polylogist: Multinomial logistic regression with ridge penalization

In NominalLogisticBiplot: Biplot representations of categorical data

Description

This function does a logistic regression between a dependent variable y and some independent variables x, and solves the separation problem in this type of regression using ridge regression and penalization.

Usage

polylogist(y, x, penalization = 0.2, cte = TRUE, tol = 1e-04, maxiter = 200, show = FALSE)

Arguments

y	Dependent variable.
x	A matrix with the independent variables.
penalization	Penalization used in the diagonal matrix to avoid singularities.
cte	Should the model have a constant?
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). The extension to nominal logistic model was made by Bull (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

L_j(G|b_jo,B_j)-λ(||b_j0|| + ||B_j||)

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

Value

An object of class "polylogist". This has 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

Author(s)

Julio Cesar Hernandez Sanchez, Jose Luis Vicente-Villardon

Maintainer: Julio Cesar Hernandez Sanchez <[e-mail]>

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(HairColor)
  data = data.matrix(HairColor)
  G = NominalMatrix2Binary(data)
  mca=afc(G,dim=2)
  depVar = data[,1]
  nomreg = polylogist(depVar,mca$RowCoordinates[,1:2],penalization=0.1)
  nomreg
  

Example output

Loading required package: mirt
Loading required package: stats4
Loading required package: lattice
Loading required package: gmodels
Loading required package: MASS
$fitted
          [,1]       [,2]
[1,] 0.4489393 0.55106073
[2,] 0.6181331 0.38186685
[3,] 0.6048331 0.39516686
[4,] 0.8674095 0.13259047
[5,] 0.1524386 0.84756143
[6,] 0.2904237 0.70957629
[7,] 0.9398776 0.06012241

$cov
          [,1]      [,2]      [,3]
[1,] 0.7283273 0.1183096 0.1899474
[2,] 0.1183096 1.0690033 0.3295355
[3,] 0.1899474 0.3295355 1.6151088

$Y
     [,1] [,2]
[1,]    1    0
[2,]    1    0
[3,]    0    1
[4,]    1    0
[5,]    0    1
[6,]    0    1
[7,]    1    0

$beta
           [,1]      [,2]      [,3]
[1,] -0.3889562 -1.290287 -1.388102

$stderr
          [,1]     [,2]     [,3]
[1,] 0.8534209 1.033926 1.270869

$logLik
[1] -2.923095

$Deviance
[1] 5.84619

$AIC
[1] 11.84619

$BIC
[1] 11.68392

attr(,"class")
[1] "polylogist"

NominalLogisticBiplot documentation built on May 2, 2019, 6:03 a.m.