NominalLogBiplotEM: Alternated EM algorithm for Nominal Logistic Biplots

In NominalLogisticBiplot: Biplot representations of categorical data

Description

This function computes, with an alternated algorithm, the row and column parameters of a Nominal Logistic Biplot for polytomous data. The row coordinates (E-step) are computed using multidimensional Gauss-Hermite quadratures and Expected a posteriori (EAP) scores and parameters for each variable or items (M-step)using Ridge Nominal Logistic Regression to solve the separation problem present when the points for different categories of a variable are completely separataed on the representation plane and the usual fitting methods do not converge. The separation problem is present in almost avery data set for which the goodness of fit is high.

Usage

NominalLogBiplotEM(x, dim = 2, nnodos = 10, tol = 1e-04,
maxiter = 100, penalization = 0.2,initial=1,alfa=1, Plot = FALSE,
showResults = FALSE)

Arguments

x	Matrix with the nominal data. The matrix must be in numerical form.
dim	Dimension of the solution
nnodos	Number of nodes for the multidimensional Gauss-Hermite quadrature
tol	Value to stop the process of iterations.
maxiter	Maximum number of iterations in the process of solving the regression coefficients.
penalization	Penalization used in the diagonal matrix to avoid singularities.
initial	Value to decide the method(1-Correspondence analysis, 2-Mirt) that calculates the initial abilities values for the individuals.
alfa	If initial parameter method is correspondence analysis, this parameter determines the weight for rows and columns.
Plot	Boolean parameter to plot the row coordinates
showResults	Boolean parameter to show all the information about the iterations.

Value

An object of class "nominal.logistic.biplot.EM".This has components:

RowCoordinates	Coordinates for the individuals in the reduced space
ColumnModels	List with information about the Nominal Logistic Models calculated for each variable including: estimated parameters with covariances and standard errors, log-likelihood, deviances, percents of correct classifications, pvalues and pseudo-Rsquared measures

Author(s)

Julio Cesar Hernandez Sanchez, Jose Luis Vicente-Villardon

Maintainer: Julio Cesar Hernandez Sanchez <[e-mail]>

References

Bock,R. & Aitkin,M. (1981),Marginal maximum likelihood estimation of item parameters: Aplication of an EM algorithm, Phychometrika 46(4), 443-459.

Gabriel, K. R. (1998). Generalised bilinear regression. Biometrika, 85(3), 689-700.

Vicente-Villard<c3><b3>n, J. L., Galindo Villard<c3><b3>n, M. P., & Bl<c3><a1>zquez Zaballos, A. (2006). Logistic biplots. Multiple correspondence analysis and related methods. London: Chapman & Hall, 503-521.

Gabriel, K. R., & Zamir, S. (1979). Lower rank approximation of matrices by least squares with any choice of weights. Technometrics, 21(4), 489-498.

See Also

polylogist, multiquad

Examples

    data(HairColor)
    data = data.matrix(HairColor)
    xEM = NominalLogBiplotEM(data, dim = 2,showResults = FALSE)
    xEM

NominalLogisticBiplot documentation built on May 2, 2019, 6:03 a.m.