homals {Gifi}R Documentation

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, ordinal = FALSE, ties = "s", knots = knotsGifi(data, "D"), 
degrees = -1, missing = "m", 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

ordinal

Whether variables should be considered as ordinal or not. Alternatively, one can specify a boolean vector of length m denoting which variables should be ordinally restricted or not.

ties

How ties should be handled: primary ("p"), secondary ("s"), or tertiary ("t")

knots

Knots specification for spline transformation (see knotsGifi)

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

This is the most general model of the Gifi family. All other models such as PRINCALS are restricted HOMALS versions (in terms of restrictions on the transformations).

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)

[Package Gifi version 0.3-9 Index]