OrdinalLogisticFit function

Fits an ordinal logistic regression with ridge penalization

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)

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 $L_j (G | b_j0 , B_j)$ we maximize

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

Returns

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

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.

Author(s)

Jose Luis Vicente-Villardon

Examples

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