RidgeMultinomialLogisticRegression function

Ridge Multinomial Logistic Regression

Function that calculates an object with the fitted multinomial logistic regression for a nominal variable. It compares with the null model, so that we will be able to compare which model fits better the variable.

RidgeMultinomialLogisticRegression(formula, data, penalization = 0.2,
cte = TRUE, tol = 1e-04, maxiter = 200, showIter = FALSE)

Arguments

• formula: The usual formula notation (or the dependent variable)
• data: The dataframe used by the formula. (or a matrix with the independent variables).
• penalization: Penalization used in the diagonal matrix to avoid singularities.
• cte: Should the model have a constant?
• tol: Value to stop the process of iterations.
• maxiter: Maximum number of iterations.
• showIter: Should the iteration history be printed?.

Returns

An object that has the following components:

• fitted: Matrix with the fitted probabilities

• cov: Covariance matrix among the estimates

• Y: Indicator matrix for the dependent variable

• beta: Estimated coefficients for the multinomial logistic regression

• stderr: Standard error of the estimates

• logLik: Logarithm of the likelihood

• Deviance: Deviance of the model

• AIC: Akaike information criterion indicator

• BIC: Bayesian information criterion indicator

• NullDeviance: Deviance of the null model

• Difference: Difference between the two deviance values

• df: Degrees of freedom

• p: p-value asociated to the chi-squared estimate

• CoxSnell: Cox and Snell pseudo R squared

• Nagelkerke: Nagelkerke pseudo R squared

• MacFaden: MacFaden pseudo R squared

• Table: Cross classification of observed and predicted responses

• PercentCorrect: Percentage of correct classifications

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

See Also

RidgeMultinomialLogisticFit

Examples

data(Protein)
  y=Protein[[2]]
  X=Protein[,c(3,11)]
  rmlr = RidgeMultinomialLogisticRegression(y,X,penalization=0.0)
  summary(rmlr)