RidgeMultinomialRegression: Ridge Multinomial Logistic Regression

In NominalLogisticBiplot: Biplot representations of categorical data

Description

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.

Usage

RidgeMultinomialRegression(y, x, penalization = 0.2,
cte = TRUE, tol = 1e-04, maxiter = 200, showIter = 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	Value to stop the process of iterations.
maxiter	Maximum number of iterations.
showIter	Should the iteration history be printed?.

Value

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
PercentCorrect	Percentage of correct classifications

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.

See Also

polylogist

Examples

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

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

$NullDeviance
[1] 9.562392

$Difference
[1] 3.716202

$df
[1] 2

$p
[1] 0.1559685

$CoxSnell
[1] 0.4119163

$Nagelkerke
[1] 0.5529903

$MacFaden
[1] 0.3886268

$PercentCorrect
[1] 71.42857

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

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