`nrm.Rd`

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, ...)
```

- 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

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.

`default`

: Default method for nrm`nrm`

: Print method for elements of class`'nrm'`

.

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

`nrm`

```
## 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
# }
```