OrdLogBipEM: Alternated EM algorithm for Ordinal Logistic Biplots

In MultBiplotR: Multivariate Analysis Using Biplots in R

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, ...) 

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.

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

Author(s)

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

## Not run: 
    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)
    
## End(Not run)

MultBiplotR documentation built on Nov. 21, 2023, 5:08 p.m.