A 'method' for objects of class phylog.prcomp. Shows the original data, and provides p-values and quantiles of the eigenvalues based on the simulated data. There is a print 'method' for this summary.
# S3 method for phylog.prcomp
summary(object, ...)an object of class phylog.prcomp such as one returned from a previous call to prcomp.phylog.
further arguments passed to or from other methods (currently not used).
A list (of class summary.phylog.prcomp) with elements
the call to function prcomp.phylog.
the eigenvalues corresponding to the original (''real'') data set.
the component-wise p-value ---see Details
the 'multiple-eigenvalue' p-value; see Details
the quantiles from the simulated eigenvalues; linear interpolation is used. Note that these quantiles are in the spirit of the ''component-wise p.values''.
the number of simulations used in the analyses
The p-values are calculated in two different ways. The 'component-wise' ones, where the p-value for a particular eigenvalue is (number of simulated data sets with eigenvalue larger than original (''real'') data + 1) / (number of simulated data sets + 1). With this approach, you can find that the p-value for, say, the second eigenvalue is smaller than the first, which is not sensible. It only makes sense to examine the second eigenvalue if the first one is ''significant'', etc. Thus, when considering the significance of the second eigenvalue we should account for the value of the first. In other words, there is only support against the null hypothesis (of no singificant second component) if both the first and the second eigenvalue from the observed data set are larger than most of the simulated data sets. We can account for what happens with the first eigenvalue by computing the p-value of the second eigenvalue as the number of simulations in which the second eigenvalue is larger than the observed, or the first simulated eigenvalue is larger than the observed one, or both (so that the only cases that count agains the null are those where both the first and second simulated eigenvalues are smaller than the observed ones). Therefore, with the second set of p-values, the p-values are increasing.
We also provide data for parallel anlysis as in Horn (1965; see also Zwick & Velicer 1986 and Lautenschlager 1989) where each eigenvalue is compared to the average eigenvalue (for that factor) obtained from a simulation. These can then be used to construct scree plots showing both the original and the simulated data.
Diaz-Uriarte, R., and Garland, T., Jr., in prep. PHYLOGR: an R package for the analysis of comparative data via Monte Carlo simulations and generalized least squares approaches.
Horn, J. L. (1965) A rationale and test for the number of factors in factor analysis. Psychometrica, 30, 179-185.
Krzanowski, W. J. (1990) Principles of multivariate analysis Oxford University Press.
Lautenschlager, G. J. (1989). A comparison of alternatives to conducting Monte Carlo analyses for determining parallel analysis criteria. Multivariate Behavioral Research, 24, 365-395.
Morrison, D. F. (1990) Multivariate statistcal methods, 3rd ed. McGraw-Hill.
Zwick, W. R., and Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432-442.
# NOT RUN {
data(SimulExample)
ex1.prcomp <- prcomp.phylog(SimulExample[,-11]) #the 11th column is a factor
summary(ex1.prcomp)
# }
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