RidgeOrdinalLogistic: Ordinal logistic regression with ridge penalization

In MultBiplotR: Multivariate Analysis Using Biplots in R

Ordinal logistic regression with ridge penalization

Description

This function performs a logistic regression between a dependent ordinal variable y and some independent variables x, and solves the separation problem using ridge penalization.

Usage

RidgeOrdinalLogistic(y, x, penalization = 0.1, tol = 1e-04, maxiter = 200, show = FALSE)

Arguments

y	Dependent variable.
x	A matrix with the independent variables.
penalization	Penalization used to avoid singularities.
tol	Tolerance for the iterations.
maxiter	Maximum number of iterations.
show	Should the iteration history be printed?.

Details

The problem of the existence of the estimators in logistic regression can be seen in Albert (1984); a solution for the binary case, based on the Firth's method, Firth (1993) is proposed by Heinze(2002). All the procedures were initially developed to remove the bias but work well to avoid the problem of separation. Here we have chosen a simpler solution based on ridge estimators for logistic regression Cessie(1992).

Rather than maximizing {L_j}(\left. {\bf{G}} \right|{{\bf{b}}_{j0}},{{\bf{B}}_j}) we maximize

{{L_j}(\left. {\bf{G}} \right|{{\bf{b}}_{j0}},{{\bf{B}}_j})} - \lambda \left( {\left\| {{{\bf{b}}_{j0}}} \right\| + \left\| {{{\bf{B}}_j}} \right\|} \right)

Changing the values of \lambda we obtain slightly different solutions not affected by the separation problem.

Value

An object of class "pordlogist". This has components:

nobs	Number of observations
J	Maximum value of the dependent variable
nvar	Number of independent variables
fitted.values	Matrix with the fitted probabilities
pred	Predicted values for each item
Covariances	Covariances matrix
clasif	Matrix of classification of the items
PercentClasif	Percent of good classifications
coefficients	Estimated coefficients for the ordinal logistic regression
thresholds	Thresholds of the estimated model
logLik	Logarithm of the likelihood
penalization	Penalization used to avoid singularities
Deviance	Deviance of the model
DevianceNull	Deviance of the null model
Dif	Diference between the two deviances values calculated
df	Degrees of freedom
pval	p-value of the contrast
CoxSnell	Cox-Snell pseudo R squared
Nagelkerke	Nagelkerke pseudo R squared
MacFaden	Nagelkerke pseudo R squared
iter	Number of iterations made

Author(s)

Jose Luis Vicente-Villardon

References

Albert,A. & Anderson,J.A. (1984),On the existence of maximum likelihood estimates in logistic regression models, Biometrika 71(1), 1–10.

Bull, S.B., Mak, C. & Greenwood, C.M. (2002), A modified score function for multinomial logistic regression, Computational Statistics and dada Analysis 39, 57–74.

Firth, D.(1993), Bias reduction of maximum likelihood estimates, Biometrika 80(1), 27–38

Heinze, G. & Schemper, M. (2002), A solution to the problem of separation in logistic regression, Statistics in Medicine 21, 2109–2419

Le Cessie, S. & Van Houwelingen, J. (1992), Ridge estimators in logistic regression, Applied Statistics 41(1), 191–201.

Examples

data(Doctors)
olb = OrdLogBipEM(Doctors,dim = 2, nnodos = 10,
            tol = 0.001, maxiter = 100, penalization = 0.2)
model = RidgeOrdinalLogistic(Doctors[, 1], olb$RowCoordinates, tol = 0.001,
        maxiter = 100, penalization = 0.2)
model

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