- "df" rval<-list(data.name="",sighat=sighat,statistic=statistic,parameter=parameter,p value=1-pchisq(statistic,parameter)) } else { cc<--n*(p+ldet-tr) statistic <- cc names(statistic) <- "Covariance equality test statistic" parameter <- 0.5*(p+1)*p names(parameter) <- "df" rval<-list(data.name="",statistic=statistic,parameter=parameter,p.value=1-pchis q(statistic,parameter)) } class(rval) <- "htest" return(rval) } -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
Do you have any leads on statistical methods for solving this problem (independent of implementation in a particular system)? This doesn't seem like an R problem as much as a more general statistical problem. Also, what do you mean by "better"? More powerful? Incorporating more information about your particular problem? I'm not aware (although I'm admittedly pretty ignorant) of any really good general alternatives to Mantel's test, given the breadth of possible applications. You could try asking in sci.stat.math or sci.stat.consult (?). I guess the only R-specific issue is that if you did have an alternative in mind it would quite probably be a permutation test of some sort, which would mean that either efficient R-coding or coding the test in C or FORTRAN and interfacing to R would be a good idea. On Wed, 26 Jul 2000, Patrik Waldmann wrote:> Hello, > > are there any good methods in R that will test if two correlation > matrices (obtained in different ways) are equal? Something better than > the Mantel test would be preferable. > > Regards, > > Patrik Waldmann > > > > -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- > r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html > Send "info", "help", or "[un]subscribe" > (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch > _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._ > >-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
"Patrik Waldmann" <Patrik.Waldmann at sysbot.lu.se> asked:
PW> are there any good methods in R that will test if two correlation
PW> matrices (obtained in different ways) are equal? Something better than
PW> the Mantel test would be preferable.
and from the reponses, it would appear that the answer is 'no'.
However, the methods outlined in:
Beran, R. and M Srivistava (1985) Bootstrap tests and confidence
regions for functions of a covariance matrix, Annals of Statistics
13:95-115, 1985.
would be easy enough to implement and do not require MVN
assumptions.
All that is required is to estimate the covariance structure under the
desired null model, to compute a statistic that measures departures
from the null, and the computation of matrix square roots, if I
recall.
--
Charles C. Berry (858) 534-2098
Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu UC San Diego
http://hacuna.ucsd.edu/members/ccb.html La Jolla, San Diego 92093-0645
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