Package 'ergm.multi'

Description

A set of extensions for the 'ergm' package to fit multilayer/multiplex/multirelational networks and samples of multiple networks. 'ergm.multi' is a part of the Statnet suite of packages for network analysis. See Krivitsky, Koehly, and Marcum (2020) doi:10.1007/s11336-020-09720-7 and Krivitsky, Coletti, and Hens (2023) doi:10.1080/01621459.2023.2242627.

Multilayer network models

Also known as multiplex, multirelational, or multivariate networks, in a multilayer network a pair of actors can have multiple simultaneous relations of different types. For example, in the Lazega lawyer data set included with this package, each pair of lawyers in the firm can have an advice relationship, a coworking relationship, a friendship relationship, or any combination thereof. Application of ERGMs to multilayer networks has a long history (Pattison and Wasserman 1999; Lazega and Pattison 1999), and a number of R packages exist for analysing and estimating them.

ergm.multi implements the general approach of Krivitsky et al. (2020) for specifying multilayer ERGMs, including Layer Logic and the various cross-layer specifications. Its features include:

seamless integration with ergm():

Multilayer specification is contained entirely in an ergm()-style formula and can be nested with any other ergm() terms, including dynamic and multi-network.

unlimited layers:

The number of layers in the modeled network is limited only by computing power.

flexibility and simplicity:

Any valid binary ERGM can be specified for any layer or a logical combination of layers using simple term operators.

heterogeneous layers:

A network can have directed and undirected layers, which can be modeled jointly.

multimode/multilevel support (experimental):

With some care, it is possible to specify models for unipartite and bipartie layers over different subsets of actors, which can be used to specify multimode models.

See Layer() and ergmTerm?L for examples.

Multi-network models

Joint modeling of independent samples of networks on disjoint sets of actors have a long history as well (Zijlstra et al. 2006, Slaughter and Koehly 2016, Stewart et al. 2019, and Vega Yon et al. 2021, for example). ergm.multi facilitates fixed-effect models for samples of networks (possibly heterogeneous in size and composition), using a multivariate linear model for each network's ERGM parameters, with network-level attributes serving as predictors, as formulated by Slaughter and Koehly (2016) and Krivitsky et al. (2023).

Its features include:

seamless integration with ergm():

Multi-network model specification is contained entirely in an ergm()-style formula and can be nested with any other ergm() terms, including dynamic and multilayer.

flexibility and simplicity:

Any valid binary or valued ERGM can be specified for the networks, using simple term operators and the network-level specification with an lm()-style formula.

See Networks(), ergmTerm?N for specification, gofN() for diagnostic facilities, and vignette("Goeyvaerts_reproduction") for a demonstration.

Author(s)

Maintainer: Pavel N. Krivitsky [email protected] (ORCID)

Other contributors:

• Mark S. Handcock [email protected] [contributor]

• David R. Hunter [email protected] [contributor]

• Chad Klumb [email protected] [contributor]

• Pietro Coletti [email protected] [contributor]

• Joyce Cheng [email protected] [contributor]

References

Krivitsky PN, Coletti P, Hens N (2023). “A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks.” Journal of the American Statistical Association, 118(544), 2213-2224. doi:10.1080/01621459.2023.2242627.

Krivitsky PN, Koehly LM, Marcum CS (2020). “Exponential-family Random Graph Models for Multi-layer Networks.” Psychometrika, 85(3), 630–659. doi:10.1007/s11336-020-09720-7.

Lazega E, Pattison PE (1999). “Multiplexity, Generalized Exchange and Cooperation in Organizations: A Case Study.” Social Networks, 21(1), 67–90. doi:10.1016/S0378-8733(99)00002-7.

Pattison P, Wasserman S (1999). “Logit Models and Logistic Regressions for Social Networks: II. Multivariate Relations.” British Journal of Mathematical and Statistical Psychology, 52(2), 169–193.

Slaughter AJ, Koehly LM (2016). “Multilevel Models for Social Networks: Hierarchical Bayesian Approaches to Exponential Random Graph Modeling.” Social Networks, 44, 334–345. doi:10.1016/j.socnet.2015.11.002.

Stewart J, Schweinberger M, Bojanowski M, Morris M (2019). “Multilevel Network Data Facilitate Statistical Inference for Curved ERGMs with Geometrically Weighted Terms.” Social Networks, 59, 98–119. doi:10.1016/j.socnet.2018.11.003.

Vega Yon GG, Slaughter A, de la Haye K (2021). “Exponential Random Graph Models for Little Networks.” Social Networks, 64, 225–238. doi:10.1016/j.socnet.2020.07.005.

Zijlstra BJH, Van Duijn MAJ, Snijders TAB (2006). “The Multilevel $p_2$ Model: A Random Effects Model for the Analysis of Multiple Social Networks.” Methodology, 2(1), 42.

See Also

Useful links:

• https://statnet.org

• Report bugs at https://github.com/statnet/ergm.multi/issues

Description

A method to obtain a network attribute table from a combined_networks object, falling back to the network::as_tibble.network() if vertex or edge attributes are required.

Usage

## S3 method for class 'combined_networks'
as_tibble(
  x,
  attrnames = (match.arg(unit) %in% c("vertices", "networks")),
  ...,
  unit = c("edges", "vertices", "networks"),
  .NetworkID = ".NetworkID",
  .NetworkName = ".NetworkName"
)

Arguments

See Also

network::as_tibble.network()

Description

This term adds one network statistic to the model for each element in d ; the $i$ th such statistic equals the number of nodes of degree d[i] in the first mode of a bipartite network, i.e. with exactly d[i] edges. The first mode of a bipartite network object is sometimes known as the "actor" mode.

This term can only be used with undirected bipartite networks.

Usage

# binary: b1degreeL(d, by=NULL, levels=NULL, Ls=NULL)

Arguments

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This term adds one network statistic to the model for each element in d ; the $i$ th such statistic equals the number of nodes of degree d[i] in the second mode of a bipartite network, i.e. with exactly d[i] edges. The second mode of a bipartite network object is sometimes known as the "event" mode. The optional term by is a character string giving the name of an attribute in the network's vertex attribute list. This term can only be used with undirected bipartite networks.

Usage

# binary: b2degree(d, by=NULL)

Arguments

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, frequently-used, undirected, binary

Description

Models marginal dependence layers within each dyad by imposing a Conway–Maxwell-Binomial (CMB) distribution on the number of layers in each dyad that have a tie.

The term adds one statistic to the model, equalling the sum over all the dyads in the network of $\log\{E!(R-E)!/R!\}$ , where $E$ is the number of layers in Ls with an edge in that dyad and $R$ being the total number of layers in Ls .

Usage

# binary: CMBL(Ls=~.)

Arguments

Details

A positive coefficient induces positive dependence and a negative one induces negative dependence.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

Given a list of compatible networks, the combine_networks() returns a single block-diagonal network, preserving attributes that can be preserved.

Usage

combine_networks(
  nwl,
  ignore.nattr = c("mnext"),
  ignore.vattr = c(),
  ignore.eattr = c(),
  blockID.vattr = ".NetworkID",
  blockName.vattr = NULL,
  detect.edgecov = FALSE,
  keep.unshared.attr = FALSE,
  subnet.cache = FALSE
)

## S3 method for class 'combined_networks'
print(x, ...)

## S3 method for class 'combined_networks'
summary(object, ...)

## S3 method for class 'summary.combined_networks'
print(x, ...)

Arguments

Value

an object of class combined_networks inheriting from network::network with a block-diagonal structure (or its bipartite equivalent) comprising the networks passed in nwl. In particular,

• the returned network's size is the sum of the input networks';

• its basic properties (directedness and bipartednes) are the same;

• the input networks' sociomatrices (both edge presence and edge attributes) are the blocks in the sociomatrix of the returned network;

• vertex attributes are concatenated;

• edge attributes are assigned to their respective edges in the returned network;

• network attributes are stored in a list; but if detect.edgecov==TRUE, those network attributes that have the same dimension as the sociomatrices of the constituent networks, they are combined into a single block-diagonal matrix that is then stored as that attribute.

In addition, two new vertex attributes, specified by blockID.vattr and (optionally) blockName.vattr contain, respectively, the index in nwl of the network from which that vertex came and its name, determined as follows:

1. If nwl is a named list, names from the list are used.

2. If not 1, but the network has an attribute title, it is used.

3. Otherwise, a numerical index is used.

If blockID.vattr already exists on the constituent networks, the index is prepended to the attribute.

The values of blockID.vattr and blockName.vattr are stored in network attributes ".blockID.vattr" and ".blockName.vattr".

Functions

• print(combined_networks): A wrapper around network::print.network() to print constituent network information and omit some internal variables.

• summary(combined_networks): A wrapper around network::summary.network() to print constituent network information and omit some internal variables.

• print(summary.combined_networks): A wrapper around network::print.summary.network() to print constituent network information and omit some internal variables.

Examples

data(samplk)

o1 <- combine_networks(list(samplk1, samplk2, samplk3))
image(as.matrix(o1))
head(get.vertex.attribute(o1, ".NetworkID"))
o2 <- combine_networks(list(o1, o1))
image(as.matrix(o2))
head(get.vertex.attribute(o2, ".NetworkID", unlist=FALSE))

data(florentine)
f1 <- combine_networks(list(business=flobusiness, marriage=flomarriage),
                       blockName.vattr=".NetworkName")
image(as.matrix(f1))
head(get.vertex.attribute(f1, ".NetworkID"))
head(get.vertex.attribute(f1, ".NetworkName"))

Description

control.gofN.ergm (or its alias, control.gofN) is intended to be used with gofN() specifically and will "inherit" as many control parameters from ergm fit as possible().

Usage

control.gofN.ergm(
  nsim = 100,
  obs.twostage = nsim/2,
  array.max = 128,
  simulate = control.simulate.ergm(),
  obs.simulate = control.simulate.ergm(),
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE
)

control.gofN(
  nsim = 100,
  obs.twostage = nsim/2,
  array.max = 128,
  simulate = control.simulate.ergm(),
  obs.simulate = control.simulate.ergm(),
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE
)

Arguments

Details

Auxiliary function as user interface for fine-tuning ERGM Goodness-of-Fit Evaluation.

Description

This term adds one network statistic to the model for each element in d where the $i$ th such statistic equals the number of dyads in the network with exactly d[i] shared partners. For a directed network, multiple shared partner definitions are possible.

dspL and ddspL are aliases for consistency with ergm.

Usage

# binary: ddspL(d, type="OTP", Ls.path=NULL, L.in_order=FALSE)

# binary: dspL(d, type="OTP", Ls.path=NULL, L.in_order=FALSE)

Arguments

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

• Outgoing Two-path ("OTP"): vertex $k$ is an OTP shared partner of ordered pair $(i,j)$ iff $i \to k \to j$. Also known as "transitive shared partner".

• Incoming Two-path ("ITP"): vertex $k$ is an ITP shared partner of ordered pair $(i,j)$ iff $j \to k \to i$. Also known as "cyclical shared partner"

• Reciprocated Two-path ("RTP"): vertex $k$ is an RTP shared partner of ordered pair $(i,j)$ iff $i \leftrightarrow k \leftrightarrow j$.

• Outgoing Shared Partner ("OSP"): vertex $k$ is an OSP shared partner of ordered pair $(i,j)$ iff $i \to k, j \to k$.

• Incoming Shared Partner ("ISP"): vertex $k$ is an ISP shared partner of ordered pair $(i,j)$ iff $k \to i, k \to j$.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This term adds one network statistic to the model for each element in d ; the $i$ th such statistic equals the number of nodes in the network of degree d[i] , i.e. with exactly d[i] edges.

This term can only be used with undirected networks; for directed networks see idegree and odegree .

Usage

# binary: degreeL(d, by=NULL, homophily=FALSE, levels=NULL, Ls=NULL)

Arguments

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This term adds one network statistic to the model for each element in d where the $i$ th such statistic equals the number of edges in the network with exactly d[i] shared partners. For a directed network, multiple shared partner definitions are possible.

espL and despL are aliases for consistency with ergm.

Usage

# binary: despL(d, type="OTP", L.base=NULL, Ls.path=NULL, L.in_order=FALSE)

# binary: espL(d, type="OTP", L.base=NULL, Ls.path=NULL, L.in_order=FALSE)

Arguments

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

• Outgoing Two-path ("OTP"): vertex $k$ is an OTP shared partner of ordered pair $(i,j)$ iff $i \to k \to j$. Also known as "transitive shared partner".

• Incoming Two-path ("ITP"): vertex $k$ is an ITP shared partner of ordered pair $(i,j)$ iff $j \to k \to i$. Also known as "cyclical shared partner"

• Reciprocated Two-path ("RTP"): vertex $k$ is an RTP shared partner of ordered pair $(i,j)$ iff $i \leftrightarrow k \leftrightarrow j$.

• Outgoing Shared Partner ("OSP"): vertex $k$ is an OSP shared partner of ordered pair $(i,j)$ iff $i \to k, j \to k$.

• Incoming Shared Partner ("ISP"): vertex $k$ is an ISP shared partner of ordered pair $(i,j)$ iff $k \to i, k \to j$.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This term adds one network statistic to the model equal to the geometrically weighted dyadwise shared partner distribution with decay parameter. Note that the GWDSP statistic is equal to the sum of GWNSP plus GWESP. For a directed network, multiple shared partner definitions are possible.

gdwdspL and dgwdspL are aliases for consistency with ergm.

Usage

# binary: dgwdspL(decay, fixed=FALSE, cutoff=30, type="OTP",
#                 Ls.path=NULL, L.in_order=FALSE)

# binary: gwdspL(decay, fixed=FALSE, cutoff=30, type="OTP",
#                Ls.path=NULL, L.in_order=FALSE)

Arguments

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

• Outgoing Two-path ("OTP"): vertex $k$ is an OTP shared partner of ordered pair $(i,j)$ iff $i \to k \to j$. Also known as "transitive shared partner".

• Incoming Two-path ("ITP"): vertex $k$ is an ITP shared partner of ordered pair $(i,j)$ iff $j \to k \to i$. Also known as "cyclical shared partner"

• Reciprocated Two-path ("RTP"): vertex $k$ is an RTP shared partner of ordered pair $(i,j)$ iff $i \leftrightarrow k \leftrightarrow j$.

• Outgoing Shared Partner ("OSP"): vertex $k$ is an OSP shared partner of ordered pair $(i,j)$ iff $i \to k, j \to k$.

• Incoming Shared Partner ("ISP"): vertex $k$ is an ISP shared partner of ordered pair $(i,j)$ iff $k \to i, k \to j$.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This term adds a statistic equal to the geometrically weighted edgewise (not dyadwise) shared partner distribution with decay parameter. For a directed network, multiple shared partner definitions are possible.

gdwespL and dgwespL are aliases for consistency with ergm.

Usage

# binary: dgwespL(decay, fixed=FALSE, cutoff=30, type="OTP", L.base=NULL,
#                 Ls.path=NULL, L.in_order=FALSE)

# binary: gwespL(decay, fixed=FALSE, cutoff=30, type="OTP", L.base=NULL,
#                Ls.path=NULL, L.in_order=FALSE)

Arguments

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

• Outgoing Two-path ("OTP"): vertex $k$ is an OTP shared partner of ordered pair $(i,j)$ iff $i \to k \to j$. Also known as "transitive shared partner".

• Incoming Two-path ("ITP"): vertex $k$ is an ITP shared partner of ordered pair $(i,j)$ iff $j \to k \to i$. Also known as "cyclical shared partner"

• Reciprocated Two-path ("RTP"): vertex $k$ is an RTP shared partner of ordered pair $(i,j)$ iff $i \leftrightarrow k \leftrightarrow j$.

• Outgoing Shared Partner ("OSP"): vertex $k$ is an OSP shared partner of ordered pair $(i,j)$ iff $i \to k, j \to k$.

• Incoming Shared Partner ("ISP"): vertex $k$ is an ISP shared partner of ordered pair $(i,j)$ iff $k \to i, k \to j$.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This term is just like gwespL and gwdspL except it adds a statistic equal to the geometrically weighted nonedgewise (that is, over dyads that do not have an edge) shared partner distribution with decay parameter. For a directed network, multiple shared partner definitions are possible.

gdwnspL and dgwnspL are aliases for consistency with ergm.

Usage

# binary: dgwnspL(decay, fixed=FALSE, cutoff=30, type="OTP", L.base=NULL,
#                 Ls.path=NULL, L.in_order=FALSE)

# binary: gwnspL(decay, fixed=FALSE, cutoff=30, type="OTP", L.base=NULL,
#                Ls.path=NULL, L.in_order=FALSE)

Arguments

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

• Outgoing Two-path ("OTP"): vertex $k$ is an OTP shared partner of ordered pair $(i,j)$ iff $i \to k \to j$. Also known as "transitive shared partner".

• Incoming Two-path ("ITP"): vertex $k$ is an ITP shared partner of ordered pair $(i,j)$ iff $j \to k \to i$. Also known as "cyclical shared partner"

• Reciprocated Two-path ("RTP"): vertex $k$ is an RTP shared partner of ordered pair $(i,j)$ iff $i \leftrightarrow k \leftrightarrow j$.

• Outgoing Shared Partner ("OSP"): vertex $k$ is an OSP shared partner of ordered pair $(i,j)$ iff $i \to k, j \to k$.

• Incoming Shared Partner ("ISP"): vertex $k$ is an ISP shared partner of ordered pair $(i,j)$ iff $k \to i, k \to j$.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

Returns a directed version of an undirected binary network

Usage

direct.network(x, rule = c("both", "upper", "lower"))

Arguments

Description

This term adds one network statistic to the model for each element in d where the $i$ th such statistic equals the number of non-edges in the network with exactly d[i] shared partners. For a directed network, multiple shared partner definitions are possible.

nspL and dnspL are aliases for consistency with ergm.

Usage

# binary: dnspL(d, type="OTP", L.base=NULL, Ls.path=NULL, L.in_order=FALSE)

# binary: nspL(d, type="OTP", L.base=NULL, Ls.path=NULL, L.in_order=FALSE)

Arguments

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

• Outgoing Two-path ("OTP"): vertex $k$ is an OTP shared partner of ordered pair $(i,j)$ iff $i \to k \to j$. Also known as "transitive shared partner".

• Incoming Two-path ("ITP"): vertex $k$ is an ITP shared partner of ordered pair $(i,j)$ iff $j \to k \to i$. Also known as "cyclical shared partner"

• Reciprocated Two-path ("RTP"): vertex $k$ is an RTP shared partner of ordered pair $(i,j)$ iff $i \leftrightarrow k \leftrightarrow j$.

• Outgoing Shared Partner ("OSP"): vertex $k$ is an OSP shared partner of ordered pair $(i,j)$ iff $i \to k, j \to k$.

• Incoming Shared Partner ("ISP"): vertex $k$ is an ISP shared partner of ordered pair $(i,j)$ iff $k \to i, k \to j$.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This is a list of 318 network objects derived from contact diary data collected by by Goeyvaerts et al. (2018). The study recruited households in Flanders and Brussels-Capital region with at least one child 12 or under. The networks are symmetrized.

Usage

data(Goeyvaerts)

Format

An object of class list of length 318.

Nonstandard Network Attributes

included

(logical) whether the network was included in Goeyvaerts's analysis. (Two were excluded.)

weekday

(logical) whether the contact diary on which the network is based was collected on a weekday, as opposed to weekend.

Nonstandard Vertex Attributes

age

(numeric) the household member's age.

gender

(character) the household member's gender ("F"/"M").

role

(character) the household member's inferred role ("Father"/"Mother"/"Child"/"Grandmother").

Licenses and Citation

When publishing results obtained using this data set, the original authors (Goeyvaerts et al. 2018) should be cited, along with this R package.

Source

The data were collected and by Goeyvaerts et al. (2018) and curated by Pietro Coletti.

References

Goeyvaerts N, Santermans E, Potter G, Torneri A, Kerckhove KV, Willem L, Aerts M, Beutels P, Hens N (2018). “Household Members Do Not Contact Each Other at Random: Implications for Infectious Disease Modelling.” Proceedings of the Royal Society B: Biological Sciences, 285(1893), 20182201. doi:10.1098/rspb.2018.2201.

See Also

vignette("Goeyvaerts_reproduction") for a vignette reproducing the Goeyvaerts analysis and performing diagnostics

Description

gofN() performs a simulation to obtain Pearson residuals for the multivariate linear model for ERGM parameters, which can then be used for a variety of diagnostics and diagnostic plots developed by Krivitsky et al. (2023).

Usage

gofN(
  object,
  GOF = NULL,
  subset = TRUE,
  control = control.gofN.ergm(),
  save_stats = FALSE,
  ...
)

## S3 method for class 'gofN'
x[i, j, ..., drop = FALSE]

## S3 method for class 'gofN'
augment(x, ...)

## S3 method for class 'gofN'
summary(object, by = NULL, ...)

Arguments

Value

An object of class gofN: a named list containing a list for every statistic in the specified GOF formula with the following elements vectors of length equal to the number of subnetworks:

In addition, the following attr-style attributes are included:

Methods (by generic)

• [: Extract a subset of statistics for which goodness-of-fit had been computed.

• augment(gofN): a method for constructing a tibble of network attributes augmented with goodness of fit information. Columns include:

  network attributes

  the attributes of each of the networks

  .stat_name

  name of the simulated statistic

  .stat_id

  index of the simulated statistic in the gofN object

  .network_id

  index of the network in the networks for which gofN was run (excluding those not in the subset)

  .fitted

  predicted value for the statistic

  .observed

  either the observed (for completely observed networks) or the predicted conditional on observed (for partially observed networks) value of the statistic

  .pearson

  the standardised Pearson residual

  .var, .var.obs

  estimated unconditional and average conditional variance of the statistic

  .weight

  inverse of the variance of the residual

• summary(gofN): A simple summary function.

References

Krivitsky PN, Coletti P, Hens N (2023). “A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks.” Journal of the American Statistical Association, 118(544), 2213-2224. doi:10.1080/01621459.2023.2242627.

See Also

plot.gofN() and autoplot.gofN() for plotting gofN objects to make residual plots; ergm::gof() for single-network goodness-of-fit simulations in ergm

Examples

data(samplk)
monks <- Networks(samplk1, samplk2, samplk3,samplk1, samplk2, samplk3,samplk1, samplk2, samplk3)
fit <- ergm(monks~N(~edges+nodematch("group")))
fit.gof <- gofN(fit) # GOF = original model
summary(fit.gof)
plot(fit.gof)
fit.gof <- gofN(fit, GOF=~triangles)
summary(fit.gof)
plot(fit.gof)


samplk1[1,]<-NA
samplk2[,2]<-NA
monks <- Networks(samplk1, samplk2, samplk3,samplk1, samplk2, samplk3,samplk1, samplk2, samplk3)
fit <- ergm(monks~N(~edges+nodematch("group")))
fit.gof <- gofN(fit) # GOF = original model
summary(fit.gof)
plot(fit.gof)
fit.gof <- gofN(fit, GOF=~triangles)
summary(fit.gof)
plot(fit.gof)
plot(fit.gof, against=~log(.fitted)) # Plot against transformed fitted values.


### If 'ggplot2' and 'ggrepel' are installed, illustrate the autoplot() method.
if(require("ggplot2") && requireNamespace("ggrepel")){
  autoplot(fit.gof)
}

# Default is good enough in this case, but sometimes, we might want to set it higher. E.g.,
## Not run: 
fit.gof <- gofN(fit, GOF=~edges, control=control.gofN.ergm(nsim=400))

## End(Not run)


### If 'generics' is installed, illustrate the augment() method.
if(require("generics")){
  augment(fit.gof)
}

Description

This term adds one network statistic to the model equal to the weighted degree distribution with decay controlled by the decay parameter, which should be non-negative, for nodes in the first mode of a bipartite network. The first mode of a bipartite network object is sometimes known as the "actor" mode.

This term can only be used with undirected bipartite networks.

Usage

# binary: gwb1degreeL(decay, fixed=FALSE, cutoff=30, levels=NULL, Ls=NULL)

Arguments

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This term adds one network statistic to the model equal to the weighted degree distribution with decay controlled by the which should be non-negative, for nodes in the second mode of a bipartite network. The second mode of a bipartite network object is sometimes known as the "event" mode.

This term can only be used with undirected bipartite networks.

Usage

# binary: gwb2degreeL(decay, fixed=FALSE, attrname=NULL, cutoff=30, levels=NULL, Ls=NULL)

Arguments

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This term adds one network statistic to the model equal to the weighted degree distribution with decay controlled by the decay parameter.

This term can only be used with undirected networks.

Usage

# binary: gwdegreeL(decay, fixed=FALSE, attrname=NULL, cutoff=30, levels=NULL)

Arguments

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This term adds one network statistic to the model equal to the weighted in-degree distribution with decay parameter. This term can only be used with directed networks.

Usage

# binary: gwidegreeL(decay, fixed=FALSE, attrname=NULL, cutoff=30, levels=NULL, Ls=NULL)

Arguments

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This term adds one network statistic to the model equal to the weighted out-degree distribution with decay parameter . This term can only be used with directed networks.

Usage

# binary: gwodegreeL(decay, fixed=FALSE, attrname=NULL, cutoff=30, levels=NULL, Ls=NULL)

Arguments

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

This term adds one network statistic to the model for each element in d ; the $i$ th such statistic equals the number of nodes in the network of in-degree d[i] , i.e. the number of nodes with exactly d[i] in-edges. This term can only be used with directed networks; for undirected networks see degree .

Usage

# binary: idegreeL(d, by=NULL, homophily=FALSE, levels=NULL)

Arguments

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

Evaluates the terms in formula on an observed or logical layers specified in formula Ls and sums the results elementwise.

Usage

# binary: L(formula, Ls=~.)

Arguments

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

A function for specifying the LHS of a multilayer (a.k.a. multiplex, a.k.a. multirelational, a.k.a. multivariate) ERGM in the framework of Krivitsky et al. (2020).

Usage

Layer(..., .symmetric = NULL, .bipartite = NULL, .active = NULL)

Arguments

Value

A network object comprising the provided layers, with layer metadata.

Due to certain optimizations, the resulting network object's network and vertex attributes should be treated as read-only: do not modify them. If you need to change existing attributes or add new ones, do so on the input networks and call Layer(...) again.

Specifying models for multilayer networks

In order to fit a model for multilayer networks, first use Layer construct an LHS network that ergm() will understand as multilayered.

Used in the formula directly, most, but not all, ergm terms will sum their statistics over the observed layers.

Some terms are layer-aware, however. By convention, layer-aware terms have capital L appended to them. For example, mutualL is a layer-aware generalization of mutual. These terms have one or more explicit (usually optional) layer specification arguments. By convention, an argument that requires one layer specification is named L= and one that requires a list of specifications (constructed by list() or c()) is named Ls=; and a specification of the form ~. is a placeholder for all observed layers.

Operator L(formula, Ls=...) can be used to evaluate arbitrary terms in the formula on specified layers.

Layer specification documentation follows.

Layer Logic

Each formula's right-hand side describes an observed layer or some "logical" layer, whose ties are a function of corresponding ties in observed layers. (Krivitsky et al. 2020)

The observed layers can be referenced either by name or by number (i.e., order in which they were passed to Layer). When referencing by number, enclose the number in quotation marks (e.g., "1") or backticks (e.g., “1”).

Arithmetical, relational, and logical operators can be used to combine them. All listed operators are implemented, as well as functions abs, round, and sign. Standard operator precedence applies, so use of parentheses is recommended to ensure the logical expression is what it looks like.

Important: For performance reasons, ergm.multi's Layer Logic implementation uses integer arithmetic. This means, in particular, that / will round down instead of returning a fraction (as %/% does in R), and round() function without a second argument (which can be negative to round to the nearest 10, 100, etc.) is not meaningful and will be ignored.

For example, if LHS is Layer(A=nwA, B=nwB), both ~`2` and ~B refer to nwB, while A&!B refers to a “logical” layer that has ties that are in nwA but not in nwB.

Transpose function t() applied to a directed layer will reverse the direction of all relations (transposing the sociomatrix). Unlike the others, it can only be used on an observed layer directly. For example, ~t(`1`)&t(`2`) is valid but ~t(`1`&`2`) is not.

At this time, logical expressions that produce complete graphs from empty graph inputs (e.g., A==B or !A) are not supported.

Summing layers

Some of the terms that call for a list of layers (i.e., have Ls= arguments) will sum the statistic over the layers. For example, Layer(nw1,nw2)~L(~edges, c(~`1`,~(`2`&!`1`))) produces the number of edges in layer 1 plus the number of edges in layer 2 but not in layer 1.

For these formulas, one can specify the layer's weight on its left-handside. For example, Layer(nw1,nw2)~L(~edges, c(3~`1`,-1~(`2`&!`1`))) will produce three times the number of edges in layer 1, minus the number of edges in layer 2 but not in layer 1.

Note

The resulting network will be the "least common denominator" network: if not all layers have the same bipartedness, all layers will appear as unipartite to the statistics, and if any are directed, all will be. However, certain operator terms, particularly Symmetrize() and S(), can be used to construct a bipartite subgraph of a unipartite graph or change directedness.

Its nonstandard network and vertex attributes will be taken from the first network in the list. The subsequent networks' attributes will be overwritten with a warning if they differ from those in the first network.

References

Krivitsky PN, Koehly LM, Marcum CS (2020). “Exponential-family Random Graph Models for Multi-layer Networks.” Psychometrika, 85(3), 630–659. doi:10.1007/s11336-020-09720-7.

See Also

Help on model specification for specific terms.

Examples

data(florentine)

# Method 1: list of networks
flo <- Layer(list(m = flomarriage, b = flobusiness))
ergm(flo ~ L(~edges, ~m)+L(~edges, ~b))

# Method 2: networks as arguments
flo <- Layer(m = flomarriage, b = flobusiness)
ergm(flo ~ L(~edges, ~m)+L(~edges, ~b))

# Method 3: edge attributes (also illustrating renaming):
flo <- flomarriage | flobusiness
flo[,, names.eval="marriage"] <- as.matrix(flomarriage)
flo[,, names.eval="business"] <- as.matrix(flobusiness)
flo # edge attributes
flo <- Layer(flo, c(m="marriage", b="business"))
ergm(flo ~ L(~edges, ~m)+L(~edges, ~b))

### Specifying modes and mixed bipartitedness

# Suppose we have a two-mode network with 5 nodes on Mode 1 and 15
# on Mode 2, and suppose that we observe two layers, one only among
# actors of Mode 1 and the other bipartite between Modes 1 and 2.

# Construct the two layers' networks:
nw1 <- network.initialize(20, dir=FALSE)
nw12 <- network.initialize(20, dir=FALSE, bipartite=5)
nw1 %v% "mode" <- rep(1:2,c(5,15))

# For testing: the maximal set of edges for each type of network:
nw1[1:5,1:5] <- 1
nw12[1:5,6:20] <- 1

# The .active argument specifies the following:
# * nw1's vertices are only active if their mode=1 (i.e., 1-2, 2-1,
#   and 2-2 can't have edges).
# * nw12's vertices are all active, but the network is bipartite,
#   so constraints will be adjusted automatically.
lnw <- Layer(nw1, nw12, .active=list(~mode==1, ~TRUE))

summary(lnw~
edges+ # 5*4/2+5*15 = 10+75 = 85
L(~edges,~`1`)+ # 5*4/2 = 10
L(~edges,~`2`)+ # 5*15 = 75
L(~edges,~(`1`|`2`))+ # This logical layer has contents of both, so also 85.
L(~edges,~(`1`&`2`)) # There is no overlap between the two layers, so 0.
)

# Layer-aware terms can be used:

nw1[,] <-0
nw1[1,2:3] <- 1
nw1[2,3] <- 1
nw12[,] <- 0
nw12[1,6:7] <- 1
nw12[2,6:7] <- 1

lnw <- Layer(nw1, nw12, .active=list(~mode==1,~TRUE))

summary(lnw~L(~triangles, ~`1`)+ # 1-2-3 triangle.
  L(~triangles, ~`1`|`2`)+ # 1-2-3, 1-2-6, 1-2-7 triangles
  dgwespL(L.base=~`1`, Ls.path=list(~`2`,~`2`)) # 1-2-6 and 1-2-7 only
)

# Because the layers are represented as a block-diagonal matrix,
# this will only count triangles entirely contained within a single
# layer, i.e., 1-2-3:
summary(lnw~triangles)

# If you need to evaluate bipartite-only statistics on the second
# layer, you need to use the S() operator to select the bipartite
# view:
summary(lnw~L(~S(~b1degree(1:3)+b2degree(1:3),1:5~6:20), ~`2`))

Description

This dataset contains a network of relations of various types among 71 lawyers (partners and associates) in a New England (Northeastern US) corporate law firm referred to as “SG&R” collected 1988–1991 by Lazega (2001).

Usage

data(Lazega)

Format

An object of class network of length 5.

Details

All relations are directed.

Nonstandard Vertex Attributes

age

(numeric) the lawyer's age.

gender

(character) the lawyer's gender ("man"/"woman").

office

(character) in which of the firm's three offices the lawyer is based ("Boston"/"Hartford"/"Providence").

practice

(character) which area of law the lawyer practices ("corporate"/"litigation").

school

(character) from which law school the lawyer graduated ("Harvard/Yale"/"UConnecticut"/"other").

seniority

(numeric) the lawyer's seniority rank in the firm (1 = high).

status

(character) the lawyer's status in the firm ("associate"/"partner").

yrs_frm

(numeric) the number of years the lawyer has been with the firm.

Nonstandard Edge Attributes

Each directed edge $i\rightarrow j$ has the following attributes:

advice

(logical) whether $i$ has reported receiving advice from $j$. (Note that as defined, advice flows from head of the directed edge to the tail.)

coworker

(logical) whether $i$ has reported receiving $j$'s assistance in preparing documents. (Note that as defined, assistance flows from head of the directed edge to the tail.)

friendship

(logical) whether $i$ considers $j$ a friend outside of work.

Licenses and Citation

When publishing results obtained using this data set, the original author (Lazega 2001) should be cited, along with this R package.

Source

This version of the dataset was retrieved from the RSiena web site and was compiled by Christopher Steven Marcum and Pavel N. Krivitsky for Krivitsky et al. (2020).

References

Krivitsky PN, Koehly LM, Marcum CS (2020). “Exponential-family Random Graph Models for Multi-layer Networks.” Psychometrika, 85(3), 630–659. doi:10.1007/s11336-020-09720-7.

Lazega E (2001). The Collegial Phenomenon: The Social Mechanisms of Cooperation among Peers in a Corporate Law Partnership. Oxford University Press. ISBN 9780199242726.

Examples

data(Lazega)
# Construct a multilayer network for ergm(). (See `?Layer` for syntax.)
LLazega <- Layer(Lazega, c("advice", "coworker", "friendship"))
# Specify a layer logic model.
efit <- ergm(LLazega ~ L(~edges + mutual, ~advice) +
                       L(~edges + mutual, ~coworker) +
                       L(~edges + mutual, ~friendship) +
                       L(~edges + mutual, ~advice&coworker) +
                       L(~edges + mutual, ~advice&friendship) +
                       L(~edges + mutual, ~coworker&friendship))
summary(efit)

Description

This non-method runs a properly weighted linear model on the raw residuals of a gofN simulation for a multi-network ERGM fit.

Usage

lm.gofN(formula, data, ...)

Arguments

Details

The formula's RHS is evaluated in an environment comprising the network statistics used in the gofN() call (which refer to the raw residuals for the corresponding statistic) and the network attributes.

The LHS is handled in a nonstandard manner, designed to make it easier to reference the usually lengthy network statistics: first, it is evaluated in the formula's environment. If the evaluation is successful and the result is numeric, these numbers are used as indices of the statistics in the gofN object to use on the RHS. If it is a character vector, it is treated as names of these statistics.

Value

A list of lm objects, one for each element of the vector on the LHS.

See Also

gofN() and related methods.

Examples

data(samplk)
# Add time indices:
samplk1 %n% "t" <- 1
samplk2 %n% "t" <- 2
samplk3 %n% "t" <- 3

monks <- Networks(samplk1, samplk2, samplk3)

fit <- ergm(monks~N(~edges+nodematch("group")))
fit.gof <- gofN(fit) # GOF = original model

# Is there a time effect we should incorporate?
fit.gof.lm <- lm.gofN((1:2)~t, data=fit.gof)

lapply(fit.gof.lm, summary)

Description

This function is to be considered experimental. Do NOT rely on it. It may, eventually, be moved to ergm, perhaps integrated into the simulate methods.

Usage

marg_cond_sim(
  object,
  nsim = 1,
  obs.twostage = nsim/2,
  GOF = NULL,
  control = control.gofN.ergm(),
  save_stats = FALSE,
  negative_info = c("error", "warning", "message", "ignore"),
  ...
)

Arguments

Value

an object of similar structure as that returned by gofN().

Description

In binary ERGMs, equal to the number of pairs of actors $i$ and $j$ for which $(i{\rightarrow}j)$ and $(j{\rightarrow}i)$ both exist.

Usage

# binary: mutualL(same=NULL, diff=FALSE, by=NULL, keep=NULL, Ls=NULL)

Arguments

Details

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

Evaluates the terms in formula on each of the networks joined using Networks function, and returns either a weighted sum or an lm-style linear model for the ERGM coefficients (Krivitsky et al. 2023). Its syntax follows that of lm closely, with sensible defaults.

The default formula (~1) sums the specified network statistics. If lm refers to any network attributes for which some networks have missing values, the term will stop with an error. This can be avoided by pre-filtering with subset, which controls which networks are affected by the term.

Usage

# binary: N(formula, lm=~1, subset=TRUE, weights=1, contrasts=NULL, offset=0, label=NULL,
#           .NetworkID=".NetworkID", .NetworkName=".NetworkName")

# valued: N(formula, lm=~1, subset=TRUE, weights=1, contrasts=NULL, offset=0, label=NULL,
#           .NetworkID=".NetworkID", .NetworkName=".NetworkName")

Arguments

Offsets and fixing parameters

By default, an N(formula, lm) term will add $p \times q$ free parameters, where $p$ is the number of free parameters (possibly curved) of the ERGM specified by formula, and $q$ is the number of parameters specified by the lm formula. That is, there would be one parameter for each combination of an ERGM parameter and a linear model parameter, in an ERGM-major order (i.e., for each ERGM parameter, the linear model parameters will be enumerated). For example, the term gwesp() has two free parameters: its coefficient and its decay rate. We can specify a model in which they depend on $\log(n)$ as N(~gwesp, ~log(n)), resulting in the following 4 parameters, with the intercept for the linear model being implicit:

#> [1] "N(1)~gwesp"            "N(log(n))~gwesp"       "N(1)~gwesp.decay"     
#> [4] "N(log(n))~gwesp.decay"

If a different linear model is desired for different ERGM terms (e.g., some are to be affected by network size while others are not), multiple N() terms can be specified. This covers most such cases, but not all. For example, suppose that for the above model, we wish for its coefficient to depend on log(n) but for the decay parameter not to. In this case, one can use the offset() decorator with partial offsetting. Then, specifying offset(N(~gwesp(), ~log(n)), 4), we get:

#> [1] "N(1)~gwesp"                    "N(log(n))~gwesp"              
#> [3] "N(1)~gwesp.decay"              "offset(N(log(n))~gwesp.decay)"

Then, setting the corresponding offset.coef = 0 will fix the coefficient of log(n) for the decay parameter at 0, while allowing a constant decay parameter to be estimated.

Note

Care should be taken to avoid multicollinearity when using this operator. As with the lm() function, lm formulas have an implicit intercept, which can be suppressed by specifying ~ 0 + ... or ~ -1 + ... on the formula. When lm is given a model with intercept and a categorical predictor (including a logical one), it will use the first level (or FALSE) as the baseline, but if the model is without intercept, it will use all levels of the first categorical predictor. This is typically what is wanted in a linear regression, but for the N operator, this can be problematic if the "intercept" effect is added by a different term. A workaround is to convert the categorical predictor to dummy variables before putting it into the lm formula.

References

Krivitsky PN, Coletti P, Hens N (2023). “A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks.” Journal of the American Statistical Association, 118(544), 2213-2224. doi:10.1080/01621459.2023.2242627.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

vignette("Goeyvaerts_reproduction") for a demonstration.

Description

Returns a network with edges optionally filtered according to a specified criterion and with edge attributes optionally computed from other edge attributes.

Usage

network_view(x, ..., .clear = FALSE, .sep = ".")

Arguments

Details

Attribute specification arguments have the form ⁠<newattrname> = <expr>⁠, where ⁠<newattrname>⁠ specifies the name of the new edge attribute (or attribute to be overwritten) and ⁠<expr>⁠ can be one of the following:

a function

The function will be passed two arguments, the edgelist tibble and the network, and must return a vector of edge attribute values to be set on the edges in the order specified.

a formula

The expression on the RHS of the formula will be evaluated with names in it referencing the edge attributes. The input network may be referenced as .nw. The expression's result is expected to be a vector of edge attribute values to be set on the edges in the order specified.

a character vector

If of length one, the edge attribute with that name will simply be copied; if greater than one, the attribute values will be concatenated wtih the .sep argument as the separator.

an object enclosed in I()

The object will be used directly to set the edge attribute.

Filtering arguments are specified the same way as attribute arguments, but they must be unnamed arguments (i.e., must be passed without the =) and must return a logical or numeric vector suitable for indexing the edge list. Multiple filtering arguments may be specified, and the edge will be kept if it satisfies all. If the conjunction of the edge's original states and the filtering results is ambiguous (i.e., NA), it will be set as missing.

Value

A network object with modified edges and edge attributes.

Examples

data(florentine)
flo <- flomarriage
flo[,,add.edges=TRUE] <- as.matrix(flomarriage) | as.matrix(flobusiness)
flo[,, names.eval="m"] <- as.matrix(flomarriage)==1
flobusiness[3,5] <- NA
flo[,, names.eval="b"] <- as.matrix(flobusiness)==1
flo
(flob <- network_view(flo, "b"))
(flobusiness) # for comparison


(flob <- network_view(flo, ~b&m))
(flobusiness & flomarriage) # for comparison


as.matrix(flob <- network_view(flo, bm=~b+m), attrname="bm")
(as.matrix(flobusiness) + as.matrix(flomarriage)) # for comparison


as.matrix(flob <- network_view(flo, ~b, bm=~b+m), attrname="bm")
as.matrix(flobusiness)*(1+as.matrix(flomarriage)) # for comparison

Description

A function for specifying the LHS of a multi-network (a.k.a. multilevel) ERGM. Typically used in conjunction with the N() term operator.

Usage

Networks(...)

Arguments

Value

A network object comprising the provided networks, with multinetwork metadata.

Due to certain optimizations, the resulting network object's network and vertex attributes should be treated as read-only: do not modify them. If you need to change existing attributes or add new ones, do so on the input networks and call Networks(...) again.

See Also

ergmTerm for specific terms.

vignette("Goeyvaerts_reproduction") for a demonstration.

Examples

data(samplk)

# Method 1: list of networks
monks <- Networks(list(samplk1, samplk2))
ergm(monks ~ N(~edges))

# Method 2: networks as arguments
monks <- Networks(samplk1, samplk2)
ergm(monks ~ N(~edges))

Description

This term adds one network statistic to the model for each element in d ; the $i$ th such statistic equals the number of nodes in the network of out-degree d[i] , i.e. the number of nodes with exactly d[i] out-edges.

Usage

# binary: odegreeL(d, by=NULL, homophily=FALSE, levels=NULL)

Arguments

Details

This term can only be used with directed networks; for undirected networks see degree .

If a list of layer specifications is given, degree of a node i is considered to be the number of edges in all layers, combined.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Plotting methods for gofN, making residual and scale-location plots.

Description

The plot() method uses R graphics.

The ggplot2::autoplot() method uses ggplot2 and ggrepel.

Usage

## S3 method for class 'gofN'
plot(
  x,
  against = NULL,
  which = 1:2,
  col = 1,
  pch = 1,
  cex = 1,
  bg = 0,
  ...,
  ask = length(which) > 1 && dev.interactive(TRUE),
  id.n = 3,
  id.label = NULL,
  main = "{type} for {sQuote(name)}",
  xlab = NULL,
  ylim = NULL,
  cex.id = 0.75
)

## S3 method for class 'gofN'
autoplot(
  x,
  against = .fitted,
  which = 1:2,
  mappings = list(),
  geom_args = list(),
  id.n = 3,
  id.label = NULL
)

Arguments

Details

For the plot() method, against and id.label can be vectors of values (enclosed in I() to be used as is), a character string identifying a network attribute, or a formula whose RHS gives an expression in terms of network attributes to plot against. The against formula may also contain a .fitted variable which will be substituted with the fitted values.

For autoplot.gofN(), against and id.label are interpreted as expressions in terms of network attributes and values generated by augment.gofN(), included .fitted for the fitted values.

Value

autoplot.gofN() returns a list of ggplot objects that if printed render to diagnostic plots. If there is only one, the object itself is returned.

Customising autoplot.gofN()

autoplot.gofN() constructs the plots out of ggplot2::ggplot(), ggplot2::geom_point() (for numeric against), ggplot2::geom_boxplot() for categorical or ordinal against), and ggplot2::geom_smooth() (for numeric or ordinal against), and ggrepel::geom_text_repel(). Mappings and arguments passed through mappings and geom_args override the respective defaults. They may have elements default (for ggplot()), point (for geom_point() and geom_boxplot()), smooth (for geom_smooth), and text (for geom_text_repel()).

See Also

gofN() for examples, plot.lm(), graphics::plot() for regression diagnostic plots and their parameters.

Description

A utility to facilitate argument completion of control lists, reexported from statnet.common.

Currently recognised control parameters

This list is updated as packages are loaded and unloaded.

Package ergm

control.ergm

drop, init, init.method, main.method, force.main, main.hessian, checkpoint, resume, MPLE.samplesize, init.MPLE.samplesize, MPLE.type, MPLE.maxit, MPLE.nonvar, MPLE.nonident, MPLE.nonident.tol, MPLE.covariance.samplesize, MPLE.covariance.method, MPLE.covariance.sim.burnin, MPLE.covariance.sim.interval, MPLE.check, MPLE.constraints.ignore, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.interval, MCMC.burnin, MCMC.samplesize, MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max, MCMC.return.stats, MCMC.runtime.traceplot, MCMC.maxedges, MCMC.addto.se, MCMC.packagenames, SAN.maxit, SAN.nsteps.times, SAN, MCMLE.termination, MCMLE.maxit, MCMLE.conv.min.pval, MCMLE.confidence, MCMLE.confidence.boost, MCMLE.confidence.boost.threshold, MCMLE.confidence.boost.lag, MCMLE.NR.maxit, MCMLE.NR.reltol, obs.MCMC.mul, obs.MCMC.samplesize.mul, obs.MCMC.samplesize, obs.MCMC.effectiveSize, obs.MCMC.interval.mul, obs.MCMC.interval, obs.MCMC.burnin.mul, obs.MCMC.burnin, obs.MCMC.prop, obs.MCMC.prop.weights, obs.MCMC.prop.args, obs.MCMC.impute.min_informative, obs.MCMC.impute.default_density, MCMLE.min.depfac, MCMLE.sampsize.boost.pow, MCMLE.MCMC.precision, MCMLE.MCMC.max.ESS.frac, MCMLE.metric, MCMLE.method, MCMLE.dampening, MCMLE.dampening.min.ess, MCMLE.dampening.level, MCMLE.steplength.margin, MCMLE.steplength, MCMLE.steplength.parallel, MCMLE.sequential, MCMLE.density.guard.min, MCMLE.density.guard, MCMLE.effectiveSize, obs.MCMLE.effectiveSize, MCMLE.interval, MCMLE.burnin, MCMLE.samplesize.per_theta, MCMLE.samplesize.min, MCMLE.samplesize, obs.MCMLE.samplesize.per_theta, obs.MCMLE.samplesize.min, obs.MCMLE.samplesize, obs.MCMLE.interval, obs.MCMLE.burnin, MCMLE.steplength.solver, MCMLE.last.boost, MCMLE.steplength.esteq, MCMLE.steplength.miss.sample, MCMLE.steplength.min, MCMLE.effectiveSize.interval_drop, MCMLE.save_intermediates, MCMLE.nonvar, MCMLE.nonident, MCMLE.nonident.tol, SA.phase1_n, SA.initial_gain, SA.nsubphases, SA.min_iterations, SA.max_iterations, SA.phase3_n, SA.interval, SA.burnin, SA.samplesize, CD.samplesize.per_theta, obs.CD.samplesize.per_theta, CD.nsteps, CD.multiplicity, CD.nsteps.obs, CD.multiplicity.obs, CD.maxit, CD.conv.min.pval, CD.NR.maxit, CD.NR.reltol, CD.metric, CD.method, CD.dampening, CD.dampening.min.ess, CD.dampening.level, CD.steplength.margin, CD.steplength, CD.adaptive.epsilon, CD.steplength.esteq, CD.steplength.miss.sample, CD.steplength.min, CD.steplength.parallel, CD.steplength.solver, loglik, term.options, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.ergm.bridge

bridge.nsteps, bridge.target.se, bridge.bidirectional, drop, MCMC.burnin, MCMC.burnin.between, MCMC.interval, MCMC.samplesize, obs.MCMC.burnin, obs.MCMC.burnin.between, obs.MCMC.interval, obs.MCMC.samplesize, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, obs.MCMC.prop, obs.MCMC.prop.weights, obs.MCMC.prop.args, MCMC.maxedges, MCMC.packagenames, term.options, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.ergm.godfather

term.options

control.gof.ergm

nsim, MCMC.burnin, MCMC.interval, MCMC.batch, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT

control.gof.formula

nsim, MCMC.burnin, MCMC.interval, MCMC.batch, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT

control.logLik.ergm

bridge.nsteps, bridge.target.se, bridge.bidirectional, drop, MCMC.burnin, MCMC.interval, MCMC.samplesize, obs.MCMC.samplesize, obs.MCMC.interval, obs.MCMC.burnin, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, obs.MCMC.prop, obs.MCMC.prop.weights, obs.MCMC.prop.args, MCMC.maxedges, MCMC.packagenames, term.options, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.san

SAN.maxit, SAN.tau, SAN.invcov, SAN.invcov.diag, SAN.nsteps.alloc, SAN.nsteps, SAN.samplesize, SAN.prop, SAN.prop.weights, SAN.prop.args, SAN.packagenames, SAN.ignore.finite.offsets, term.options, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT

control.simulate

MCMC.burnin, MCMC.interval, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.batch, MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, term.options, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.simulate.ergm

MCMC.burnin, MCMC.interval, MCMC.scale, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.batch, MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, term.options, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.simulate.formula

MCMC.burnin, MCMC.interval, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.batch, MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, term.options, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.simulate.formula.ergm

MCMC.burnin, MCMC.interval, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.batch, MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, term.options, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

See Also

statnet.common::snctrl()

A split() method for network::network objects.

Description

Split a network into subnetworks on a factor.

Usage

## S3 method for class 'network'
split(x, f, drop = FALSE, sep = ".", lex.order = FALSE, ...)

Arguments

Value

A network.list containing the networks. These networks will inherit all vertex and edge attributes, as well as relevant network attributes.

See Also

network::get.inducedSubgraph()

Description

This term adds one statistic to the model, equal to the number of cross-layer two-stars or two-paths in the network.

Usage

# binary: twostarL(Ls, type, distinct=TRUE)

Arguments

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

None

Description

Given a network created by combine_networks(), uncombine_network() returns a list of networks, preserving attributes that can be preserved.

Usage

uncombine_network(
  nw,
  split.vattr = nw %n% ".blockID.vattr",
  names.vattr = nw %n% ".blockName.vattr",
  use.subnet.cache = FALSE
)

Arguments

Value

a list of network::networks containing subgraphs on split.vattr. In particular,

• their basic properties (directedness and bipartednes) are the same as those of the input network;

• vertex attributes are split;

• edge attributes are assigned to their respective edges in the returned networks.

If split.vattr is a vector, only the first element is used and it's "popped".

See Also

split.network()

Examples

data(samplk)

o1 <- combine_networks(list(samplk1, samplk2, samplk3))
image(as.matrix(o1))

ol <- uncombine_network(o1)

Description

For a directed network, only dyads $(i,j)$ for which $i < j$ may be toggled. Optional argument attr controls which subgraphs are thus restricted.

Usage

# upper_tri(attr = NULL)

Arguments

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

None