MultBiplotR (version 23.11.0)

OrdLogBipEM: Alternated EM algorithm for Ordinal Logistic Biplots

Description

This function computes, with an alternated algorithm, the row and column parameters of an Ordinal Logistic Biplot for ordered 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 Ordinal Logistic Regression to solve the separation problem present when the points for different categories of a variable are completely separated 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

OrdLogBipEM(Data, freq=NULL, dim = 2, nnodes = 15, 
tol = 0.0001, maxiter = 100, maxiterlogist = 100, 
penalization = 0.2, show = FALSE, initial = 1, alfa = 1, 
Orthogonalize=TRUE, Varimax=TRUE, ...)

Value

An object of class "Ordinal.Logistic.Biplot".This has components:

RowCoordinates

Coordinates for the rows or the individuals

ColumnParameters

List with information about the Ordinal Logistic Models calculated for each variable including: estimated parameters with thresholds,percents of correct classifications,and pseudo-Rsquared

loadings

factor loadings

LogLikelihood

Logarithm of the likelihood

r2

R squared coefficient

Ncats

Number of the categories of each variable

Arguments

Data

Data frame with the ordinal data. All the variables must be ordered factors.

freq

Frequencies for compacted tables

dim

Dimension of the solution

nnodes

Number of nodes for the multidimensional Gauss-Hermite quadrature

tol

Value to stop the process of iterations.

maxiter

Maximum number of iterations for the biplot procedure.

maxiterlogist

Maximum number of iterations for the logistic regression step or the Mirt initial configuration.

penalization

Penalization used in the diagonal matrix to avoid singularities.

show

Boolean parameter to specify if the user wants to see every iteration.

initial

Method used to choose the initial ability in the algorithm. Default value is 1.

alfa

Optional parameter to calculate row and column coordinates in Simple correspondence analysis if the initial parameter is equal to 1.

Orthogonalize

Should the final row coordinates be orthogonalized?. The column parameters have to be recalculated.

Varimax

Should the final row coordinates be rotated using the varimax procedure?.

...

Aditional argunments for mirt.

Author

Jose Luis Vicente-Villardon

References

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

Examples

if (FALSE) {
    data(Doctors)
    olb = OrdLogBipEM(Doctors,dim = 2, nnodes = 10, initial=4,
    tol = 0.001, maxiter = 100, penalization = 0.1, show=TRUE)
    olb
    summary(olb)
    PlotOrdinalResponses(olb)
    }