OrdinalLogBiplotEM: 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 every data set for which the goodness of fit is high.

Usage

OrdinalLogBiplotEM(x,dim = 2, nnodos = 15, tol = 0.001, maxiter = 100, penalization = 0.2,show=FALSE,initial=1,alfa=1)

Arguments

Matrix with the ordinal 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.

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.

Value

RowCoordinates: Coordinates for the rows or 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

References

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

Examples

Run this code

    data(LevelSatPhd)
    dataSet = CheckDataSet(LevelSatPhd)
    datanom = dataSet$datanom
    olb = OrdinalLogBiplotEM(datanom,dim = 2, nnodos = 10,
          tol = 0.001, maxiter = 100, penalization = 0.2)
    olb