homals: Multiple Correspondence Analysis (HOMALS).

Description

Fits a multiple correspondence analysis (MCA). The default is to take each input variable as nominal. Through restrictions on the transformations (ordinal in conjunction with splines) various generalizations of MCA can be achieved.

Usage

homals(data, ndim = 2, levels = "nominal", ordinal, knots, ties = "s", 
degrees = -1, missing = "s", normobj.z = TRUE, active = TRUE, itmax = 1000, 
eps = 1e-6, verbose = FALSE)

Value

transform: Optimally transformed scores
rhat: Induced correlation matrix
evals: Eigenvalues of induced correlation matrix
objectscores: Object scores (rows)
scoremat: Optimally scaled data matrix (first dimension)
quantifications: Category quantifications
dmeasures: Discimination matrices
lambda: Average discrimination matrix
weights: Component weights
loadings: Component loadings
ntel: Number of iterations
f: Loss function value
data: Original data frame
datanum: Numerical data frame
ndim: Number of extracted dimensions
call: Function call

Arguments

data: Input data frame: n observations, m variables
ndim: Number of dimensions to be computed
levels: A vector of length m denoting basic scale levels ("nominal", "ordinal", "metric"; see details
ordinal: If knots are specified manually, a boolean vector of length m denotes which variables should be ordinally restricted or not (see details)
knots: Scale levels can be specified manually using splines (see knotsGifi). If knots is set, this overrides level (see details)
ties: How ties should be handled: primary ("p"), secondary ("s"), or tertiary ("t")
degrees: Spline degrees. If different degrees should be used across variables, a vector of length m can be specified. The default value of -1 indicates nominal scale level (overrides the ordinal argument).
missing: How missing values should be handled: multiple ("m"), single ("s"), or average ("a")
active: Which variables should be active or inactive (also as vector of length m)
normobj.z: If TRUE, object scores are z-scores, if FALSE, they are restricted to SS of 1.
itmax: Maximum number of iterations
eps: Convergence criterion
verbose: Iteration printout

Details

The measurement (or scale) levels of the variables are incorporated via spline transformations. If the user only needs simple scale levels like nominal, ordinal, and metric, a corresponding vector can be specified in the levels argument without setting knots and ordinal. The corresponding spline transformations (unrestricted, monotone, and linear) are then created internally. If all scale level transformations are the same, ordinal can be a single value. For more advanced transformations such as polynomial or more flexible splines, the knots and ordinal arguments need to be specified instead of levels.

References

Gifi, A. (1990). Nonlinear Multivariate Analysis. New York: Wiley.

De Leeuw, J., Mair, P., Groenen, P. J. F. (2017). Multivariate Analysis with Optimal Scaling.

Examples

Run this code

## multiple CA 
fithart <- homals(hartigan)
fithart
summary(fithart)

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