This function fits a logistic regression between a dependent ordinal variable y and some independent variables x, and solves the separation problem using ridge penalization.
OrdinalLogisticFit(y, x, penalization = 0.1, tol = 1e-04, maxiter = 200, show = FALSE)An object of class "pordlogist". This has components:
Number of observations
Maximum value of the dependent variable
Number of independent variables
Matrix with the fitted probabilities
Predicted values for each item
Covariances matrix
Matrix of classification of the items
Percent of good classifications
Estimated coefficients for the ordinal logistic regression
Thresholds of the estimated model
Logarithm of the likelihood
Penalization used to avoid singularities
Deviance of the model
Deviance of the null model
Diference between the two deviances values calculated
Degrees of freedom
p-value of the contrast
Cox-Snell pseudo R squared
Nagelkerke pseudo R squared
Nagelkerke pseudo R squared
Number of iterations made
Dependent variable.
A matrix with the independent variables.
Penalization used to avoid singularities.
Tolerance for the iterations.
Maximum number of iterations.
Should the iteration history be printed?.
Jose Luis Vicente-Villardon
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.
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.