HDMD: Statistical Analysis Tools for High Dimension Molecular Data (HDMD)

High Dimensional Molecular Data (HDMD) typically have many more variables or dimensions than observations or replicates (D>>N). This can cause many statistical procedures to fail, become intractable, or produce misleading results. This package provides several tools to reduce dimensionality and analyze biological data for meaningful interpretation of results. Factor Analysis (FA), Principal Components Analysis (PCA) and Discriminant Analysis (DA) are frequently used multivariate techniques. However, PCA methods \code{\link{prcomp}} and \code{\link{princomp}} do not reflect the proportion of total variation of each principal component. \code{\link{Loadings.variation}} displays the relative and cumulative contribution of variation for each component by accounting for all variability in data. When D>>N, the maximum likelihood method cannot be applied in FA and the the principal axes method must be used instead, as in \code{\link{factor.pa}} of the \code{\link{psych}} package. The \code{\link{factor.pa.ginv}} function in this package further allows for a singular covariance matrix by applying a general inverse method to estimate factor scores. Moreover, \code{\link{factor.pa.ginv}} removes and warns of any variables that are constant, which would otherwise create an invalid covariance matrix. \code{\link{Promax.only}} further allows users to define rotation parameters during factor estimation. Similar to the Euclidean distance, the Mahalanobis distance estimates the relationship among groups. \code{\link{pairwise.mahalanobis}} computes all such pairwise Mahalanobis distances among groups and is useful for quantifying the separation of groups in DA. Genetic sequences are composed of discrete alphabetic characters, which makes estimates of variability difficult. \code{\link{MolecularEntropy}} and \code{\link{MolecularMI}} calculate the entropy and mutual information to estimate variability and covariability, respectively, of DNA or Amino Acid sequences. Functional grouping of amino acids (Atchley et al 1999) is also available for entropy and mutual information estimation. Mutual information values can be normalized by \code{\link{NMI}} to account for the background distribution arising from the stochastic pairing of independent, random sites. Alternatively, discrete alphabetic sequences can be transformed into biologically informative metrics to be used in various multivariate procedures. \code{\link{FactorTransform}} converts amino acid sequences using the amino acid indices determined by Atchley et al 2005.

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