dominanceanalysis-package {dominanceanalysis}

Dominance analysis for general, generalized and mixed linear models

Description

The dominanceanalysis package allows to perform the dominance analysis for multiple regression models, such as OLS (univariate and multivariate), GLM and HLM. The dominance analysis on this package is performed by dominanceAnalysis function. To perform bootstrap procedures you should use bootDominanceAnalysis function. For both, standard print and summary functions are provided.

Main Features

• Provides complete, conditional and general dominance analysis for lm (univariate and multivariate), lmer and glm (family=binomial) models.

• Covariance / correlation matrixes could be used as input for OLS dominance analysis, using lmWithCov and mlmWithCov methods, respectively.

• Multiple criteria can be used as fit indices, which is useful especially for HLM.

About Dominance Analysis

Dominance analysis is a method developed to evaluate the importance of each predictor in the selected regression model: "one predictor is 'more important than another' if it contributes more to the prediction of the criterion than does its competitor at a given level of analysis." (Azen & Budescu, 2003, p.133).

The original method was developed for OLS regression (Budescu, 1993). Later, several definitions of dominance and bootstrap procedures were provided by Azen & Budescu (2003), as well as adaptations to Generalized Linear Models (Azen & Traxel, 2009) and Hierarchical Linear Models (Luo & Azen, 2013).

Author(s)

Claudio Bustos [e-mail], Filipa Coutinho Soares (documentation)

References

• Budescu, D. V. (1993). Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression. Psychological Bulletin, 114(3), 542-551. doi:10.1037/0033-2909.114.3.542

• Azen, R., & Budescu, D. V. (2003). The dominance analysis approach for comparing predictors in multiple regression. Psychological Methods, 8(2), 129-148. doi:10.1037/1082-989X.8.2.129

• Azen, R., & Budescu, D. V. (2006). Comparing Predictors in Multivariate Regression Models: An Extension of Dominance Analysis. Journal of Educational and Behavioral Statistics, 31(2), 157-180. doi:10.3102/10769986031002157

• Azen, R., & Traxel, N. (2009). Using Dominance Analysis to Determine Predictor Importance in Logistic Regression. Journal of Educational and Behavioral Statistics, 34(3), 319-347. doi:10.3102/1076998609332754

• Luo, W., & Azen, R. (2013). Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis. Journal of Educational and Behavioral Statistics, 38(1), 3-31. doi:10.3102/1076998612458319

See Also

dominanceAnalysis , bootDominanceAnalysis

Examples

# Basic dominance analysis

data(longley)
lm.1<-lm(Employed~.,longley)
da<-dominanceAnalysis(lm.1)
print(da)
summary(da)
plot(da,which.graph='complete')
plot(da,which.graph='conditional')
plot(da,which.graph='general')

# Dominance analysis for HLM

library(lme4)
x1<-rnorm(1000)
x2<-rnorm(1000)
g<-gl(10,100)
g.x<-rnorm(10)[g]
y<-2*x1+x2+g.x+rnorm(1000,sd=0.5)
lmm1<-lmer(y~x1+x2+(1|g))
lmm0<-lmer(y~(1|g))
da.lmm<-dominanceAnalysis(lmm1, null.model=lmm0)
print(da.lmm)
summary(da.lmm)


# GLM analysis

x1<-rnorm(1000)
x2<-rnorm(1000)
x3<-rnorm(1000)
y<-runif(1000)<(1/(1+exp(-(2*x1+x2+1.5*x3))))
glm.1<-glm(y~x1+x2+x3,family="binomial")
da.glm<-dominanceAnalysis(glm.1)
print(da.glm)
summary(da.glm)

# Bootstrap procedure


da.boot<-bootDominanceAnalysis(lm.1,R=1000)
summary(da.boot)

da.glm.boot<-bootDominanceAnalysis(glm.1,R=200)
summary(da.glm.boot)