homals: Multiple Correspondence Analysis (HOMALS).

In Gifi: Multivariate Analysis with Optimal Scaling

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)

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 restriction 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.

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

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.

See Also

princals, plot.homals

Examples

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

Gifi documentation built on Sept. 28, 2022, 3 a.m.