Fitting gHypEG regression models for multi-edge networks.

nrm is used to fit multi-edge network regression models.

nrm(
  w,
  adj,
  xi = NULL,
  pval = 0.01,
  directed = TRUE,
  selfloops = TRUE,
  regular = FALSE,
  ...
)

# S3 method for default
nrm(
  w,
  adj,
  xi = NULL,
  pval = 0.01,
  directed = FALSE,
  selfloops = FALSE,
  regular = FALSE,
  ci = TRUE,
  significance = FALSE,
  null = FALSE,
  init = NULL,
  ...
)

# S3 method for nrm
print(x, suppressCall = FALSE, ...)

Arguments

w: an object of class 'list' containing the predictors layers (explanatory variables/covariates) of the multiplex, passed as adjacency matrices. The entries of the list can be named.
adj: matrix. The adjacency matrix of the response network (dependent variable).
xi: optional matrix. Passes a non-standard \(\Xi\) matrix.
pval: the significance level used to compute confidence intervals of the parameters. Per default, set to 0.01.
directed: logical. If TRUE the response variable is considered the adjacency matrix of directed graph. If FALSE only the upper triangular of adj is considered. Default set to FALSE.
selfloops: logical. Whether selfloops are allowed. Default set to FALSE.
regular: logical. Whether the gHypEG regression should be performed with correction of combinatorial effects (TRUE) or without (FALSE).
...: optional arguments to print or plot methods.
ci: logical. Whether to compute confidences for the parameters. Defaults to TRUE.
significance: logical. Whether to test the model significance against the null by means of lr-test.
null: logical. Is this a null model? Used for internal routines.
init: numeric. Vector of initial values used for numerical MLE. If only a single value is passed, this is repeated to match the number of predictors in w.
x: object of class 'nrm'
suppressCall: logical, indicating whether to print the call that generated x

Value

nrm returns an object of class 'nrm'.

The function summary is used to obtain and print a summary and analysis of the results. The generic accessory functions coefficients, etc, extract various useful features of the value returned by nrm.

An object of class 'nrm' is a list containing at least the following components:

coef: a named vector of coefficients.
confint: a named matrix with confidence intervals and standard deviation for each coefficient.
omega: the estimated propensity matrix.
xi: the matrix of possibilities.
loglikelihood: log-likelihood of the estimated model.
AIC: AIC of the estimated model.
R2: Mc Fadden pseudo R-squared
csR2: Cox and Snells pseudo R-squared
significance: the p-value of the likelihood-ratio test for the estimated model against the null.

Methods (by class)

nrm(default): Default method for nrm

Methods (by generic)

print(nrm): Print method for elements of class 'nrm'.

References

Casiraghi, Giona. 'Multiplex Network Regression: How do relations drive interactions?.' arXiv preprint arXiv:1702.02048 (2017).

Author

Giona Casiraghi

Examples


## For a complete example see the vignette

data('highschool.predictors')

highschool.m <- nrm(w=highschool.predictors[1], adj=contacts.adj, directed=FALSE,
  selfloops=FALSE)

highschool.m
#> Call:
#> nrm.default(w = highschool.predictors[1], adj = contacts.adj, 
#>     directed = FALSE, selfloops = FALSE)
#> 
#> Coefficients:
#>         Estimate   Std.Err t value    Pr(>t)    
#> gender 0.3160804 0.0021095  149.84 < 2.2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> R2:
#>  McFadden R2 Cox Snell R2 
#>   0.01717056   0.11851816 

# \donttest{
data('highschool.predictors')

highschool.m <- nrm(w=highschool.predictors, adj=contacts.adj, directed=FALSE,
  selfloops=FALSE)

highschool.m
#> Call:
#> nrm.default(w = highschool.predictors, adj = contacts.adj, directed = FALSE, 
#>     selfloops = FALSE)
#> 
#> Coefficients:
#>              Estimate    Std.Err t value    Pr(>t)    
#> gender      0.0773066  0.0021205  36.456 < 2.2e-16 ***
#> class       1.3920467  0.0047051 295.862 < 2.2e-16 ***
#> topic       0.9996831  0.0089452 111.757 < 2.2e-16 ***
#> friendship  0.6958169  0.0024252 286.905 < 2.2e-16 ***
#> facebook   -0.0886211  0.0023652  37.469 < 2.2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> R2:
#>  McFadden R2 Cox Snell R2 
#>    0.5474069    0.9800463 
# }