This function assesses innate features and the association of two centrality measures (or any two other continuous variables) from the aspect of distribution mode, dependence, linearity, monotonicity, partial-moments based correlation, and conditional probability of deviating from corresponding means in opposite direction. This function assumes one variable as dependent and the other as independent for regression analyses. The non-linear nature of the association of two centrality measures is evaluated based on generalized additive models (GAM). The monotonicity of the association is evaluated based on comparing the squared coefficient of Spearman correlation and R-squared of rank regression analysis. Also, the correlation between two variables is assessed via non-linear non-parametric statistics (NNS). For the conditional probability assessment, the independent variable is considered as the condition variable.

double.cent.assess(
data,
nodes.colname,
dependent.colname,
independent.colname,
plot = FALSE
)

## Arguments

data

A data frame containing the values of two continuous variables and the name of observations (nodes).

nodes.colname

The character format (quoted) name of the column containing the name of observations (nodes).

dependent.colname

The character format (quoted) name of the column containing the values of the dependent variable.

independent.colname

The character format (quoted) name of the column containing the values of the independent variable.

plot

logical; FALSE (default) Plots quadrant means of NNS correlation analysis.

## Value

A list of 11 objects including: - Summary of the basic statistics of two centrality measures (or any two other continuous variables). - The results of normality assessment of two variable (p-value > 0.05 imply that the variable is normally distributed). - Description of the normality assessment of the dependent variable. - Description of the normality assessment of the independent variable. - Results of the generalized additive modeling (GAM) of the data. - The association type based on simultaneous consideration of normality assessment, GAM Computation with smoothness estimation, Spearman correlation, and ranked regression analysis of splines. - The Hoeffding's D Statistic of dependence (ranging from -0.5 to 1). - Description of the dependence significance. - Correlation between variables based on the NNS method. - The last two objects are the conditional probability of deviation of two centrality measures from their corresponding means in opposite directions based on both the entire network and the split-half random sample of network nodes.

ad.test for Anderson-Darling test for normality, gam for Generalized additive models with integrated smoothness estimation, lm for Fitting Linear Models, hoeffd for Matrix of Hoeffding's D Statistics, and NNS.dep for NNS Dependence

Other centrality association assessment functions: cond.prob.analysis(), double.cent.assess.noRegression()

## Examples

if (FALSE) {
MyData <- centrality.measures
My.metrics.assessment <- double.cent.assess(data = MyData,
nodes.colname = rownames(MyData),
dependent.colname = "BC",
independent.colname = "NC")
}