Principal components, factor analysis, correspondence analysis

dma: seven related methods for reducing a data matrix to a handful of derived scores, selected with alg – principal components (1, from the raw data; 2, from a covariance or correlation matrix already computed), factor analysis (3, 4, the same two starting points but with eigenvectors rescaled as loadings), dual scaling and correspondence analysis (5, 6, for a frequency table rather than a data matrix), and a direct SVD-based projection (7). Verified against prcomp for algorithm 1: eigenvalues match exactly, eigenvectors match up to sign (an ordinary, harmless ambiguity in any eigendecomposition).

Usage

tda_dma(
  data,
  alg = 1,
  preprocess = NULL,
  ns = NULL,
  variables = NULL,
  options = list(),
  dir = tempfile("tda"),
  ...
)

Arguments

data: a data frame or matrix. For algorithms 1–4 and 7, a standard data matrix (rows are cases); for 2 and 4, a covariance or correlation matrix (square, symmetric); for 5 and 6, a frequency table.
alg: which of the seven algorithms; see Description. Default 1, ordinary principal components.
preprocess: preprocessing, for algorithms 1, 5 and 7 only – for alg = 1: 1 nothing (TDA's default), 2 mean centre, 3 standardize; for alg 5 or 7: 2/3 convert to row or table relative frequencies.
ns: keep at most this many components; all of them by default.
variables: optional subset of data's column names to use, instead of all of them.
options: a named list of further TDA options, passed through.
dir: working directory.
...: passed to tda_run. Further dma options can be given the same way, notably opt= (algorithm variant) and pcf= (print classification frequencies).

Value

A list with values (the eigenvalues), percent (each eigenvalue's share of the total, as TDA prints it), vectors (the eigenvectors or factor loadings, one column per component, row names taken from data), and scores (the derived score for each case, one column per component) – scores is empty for algorithms where TDA does not calculate it (2 and 4).

Details

TDA's v= (choosing a subset of variables from a larger data matrix) needs variable names that start uppercase, the same rule as anywhere else in TDA – lowercase R column names are displayed correctly when declared but cannot be referenced again later in the same script, including by v= itself, failing with a “Syntax error or undefined variables” that gives no hint the name's case is the problem. variables handles this automatically; there is no need to rename columns yourself first.

Examples

set.seed(1)
d <- data.frame(x1 = rnorm(30), x2 = rnorm(30))
d$x3 <- d$x1 + d$x2 + rnorm(30, sd = 0.3)   # correlated with both
pc <- tda_dma(d)
pc$values                 # most of the variance is in the first PC
#> [1] 2.70895046 0.70467635 0.01930123
pc$vectors                # loadings: x3 dominates it
#>          PC1         PC2        PC3
#> x1 0.4244330  0.72193373 -0.5465056
#> x2 0.3387373 -0.68633924 -0.6435802
#> x3 0.8397105 -0.08803484  0.5358509
head(pc$scores)
#>             PC1        PC2          PC3
#> [1,]  1.4142045 -1.5126624  0.246377700
#> [2,]  0.1011365  0.1970438  0.002808551
#> [3,] -0.4257493 -0.8481232  0.078019005
#> [4,]  1.9603115  1.0521724 -0.006699393
#> [5,] -1.3934880  1.2948640  0.025353851
#> [6,] -1.4786799 -0.2037191  0.083798313

# a subset of the variables, instead of all of them
tda_dma(d, variables = c("x1", "x2"))$values
#> [1] 0.8711004 0.6407060