Promax.only is an oblique rotation of factor loadings. This function is directly derived from the Promax function in the psych package, but only performs the promax rotation without first specifying a varimax orthogonal rotation. Further specifying the power of the fitting function allows for greater versatility.
Mutual information (MI) represents the interdependence of two discrete random variables and is analogous to covariation in continuous data. The intersection of entropy space of two random variables bound MI and quantifies the reduction in uncertainty of one variable given the knowledge of a second variable. However, MI must be normalized by a leveling ratio to account for the background distribution arising from the stochastic pairing of independent, random sites. Martin et al. (2005) found that the background MI, particularly from phylogenetic covariation, has a contributable effect for multiple sequence alignments (MSAs) with less than 125 to 150 sequences.
Mutual information (MI) represents the interdependence of two discrete random variables. Thus MI quantifies the reduction in uncertainty of one variable given the knowledge of a second variable. Placing entropy values on the diagonal of a MI matrix forms a structure comparable to a covariance matrix appropriate for variability decomposition. MI identifies pairs of statistically dependent or coupled sites where MI=1 indicates complete coupling.
Entropy (H) is a measure of uncertainty for a discrete random variable and is analogous to variation in continuous data. Traditionally the logarithm base for entropy is calculated with unit bits (b=2), nats (b=e) or dits (b=10). Alternatively, entropy estimates can be normalized to a common scale where 0<=H<=1 by setting b=n, the number of possible states. For DNA (n=4 nucleotide) or protein (n=20 amino acid) sequences, normalized entropy H=0 indicates an invariable site while H=1 represents a site where all states occur with equal probability.
Principal Component Analysis (PCA) methods prcomp and princomp do not accurately reflect the proportion of total variation of each principal component. Instead princomp calculates these values on the eigenvalue adjusted data, which misleadingly indicates that each component contributes equally to the variability in the loadings output. prcomp does not report the proportion of variablity. To rectify this, Loadings.variation displays the relative and cumulative contribution of variation for each component by accounting for all variability in data. Component variation is reported by the lambda value (which corresponds to the eigenvalue in princomp), while the proportion and cumulative variation relate these values to the total variability in data.
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 covering Factor Analysis (FA), Principal Components Analysis (PCA) and Discriminant Analysis (DA) to reduce dimensionality and analyze biological data for meaningful interpretation of results. Since genetic (DNA or Amino Acid) sequences are composed of discrete alphabetic characters, entropy and mutual information are often used to estimate variability and covariability, respectively. Alternatively, discrete alphabetic sequences can be transformed into biologically informative metrics to be used in various multivariate procedures. This package provide moleculr entropy and mutual information estimates as well as a metric transformation to convert amino acid letters into indices determined by Atchley et al 2005.
Based off the work done by Atchley et al 2005, Amino Acids are transformed into 5 metrics according to factor analysis scores representing Factor1 (PAH): Polarity, Accessibility, Hydrophobicity; Factor2 (PSS): Propensity for Secondary Structure; Factor3 (MS) : Molecular Size; Factor4 (CC): Codon Composition; Factor5 (EC): Electrostatic Charge. These numerics provide a biologically meaningful value that establishes a platform capable of handling rigorous statistical techniques such as analysis of variance, regression, discriminant analysis, etc.
For data with more variables than observations (D>>N), the covariance matrix is singular and a general inverse is used to determine the inverse correlation matrix and estimate scores. Using the principal axes method of Factor Analysis, communalities are estimated by iteratively updating the diagonal of the correlation matrix and solving the eigenvector decomposition. Communalities for each variable are estimated according to the number of factors and convergence is defined by the stabalization of total communalities between iterations.
Amino Acids have several distinct and overlapping physiochemical characteristics. The single letter abbreviation for each amino acid is sorted alphabetically in the character vector AminoAcids. AAbyGroup, small, polar, and hydrophobic correspond to this order and describe various amino acid attributes.
● Data Source:
CranContrib
● Keywords:
● Alias: AAGroups, AAbyGroup, AminoAcids, hydrophobic, polar, small
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