,
Filipa Coutinho Soares [aut] | Title: | Dominance Analysis |
|---|---|
| Description: | Dominance analysis is a method that allows to compare the relative importance of predictors in multiple regression models: ordinary least squares, generalized linear models, hierarchical linear models, beta regression and dynamic linear models. The main principles and methods of dominance analysis are described in Budescu, D. V. (1993) <doi:10.1037/0033-2909.114.3.542> and Azen, R., & Budescu, D. V. (2003) <doi:10.1037/1082-989X.8.2.129> for ordinary least squares regression. Subsequently, the extensions for multivariate regression, logistic regression and hierarchical linear models were described in Azen, R., & Budescu, D. V. (2006) <doi:10.3102/10769986031002157>, Azen, R., & Traxel, N. (2009) <doi:10.3102/1076998609332754> and Luo, W., & Azen, R. (2013) <doi:10.3102/1076998612458319>, respectively. |
| Authors: | Claudio Bustos Navarrete [aut, cre, cph]
,
Filipa Coutinho Soares [aut] |
| Maintainer: | Claudio Bustos Navarrete <[email protected]> |
| License: | GPL-2 |
| Version: | 2.1.0.9000 |
| Built: | 2025-02-17 03:30:37 UTC |
| Source: | https://github.com/clbustos/dominanceanalysis |
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.
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.
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).
Claudio Bustos [email protected], Filipa Coutinho Soares (documentation)
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
dominanceAnalysis , bootDominanceAnalysis
# 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)# 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)
Retrieve the average contribution for each predictor. Is calculated averaging all contribution by level. The average contribution defines general dominance.
averageContribution(da.object, fit.functions = NULL)averageContribution(da.object, fit.functions = NULL)
da.object |
dominanceAnalysis object |
fit.functions |
name of the fit indices to retrieve. If NULL, all fit indices will be retrieved |
a list. Key corresponds to fit-index and the value is vector, with average contribution for each variable
Other retrieval methods:
contributionByLevel(),
dominanceBriefing(),
dominanceMatrix(),
getFits()
data(longley) da.longley<-dominanceAnalysis(lm(Employed~.,longley)) averageContribution(da.longley)data(longley) da.longley<-dominanceAnalysis(lm(Employed~.,longley)) averageContribution(da.longley)
Bootstrap average values and corresponding standard errors for each predictor in the dominance analysis. These values are used for assessing general dominance.
bootAverageDominanceAnalysis( x, R, constants = c(), terms = NULL, fit.functions = "default", null.model = NULL, ... )bootAverageDominanceAnalysis( x, R, constants = c(), terms = NULL, fit.functions = "default", null.model = NULL, ... )
x |
A model object, like 'lm', 'glm', or 'lmer'. |
R |
An integer indicating the number of bootstrap resamples to be performed. |
constants |
A character vector specifying predictors that should remain constant in the bootstrap analysis. Default is an empty vector. |
terms |
An optional vector of terms (predictors) to be analyzed. If NULL, terms are obtained from the model. Default is NULL. |
fit.functions |
A vector of functions providing fit indices for the model. See 'fit.functions' parameter in 'dominanceAnalysis' function. |
null.model |
An optional model object specifying the null model for linear mixed models, used as a baseline for testing submodels. Default is NULL. |
... |
Additional arguments passed to 'dominanceAnalysis' method |
Use summary() to obtain a nicely formatted data.frame object.
An object of class 'bootAverageDominanceAnalysis' containing: -
boot |
The results of the bootstrap analysis in a |
preds |
The predictors analyzed |
fit.functions |
The fit functions used in the analysis |
R |
The number of bootstrap resamples |
eg |
expanded grid of predictors by fit functions |
terms |
The terms analyzed |
lm.1 <- lm(Employed ~ ., longley) da.ave.boot <- bootAverageDominanceAnalysis(lm.1, R = 1000) summary(da.ave.boot)lm.1 <- lm(Employed ~ ., longley) da.ave.boot <- bootAverageDominanceAnalysis(lm.1, R = 1000) summary(da.ave.boot)
Implements a bootstrap procedure as presented by Azen and Budescu (2003).
Provides the expected level of dominance of predictor over ,
as the degree to which the pattern found in the sample is reproduced in the
bootstrap samples.
bootDominanceAnalysis( x, R, constants = c(), terms = NULL, fit.functions = "default", null.model = NULL, ... )bootDominanceAnalysis( x, R, constants = c(), terms = NULL, fit.functions = "default", null.model = NULL, ... )
x |
An object of class |
R |
The number of bootstrap resamples. |
constants |
A vector of predictors to remain unchanged between models, i.e., variables not subjected to bootstrap analysis. |
terms |
A vector of terms to be analyzed. By default, terms are obtained from the model. |
fit.functions |
A list of functions providing fit indices for the model.
Refer to |
null.model |
Applicable only for linear mixed models. It refers to the null model against which to test the submodels, i.e., only random effects, without any fixed effects. |
... |
Additional arguments provided to |
Use summary() to obtain a nicely formatted data.frame.
An object of class bootDominanceAnalysis containing:
boot |
The results of the bootstrap analysis. |
preds |
The predictors analyzed. |
fit.functions |
The fit functions used in the analysis. |
c.names |
A vector where each value represents the name of a specific dominance analysis result. Names are prefixed with the type of dominance (complete, conditional, or general), and the fit function used, followed by the names of the first and second predictors involved in the comparison. |
m.names |
Names of each one the predictor pairs. |
terms |
The terms analyzed. |
R |
The number of bootstrap resamples. |
lm.1 <- lm(Employed ~ ., longley) da.boot <- bootDominanceAnalysis(lm.1, R = 1000) summary(da.boot)lm.1 <- lm(Employed ~ ., longley) da.boot <- bootDominanceAnalysis(lm.1, R = 1000) summary(da.boot)
Retrieve the average contribution by level for each predictor in a dominance analysis. The average contribution defines conditional dominance.
contributionByLevel(da.object, fit.functions = NULL)contributionByLevel(da.object, fit.functions = NULL)
da.object |
dominanceAnalysis object |
fit.functions |
name of the fit indices to retrieve. If NULL, all fit indices will be retrieved |
a list. Key corresponds to fit-index and the value is a matrix, with contribution of each variable by level
Other retrieval methods:
averageContribution(),
dominanceBriefing(),
dominanceMatrix(),
getFits()
data(longley) da.longley<-dominanceAnalysis(lm(Employed~.,longley)) contributionByLevel(da.longley)data(longley) da.longley<-dominanceAnalysis(lm(Employed~.,longley)) contributionByLevel(da.longley)
Note that the Nagelkerke and Estrella coefficients are designed for discrete dependent variables
and thus cannot be used in this context. Instead, the Cox and Snell coefficient is recommended,
along with the pseudo-. It is worth noting that McFadden's index may produce
negative values and should be avoided.
da.betareg.fit(original.model, newdata = NULL, ...)da.betareg.fit(original.model, newdata = NULL, ...)
original.model |
Original fitted model |
newdata |
Data used in update statement |
... |
ignored |
A function described by using-fit-indices. You could retrieve following indices:
r2.pseudoProvided by betareg by default
r2.mMcFadden(1974)
r2.csCox and Snell(1989).
Cox, D. R., & Snell, E. J. (1989). The analysis of binary data (2nd ed.). London, UK: Chapman and Hall.
Estrella, A. (1998). A new measure of fit for equations with dichotomous dependent variables. Journal of Business & Economic Statistics, 16(2), 198-205. doi: 10.1080/07350015.1998.10524753.
McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.), Frontiers in econometrics (pp. 104-142). New York, NY: Academic Press.
Shou, Y., & Smithson, M. (2015). Evaluating Predictors of Dispersion:A Comparison of Dominance Analysis and Bayesian Model Averaging. Psychometrika, 80(1), 236-256.
Other fit indices:
da.clm.fit(),
da.dynlm.fit(),
da.glm.fit(),
da.lm.fit(),
da.lmWithCov.fit(),
da.lmerMod.fit(),
da.mlmWithCov.fit()
Provides fit indices for ordinal regression models, based on the Nagelkerke (1991) method.
da.clm.fit(original.model, newdata = NULL, ...)da.clm.fit(original.model, newdata = NULL, ...)
original.model |
Original fitted model |
newdata |
Data used in update statement |
... |
ignored |
A function described by using-fit-indices description for interface.
You could retrieve r2.n index, corresponding to Nagelkerke method.
Nagelkerke, N. J. D. (1991). A Note on a General Definition of the Coefficient of Determination. Biometrika, 78(3), 691-692. doi:10.1093/biomet/78.3.691
Other fit indices:
da.betareg.fit(),
da.dynlm.fit(),
da.glm.fit(),
da.lm.fit(),
da.lmWithCov.fit(),
da.lmerMod.fit(),
da.mlmWithCov.fit()
dynlm models.Uses (coefficient of determination) as fit index
da.dynlm.fit(original.model, newdata = NULL, ...)da.dynlm.fit(original.model, newdata = NULL, ...)
original.model |
Original fitted model |
newdata |
Data used in update statement |
... |
ignored |
A function described by using-fit-indices description for interface
Other fit indices:
da.betareg.fit(),
da.clm.fit(),
da.glm.fit(),
da.lm.fit(),
da.lmWithCov.fit(),
da.lmerMod.fit(),
da.mlmWithCov.fit()
These functions are only available for logistic regression models and are based on the work of Azen and Traxel (2009).
da.glm.fit(original.model, newdata = NULL, ...)da.glm.fit(original.model, newdata = NULL, ...)
original.model |
Original fitted model |
newdata |
Data used in update statement |
... |
ignored |
Check daRawResults.
A function described by using-fit-indices. You could retrieve the following indices:
r2.mMcFadden(1974)
r2.csCox and Snell(1989). Use with caution, because don't have 1 as upper bound
r2.nNagelkerke(1991), that corrects the upper bound of Cox and Snell(1989) index
r2.eEstrella(1998)
Azen, R. and 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.
Nagelkerke, N. J. D. (1991). A note on a general definition of the coefficient of determination. Biometrika, 78(3), 691-692. doi:10.1093/biomet/78.3.691.
Cox, D. R., & Snell, E. J. (1989). The analysis of binary data (2nd ed.). London, UK: Chapman and Hall.
Estrella, A. (1998). A new measure of fit for equations with dichotomous dependent variables. Journal of Business & Economic Statistics, 16(2), 198-205. doi: 10.1080/07350015.1998.10524753
McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.), Frontiers in econometrics (pp. 104-142). New York, NY: Academic Press.
Other fit indices:
da.betareg.fit(),
da.clm.fit(),
da.dynlm.fit(),
da.lm.fit(),
da.lmWithCov.fit(),
da.lmerMod.fit(),
da.mlmWithCov.fit()
x1<-rnorm(1000) x2<-rnorm(1000) x3<-rnorm(1000) y<-factor(runif(1000) > exp(x1+x2+x3)/(1+exp(x1+x2+x3))) df.1=data.frame(x1,x2,x3,y) glm.1<-glm(y~x1+x2+x3,data=df.1,family=binomial) da.glm.fit(original.model=glm.1)("names") da.glm.fit(original.model=glm.1)(y~x1)x1<-rnorm(1000) x2<-rnorm(1000) x3<-rnorm(1000) y<-factor(runif(1000) > exp(x1+x2+x3)/(1+exp(x1+x2+x3))) df.1=data.frame(x1,x2,x3,y) glm.1<-glm(y~x1+x2+x3,data=df.1,family=binomial) da.glm.fit(original.model=glm.1)("names") da.glm.fit(original.model=glm.1)(y~x1)
lm models.Uses (coefficient of determination) as fit index
da.lm.fit(original.model, newdata = NULL, ...)da.lm.fit(original.model, newdata = NULL, ...)
original.model |
Original fitted model |
newdata |
Data used in update statement |
... |
ignored |
A function described by using-fit-indices description for interface.
You could retrieve r2 index.
Other fit indices:
da.betareg.fit(),
da.clm.fit(),
da.dynlm.fit(),
da.glm.fit(),
da.lmWithCov.fit(),
da.lmerMod.fit(),
da.mlmWithCov.fit()
x1<-rnorm(1000) x2<-rnorm(1000) y <-x1+x2+rnorm(1000) df.1=data.frame(y=y,x1=x1,x2=x2) lm.1<-lm(y~x1+x2) da.lm.fit(lm.1)("names") da.lm.fit(lm.1)(y~x1)x1<-rnorm(1000) x2<-rnorm(1000) y <-x1+x2+rnorm(1000) df.1=data.frame(y=y,x1=x1,x2=x2) lm.1<-lm(y~x1+x2) da.lm.fit(lm.1)("names") da.lm.fit(lm.1)(y~x1)
Provides fit indices for hierarchical linear models, based on Nakagawa et al.(2017) and Luo and Azen (2013).
da.lmerMod.fit(original.model, null.model, newdata = NULL, ...)da.lmerMod.fit(original.model, null.model, newdata = NULL, ...)
original.model |
Original fitted model |
null.model |
needed for HLM models |
newdata |
Data used in update statement |
... |
ignored |
A function described by using-fit-indices description for interface. By default, four indices are provided:
rb.r2.1 |
Amount of Level-1 variance explained by the addition of the predictor. |
rb.r2.2 |
Amount of Level-2 variance explained by the addition of the predictor. |
sb.r2.1 |
Proportional reduction in error of predicting scores at Level 1 |
sb.r2.2 |
Proportional reduction in error of predicting cluster means at Level 2 |
If performance library is available, the two following indices are also available:
n.marg |
Marginal R2 coefficient based on Nakagawa et al. (2017). Considers only the variance of the fixed effects. |
n.cond |
Conditional R2 coefficient based on Nakagawa et al. (2017). Takes both the fixed and random effects into account. |
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
Nakagawa, S., Johnson, P. C. D., and Schielzeth, H. (2017). The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded. Journal of The Royal Society Interface, 14(134), 20170213.
Other fit indices:
da.betareg.fit(),
da.clm.fit(),
da.dynlm.fit(),
da.glm.fit(),
da.lm.fit(),
da.lmWithCov.fit(),
da.mlmWithCov.fit()
Uses (coefficient of determination).
See lmWithCov.
da.lmWithCov.fit(base.cov, ...)da.lmWithCov.fit(base.cov, ...)
base.cov |
variance/covariance matrix |
... |
ignored |
A function described by using-fit-indices description for interface.
You could retrieve r2 index.
Other fit indices:
da.betareg.fit(),
da.clm.fit(),
da.dynlm.fit(),
da.glm.fit(),
da.lm.fit(),
da.lmerMod.fit(),
da.mlmWithCov.fit()
Provides coefficient of determination for multivariate models.
da.mlmWithCov.fit(base.cov, ...)da.mlmWithCov.fit(base.cov, ...)
base.cov |
variance/covariance matrix |
... |
ignored |
A list with several fit indices
r.squared.xyCorresponds to
p.squared.yxCorresponds to
See mlmWithCov
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
Other fit indices:
da.betareg.fit(),
da.clm.fit(),
da.dynlm.fit(),
da.glm.fit(),
da.lm.fit(),
da.lmWithCov.fit(),
da.lmerMod.fit()
Dominance analysis for OLS (univariate and multivariate), GLM and LMM models
dominanceAnalysis( x, constants = c(), terms = NULL, fit.functions = "default", newdata = NULL, null.model = NULL, ... )dominanceAnalysis( x, constants = c(), terms = NULL, fit.functions = "default", newdata = NULL, null.model = NULL, ... )
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 dominates
when is chosen over 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
values.
Currently, seven models are implemented:
Provides or coefficient of determination. See da.lm.fit
Provides four fit indices recommended by Azen & Traxel (2009): Cox and Snell(1989), McFadden (1974), Nagelkerke (1991), and Estrella (1998). See da.glm.fit
Provides four fit indices recommended by Lou & Azen (2012). See da.lmerMod.fit
Provides for a correlation/covariance matrix. See lmWithCov to create the model and da.lmWithCov.fit for the fit index function.
Provides both and for multivariate regression models using a correlation/covariance matrix. See mlmWithCov to create the model and da.mlmWithCov.fit for the fit index function
Provides 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
.
Provides pseudo-, 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
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')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')
Retrieve a briefing for complete, conditional and general dominance
dominanceBriefing(da.object, fit.functions = NULL, abbrev = FALSE)dominanceBriefing(da.object, fit.functions = NULL, abbrev = FALSE)
da.object |
a |
fit.functions |
name of the fit indices to retrieve. If NULL, all fit indices will be retrieved |
abbrev |
if TRUE |
a list. Each element is a data.frame, that comprises the dominance analysis for a specific fit index. Each data.frame have the predictors as row and each column reports the predictors that are dominated for each predictor
Other retrieval methods:
averageContribution(),
contributionByLevel(),
dominanceMatrix(),
getFits()
# For matrix or data.frame data(longley) da.longley<-dominanceAnalysis(lm(Employed~.,longley)) dominanceBriefing(da.longley, abbrev=FALSE) dominanceBriefing(da.longley, abbrev=TRUE)# For matrix or data.frame data(longley) da.longley<-dominanceAnalysis(lm(Employed~.,longley)) dominanceBriefing(da.longley, abbrev=FALSE) dominanceBriefing(da.longley, abbrev=TRUE)
This methods calculates or retrieve dominance matrix
This methods allows a common interface to retrieve all dominance matrices from dominanceAnalysis objects
dominanceMatrix(x, ...) ## S3 method for class 'data.frame' dominanceMatrix(x, undefined.value = 0.5, ordered = FALSE, ...) ## S3 method for class 'matrix' dominanceMatrix(x, undefined.value = 0.5, ordered = FALSE, ...) ## S3 method for class 'dominanceAnalysis' dominanceMatrix( x, type, fit.functions = NULL, drop = TRUE, ordered = FALSE, ... )dominanceMatrix(x, ...) ## S3 method for class 'data.frame' dominanceMatrix(x, undefined.value = 0.5, ordered = FALSE, ...) ## S3 method for class 'matrix' dominanceMatrix(x, undefined.value = 0.5, ordered = FALSE, ...) ## S3 method for class 'dominanceAnalysis' dominanceMatrix( x, type, fit.functions = NULL, drop = TRUE, ordered = FALSE, ... )
x |
matrix (calculate) or dominanceAnalysis (retrieve) |
... |
extra arguments. Not used |
undefined.value |
value when no dominance can be established |
ordered |
Logical. If TRUE, sort the output according to dominance. |
type |
type of dominance matrix to retrieve. Could be complete, conditional or general |
fit.functions |
name of the fit indices to retrieve. If NULL, all fit indices will be retrieved |
drop |
if TRUE and just one fit index is available, returns a matrix. Else, returns a list |
To calculate a dominance matrix from a matrix or dataframe, use
dominanceMatrix(x,undefined.value).
To retrieve the dominance matrices from a dominanceAnalysis object, use
dominanceMatrix(x,type,fit.function,drop)
for matrix and data-frame, returns a matrix representing dominance.
1 represents domination of the row variable over the column variable,
0 dominance of the column over the row variable.
Undefined dominance is represented by undefined.value parameter.
For dominanceAnalysis object, returns a matrix, if drop parameter
if TRUE and just one index is available. Else, a list is returned, with
keys as name of fit-indices and values as matrices, as described previously.
Other retrieval methods:
averageContribution(),
contributionByLevel(),
dominanceBriefing(),
getFits()
# For matrix or data.frame mm<-data.frame(a=c(5,3,2),b=c(4,2,1),c=c(5,4,3)) dominanceMatrix(mm) # For dominanceAnalysis data(longley) da.longley<-dominanceAnalysis(lm(Employed~.,longley)) dominanceMatrix(da.longley,type="complete")# For matrix or data.frame mm<-data.frame(a=c(5,3,2),b=c(4,2,1),c=c(5,4,3)) dominanceMatrix(mm) # For dominanceAnalysis data(longley) da.longley<-dominanceAnalysis(lm(Employed~.,longley)) dominanceMatrix(da.longley,type="complete")
Retrieve fit matrix or matrices for a given dominanceAnalysis object
getFits(da.object, fit.functions = NULL)getFits(da.object, fit.functions = NULL)
da.object |
dominanceAnalysis object |
fit.functions |
name of the fit indices to retrieve. If NULL, all fit indices will be retrieved |
a list. Key corresponds to fit-index and the value is a matrix, with fits values
Other retrieval methods:
averageContribution(),
contributionByLevel(),
dominanceBriefing(),
dominanceMatrix()
data(longley) da.longley<-dominanceAnalysis(lm(Employed~.,longley)) getFits(da.longley)data(longley) da.longley<-dominanceAnalysis(lm(Employed~.,longley)) getFits(da.longley)
Calculates several measures of fit for Linear Mixed Models based on Lou and Azen (2013) text. Models could be lmer or lme models.
lmmR2(m.null, m.full)lmmR2(m.null, m.full)
m.null |
Null model (only with random intercept effects) |
m.full |
Full model |
lmmR2 class
Calculate regression coefficients and for an OLS regression.
Could be used with dominanceAnalysis to
perform a dominance analysis without the original data.
lmWithCov(f, x)lmWithCov(f, x)
f |
formula for lm model |
x |
correlation/covariance matrix |
coef |
regression coefficients |
r.squared |
|
formula |
formula provided as parameter |
cov |
covariance/correlation matrix provided as parameter |
cov.m<-matrix(c(1,0.2,0.3, 0.2,1,0.5,0.3,0.5,1),3,3, dimnames=list(c("x1","x2","y"),c("x1","x2","y"))) lm.cov<-lmWithCov(y~x1+x2,cov.m) da<-dominanceAnalysis(lm.cov)cov.m<-matrix(c(1,0.2,0.3, 0.2,1,0.5,0.3,0.5,1),3,3, dimnames=list(c("x1","x2","y"),c("x1","x2","y"))) lm.cov<-lmWithCov(y~x1+x2,cov.m) da<-dominanceAnalysis(lm.cov)
Calculate and for multivariate regression
Could be used with dominanceAnalysis to
perform a multivariate dominance analysis without original
data.
mlmWithCov(f, x)mlmWithCov(f, x)
f |
formula. Should use |
x |
correlation/covariance matrix |
r.squared.xy |
|
p.squared.yx |
|
formula |
formula provided as parameter |
cov |
covariance/correlation matrix provided as parameter |
library(car) cor.m<-matrix(c( 1.0000000, 0.7951377, 0.2617168, 0.6720053, 0.3390278, 0.7951377, 1.0000000, 0.3341037, 0.5876337, 0.3404206, 0.2617168, 0.3341037, 1.0000000, 0.3703162, 0.2114153, 0.6720053, 0.5876337, 0.3703162, 1.0000000, 0.3548077, 0.3390278, 0.3404206, 0.2114153, 0.3548077, 1.0000000), 5,5, byrow = TRUE, dimnames = list( c("na","ss","SAT","PPVT","Raven"), c("na","ss","SAT","PPVT","Raven"))) lwith<-mlmWithCov(cbind(na,ss)~SAT+PPVT+Raven,cor.m) da<-dominanceAnalysis(lwith) print(da) summary(da)library(car) cor.m<-matrix(c( 1.0000000, 0.7951377, 0.2617168, 0.6720053, 0.3390278, 0.7951377, 1.0000000, 0.3341037, 0.5876337, 0.3404206, 0.2617168, 0.3341037, 1.0000000, 0.3703162, 0.2114153, 0.6720053, 0.5876337, 0.3703162, 1.0000000, 0.3548077, 0.3390278, 0.3404206, 0.2114153, 0.3548077, 1.0000000), 5,5, byrow = TRUE, dimnames = list( c("na","ss","SAT","PPVT","Raven"), c("na","ss","SAT","PPVT","Raven"))) lwith<-mlmWithCov(cbind(na,ss)~SAT+PPVT+Raven,cor.m) da<-dominanceAnalysis(lwith) print(da) summary(da)
dominanceAnalysis objectPlot for a dominanceAnalysis object
## S3 method for class 'dominanceAnalysis' plot( x, which.graph = c("general", "complete", "complete_no_facet", "conditional"), fit.function = NULL, complete_flipped_axis = TRUE, ... )## S3 method for class 'dominanceAnalysis' plot( x, which.graph = c("general", "complete", "complete_no_facet", "conditional"), fit.function = NULL, complete_flipped_axis = TRUE, ... )
x |
a |
which.graph |
which graph to plot |
fit.function |
name of the fit indices to retrieve. If NULL, first index will be used |
complete_flipped_axis |
For complete and complete_no_facet plot, set the R2 on X axis to allow easier visualization |
... |
unused |
a ggplot object
data(longley) lm.1<-lm(Employed~.,longley) da<-dominanceAnalysis(lm.1) # By default, plot() shows the general dominance plot plot(da) # Parameter which.graph defines which type of dominance to plot plot(da,which.graph='conditional') plot(da,which.graph='complete') # Parameter complete_flipped_axis allows to flip axis on complete plot, to better visualization plot(da,which.graph='complete', complete_flipped_axis=TRUE) plot(da,which.graph='complete', complete_flipped_axis=FALSE)data(longley) lm.1<-lm(Employed~.,longley) da<-dominanceAnalysis(lm.1) # By default, plot() shows the general dominance plot plot(da) # Parameter which.graph defines which type of dominance to plot plot(da,which.graph='conditional') plot(da,which.graph='complete') # Parameter complete_flipped_axis allows to flip axis on complete plot, to better visualization plot(da,which.graph='complete', complete_flipped_axis=TRUE) plot(da,which.graph='complete', complete_flipped_axis=FALSE)
Replace terms by name using the terms definition
replaceTermsInString(string, replacement)replaceTermsInString(string, replacement)
string |
string to be updated |
replacement |
string with replacement for strings. values are replaced by names |
The dataset contains information about points distributed across a small oceanic island (Soares, 2017). In each of these points, a 10-minute count was carried out to record the species presence (assuming 1 if the species was present, or 0 if it was absent). The species' presence/absence is the binary response variable (i.e., dependent variable). Additionally, all sampled points were characterized by multiple environmental variables.
tropicbirdtropicbird
A data frame with 2398 rows and 8 variables:
Point identification
remoteness is an index that represents the difficulty of movement through the landscape, with the highest values corresponding to the most remote areas
land use is an index that represents the land-use intensification, with the highest values corresponding to the more humanized areas (e.g., cities, agricultural areas, horticultures, oil-palm monocultures)
altitude is a continuous variable, with the highest values corresponding to the higher altitude areas
slope is a continuous variable, with the highest values corresponding to the steepest areas
rainfall is a continuous variable, with the highest values corresponding to the rainy wet areas
distance to the coast is the minimum linear distance between each point and the coast line, with the highest values corresponding to the points further away from the coastline
Species presence
Soares, F.C., 2017. Modelling the distribution of Sao Tome bird species: Ecological determinants and conservation prioritization. Faculdade de Ciencias da Universidade de Lisboa.
dominanceAnalysis tries to infer, based on the class of the
model provided, the appropriate fit indices, using the scheme
da.CLASS.fit for name. This method has two interfaces, one for retrieving
the names of the fit indices, and another to retrieve the indices based
on the data.
original.model |
Original fitted model |
newdata |
Data used in update statement |
null.model |
Null model, only needed for HLM models. |
base.cov |
Required if only a covariance/correlation matrix is provided. |
Interfaces are:
da.CLASS.fit("names") returns a vector with names for fit indices
da.CLASS.fit(original.model, data, null.model, base.cov=NULL) returns a function with one parameter, the formula to calculate the submodel.