Description Usage Arguments Value Definition of Dominance Analysis Types of dominance Fit indices availables References Examples

View source: R/dominanceAnalysis.r

Dominance analysis for OLS (univariate and multivariate), GLM and LMM models

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`x` |
fitted model (lm, glm, betareg), lmWithCov or mlmWithCov object |

`constants` |
vector of predictors to remain unchanged between models |

`terms` |
vector of terms to be analyzed. By default, obtained from the model |

`fit.functions` |
Name of the method used to provide fit indices |

`newdata` |
optional data.frame, that update data used on original model |

`null.model` |
for mixed models, null model against to test the submodels |

`...` |
Other arguments provided to lm or lmer (not implemented yet) |

`predictors` |
Vector of predictors. |

`constants` |
Vector of constant variables. |

`terms` |
Vector of terms to be analyzed. |

`fit.functions` |
Vector of fit indices names. |

`fits` |
List with raw fits indices. See |

`contribution.by.level` |
List of mean contribution of each predictor by level for each fit index. Each element is a data.frame, with levels as rows and predictors as columns, for each fit index. |

`contribution.average` |
List with mean contribution of each predictor for all levels. These values are obtained for every fit index considered in the analysis. Each element is a vector of mean contributions for a given fit index. |

`complete` |
Matrix for complete dominance. |

`conditional` |
Matrix for conditional dominance. |

`general` |
Matrix for general dominance. |

Budescu (1993) developed a clear and intuitive definition of importance in regression models, that states that a predictor's importance reflects its contribution in the prediction of the criterion and that 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.

The original paper (Bodescu, 1993) defines that variable *X_1* dominates
*X_2* when *X_1* is chosen over *X_2* in all possible subset of models
where only one of these two predictors is to be entered.
Later, Azen & Bodescu (2003), name the previously definition as 'complete dominance'
and two other types of dominance: conditional and general dominance.
Conditional dominance is calculated as the average of the additional contributions
to all subset of models of a given model size. General dominance is calculated
as the mean of average contribution on each level.

To obtain the fit-indices for each model, a function called `da.<model>.fit`

is executed. For example, for a lm model, function `da.lm.fit`

provides
*R^2* values.
Currently, seven models are implemented:

- lm
Provides

*R^2*or coefficient of determination. See`da.lm.fit`

- glm
Provides four fit indices recommended by Azen & Traxel (2009): Cox and Snell(1989), McFadden (1974), Nagelkerke (1991), and Estrella (1998). See

`da.glm.fit`

- lmerMod
Provides four fit indices recommended by Lou & Azen (2012). See

`da.lmerMod.fit`

- lmWithCov
Provides

*R^2*for a correlation/covariance matrix. See`lmWithCov`

to create the model and`da.lmWithCov.fit`

for the fit index function.- mlmWithCov
Provides both

*R^2_{XY}*and*P^2_{XY}*for multivariate regression models using a correlation/covariance matrix. See`mlmWithCov`

to create the model and`da.mlmWithCov.fit`

for the fit index function- dynlm
Provides

*R^2*for dynamic linear models. There is no literature reference about using dominance analysis on dynamic linear models, so you're warned!. See`da.dynlm.fit`

.

- betareg
Provides pseudo-

*R^2*, Cox and Snell(1989), McFadden (1974), and Estrella (1998). You could set the link function using link.betareg if automatic detection of link function doesn't work.

See `da.betareg.fit`

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

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

Luo, W., & Azen, R. (2012). Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis. Journal of Educational and Behavioral Statistics, 38(1), 3-31. doi:10.3102/1076998612458319

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
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')
# Maintaining year as a constant on all submodels
da.no.year<-dominanceAnalysis(lm.1,constants='Year')
print(da.no.year)
summary(da.no.year)
plot(da.no.year,which.graph='complete')
# Parameter terms could be used to group variables
da.terms=c(GNP.rel='GNP.deflator+GNP',
pop.rel='Unemployed+Armed.Forces+Population+Unemployed',
year='Year')
da.grouped<-dominanceAnalysis(lm.1,terms=da.terms)
print(da.grouped)
summary(da.grouped)
plot(da.grouped, which.graph='complete')
``` |

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