Function to compute weighted change statistics for geometrically weighted terms.

Description

Computes geometric weights for a pre-specified subgraph count given a known decay parameter. Intended primarily for use with ergm.MSE to simplify specifications for values of lower-order terms.

Usage

GW_helper(term_count,
            decay,
            lower_bound=0)

Arguments

Details

Computes the weighted value to assign to change statistics for a desired subgraph count. term_count corresponds to the subgraph count to assign geometric weights. For example, consider an ERGM specification where triadic effects are specified with a gwesp statistic. GW_helper would be used to determine the change statistic for a given triad count. If the triad count is 2, this would be specified by setting the term_count argument to equal 2 and providing the decay parameter used to estimate the gwesp term in an ergm call. GW_helper would return the change statistic for the gwesp term when a potential tie increases the triad count to a value of 2, weighted by decay.

The lower_bound argument assigns the baseline value for the subgraph count in question. By default, lower_bound is set to 0. This means that, in the above example, if term_count is set to 2, the default behavior of GW_helper is to calculate the weighted change statistic for a gwesp term that increases the number of triangles from 0 to 2. If lower_bound is set to 1 and term_count is set to 3, then GW_helper will calculate the change statistic when increasing the number of triangles from 1 to 3. Since geometrically weighted terms assign diminishing weights for each statistic added, selection of lower_bound and term_count will affect the value of the resulting change statistic in meaningful ways.

If the geometrically weighted term is estimated with fixed decay, decay is the value provided by the researcher within the ergm formula. If the term is estimated without fixed decay, decay is the decay parameter estimate from the data corresponding to a single entry in the ergm summary table parameter vector.

Value

Returns a scalar value reflecting the change statistic for a potential tie that increases the subgraph count captured by a geometrically weighted term by the values assigned to lower_bound and term_count. Intended primarily to facilitate use of ergm.MSE and ergm.msma.

Author(s)

Scott Duxbury, Associate Professor, University of North Carolina–Chapel Hill, Department of Sociology.

References

Duxbury, Scott W. 2025. "Marginal Structural Effects for ERGM" Working paper.

Hunter, David. 2007. "Curved Exponential Family Models for Social Networks" Social Networks.

Examples

library(ergm)
set.seed(21093)
data("faux.dixon.high")

# fit a model
my.ergm<-ergm(faux.dixon.high~edges+
                nodeicov("grade")+
                nodeocov("grade")+
                nodeifactor("sex")+
                nodeofactor("sex")+
                absdiff("grade")+
                nodematch("sex")+
                mutual+
                gwidegree(.5,fixed=TRUE))

#for a fixed decay of .5, what is the change statistic for a tie that increases
  # degree from 0 to 2?

GW_helper(2,.5)

#for a fixed decay of .5, what is the change statistic for a tie that increases
  # degree from 1 to 2?
GW_helper(2,.5,lower_bound=1)


##within a call to ergm.MSE
  #creating a single mutual tie requires, at a minimum, increasing indegree
    #from 0 to 1 for the recipient node

ergm.MSE(my.ergm,
          substructural_effect="mutual",
          lower_order_term="gwideg.fixed.0.5",
          at.lower_order_term=GW_helper(1,.5),
          estimate="MSEm")


#What happens if the tie moves indegree from 4 to 5 for the recipient node?

ergm.MSE(my.ergm,
          substructural_effect="mutual",
          lower_order_term="gwideg.fixed.0.5",
          at.lower_order_term=GW_helper(5,.5,lower_bound=4),
          estimate="MSEm")
  

Function to compute tie probabilities for each dyad.

Description

Computes tie probabilities for each dyad. Largely a wrapper for edgeprob() in btergm.

Usage

edge.prob2(model,verbose=FALSE)

Arguments

Details

Computes tie probabilities for each dyad in the ERGM sample space.This function is largely a wrapper for the edgeprob function in btergm, but can be applied to curved ERGMs.

Value

Returns a dataframe where weach row is a dyad and each column is a term in the model, an identification variable for the vertices/dyads, or the estimated probability of observing a tie. See edgeprob() in btergm for more details.

Author(s)

Scott Duxbury, Associate Professor, University of North Carolina–Chapel Hill, Department of Sociology. original author is Philip Leifeld at University of Essex.

See Also

edgeprob

Examples

library(ergm)


data("faux.dixon.high")


my.ergm<-ergm(faux.dixon.high~edges+
                nodeifactor("sex")+
                nodeofactor("sex")+
                nodematch("sex")+
                mutual)
edge.prob2(my.ergm)

Function to compute average marginal effects in ERGM.

Description

ERGM function to compute average marginal effects for main effects or at various levels of a moderator. Also provides tests of significance for second differences for interaction terms. Currently accepts ergm, btergm, mtergm, ergm.count, mlergm, and ergm.multi objects. See ergm.MEM to compute marginal effects at means.

Usage

ergm.AME(model,
        var1,
        var2=NULL,
        inter=NULL,
        at.2=NULL,
        at.controls=NULL,
        control_vals=NULL,
        return.dydx=FALSE,
        return.at.2=FALSE)

Arguments

Details

Computes the AME for variables specified. If var2 and inter are left at NULL, this is the simple AME. All AMEs are computed as tie probabilities (not on the linear scale). Standard errors are estimated using the Delta method. If a moderator is specified using var2 and inter, a table of AMEs is returned at each level of at.2. If at.2=NULL, this is computed for every unique level of var2. So, if var2 has many levels and the model is complex, run times may be restrictive when at.2 is left NULL.

When at.2 and var2 are specified, a table of second differences is also returned. The table of second differences assesses whether the difference in marginal effects is significant between levels of a moderator (values of at.2). If the moderator is binary, the second difference tests the overall significance of an interaction. The tests statistic is a Wald test.

If more than 2 values of at.2 are specified, the function also computes the average absolute Wald test statistic and average second difference. The average second difference measures the average change in the AME of var1 between levels of a moderator. The average absolute Wald test is the mean absolute value of the Wald tests for all second differences. It assesses whether, on average, there is a significant difference between the second differences and zero. A significant result means the interaction is significant.

Note that when an interaction term is an absolute difference between nodal covariates, ergm.AME holds the value of var1 at its mean. This is because the partial derivative for the absolute difference between covariates treats allows var1 to vary, which tells us little about tendencies towards tie variables when two nodal covariates are at similar values. Thus, the mean is used as a representative value at which to compute the AME for absolute differences.

If at.controls and control_vals are provided, the AME is calculated while holding specified control variables at fixed values provided in control_vals, rather than their observed vales.

Value

If var2 and inter=NULL, then a table is returned with the AME for var1, its standard error, and test statistic. Note again that all AMEs are in the metric of tie probabilities, not log-odds.

If a moderator is specified, a list is returned with the following elements:

Warning

Note that AMEs can take a long time to estimate in large networks or high dimensional models. If AME computation time proves to be restrictive, see the ergm.MEM function, which computes marginal effects at means.

Note

Syntax is loosely based on the margins package by Thomas Leeper and Stata's margins commands. Currently only available for two-way interactions.

Author(s)

Scott Duxbury, Associate Professor, University of North Carolina–Chapel Hill, Department of Sociology.

References

Duxbury, Scott W. 2023. "The Problem of Scaling in Exponential Random Graph Models." Sociological Methods & Research.

Duxbury, Scott W., and Jenna Wertsching. 2023. "Scaling Bias in Pooled Exponential Random Graph Models." Social Networks.

Long, J. Scott, and Sarah Mustillo. 2018. "Using Predictions and Marginal Effects to Compare Groups in Regression Models for Binary Outcomes." Sociological Methods and Research

Mize, Trenton D. 2019. "Best Practices for Estimating, Interpreting, and Presenting Nonlinear Interaction Effects." Sociological Science

See Also

ergm.MEM ergm.mma margins

Examples

library(ergm)


data("faux.dixon.high")


set.seed(21093)

my.ergm<-ergm(faux.dixon.high~edges+
                nodeicov("grade")+
                nodeocov("grade")+
                nodeifactor("sex")+
                nodeofactor("sex")+
                absdiff("grade")+
                nodematch("sex")+
                mutual)

#main effect
main.eff<-ergm.AME(my.ergm,"mutual")

#main effect of "mutual" when sender and receiver effects for sex == 1
ergm.AME(my.ergm,"mutual",
              at.controls=c("nodeifactor.sex.2","nodeofactor.sex.2"),
              control_vals=c(1,1))


##with moderator
sex.inter<-ergm.AME(my.ergm,"nodeifactor.sex.2","nodeofactor.sex.2","nodematch.sex")

##with moderator at specific values
grade.inter<-ergm.AME(my.ergm,"nodeicov.grade","nodeocov.grade","absdiff.grade",
            at.2=c(9,12))

##when moderator changes from mean to mean +sd

tie.probs<-edge.prob2(my.ergm)
m<-mean(tie.probs$nodeocov.grade)
m.sd<-m+sd(tie.probs$nodeocov.grade)

grade.inter.at.means<-ergm.AME(my.ergm,"nodeicov.grade","nodeocov.grade",
                              "absdiff.grade",at.2=c(m,m.sd))

Function to compute marginal effects at means in ERGM.

Description

ERGM function to compute marginal effects at means for main effects or at various levels of a moderator. Also provides tests of significance for second differences for interaction terms. Currently accepts ergm, btergm, mtergm, ergm.count, mlergm, and ergm.multi objects. See ergm.AME to compute average marginal effect.

Usage

ergm.MEM(model,
         var1,
         var2=NULL,
         inter=NULL,
         at.2=NULL,
         at.controls=NULL,
         control_vals=NULL,
         return.dydx=FALSE)

Arguments

Details

Largely a wrapper for ergm.AME. The only difference is that marginal effects are computed at variable means.

Computes the MEM for variables specified. If var2 and inter are left at NULL, this is the simple MEM. All MEMs are computed as tie probabilities (not on the linear scale). Standard errors are computed using the Delta method. If a moderator is specified using var2 and inter, a table of MEMs is returned at each level of at.2. If at.2=NULL, this is computed for every unique level of var2.

When at.2 and var2 are specified, a table of second differences is also returned. The table of second differences assesses whether the difference in marginal effects is significant between levels of a moderator (values of at.2). If the moderator is binary, the second difference tests the overall significance of an interaction. The tests statistic is a Wald test.

If more than 2 values of at.2 are specified, the function also computes the average absolute Wald test statistic and average second difference. The average second difference measures the average change in the MEM of var1 between levels of a moderator. The average absolute Wald test is the mean absolute value of the Wald tests for all second differences. It assesses whether, on average, there is a significant difference between the second differences and zero. A significant result means the interaction is significant.

If at.controls and control_vals are provided, the MEM is calculated while holding specified control variables at fixed values provided in control_vals, rather than at their means

Value

If var2 and inter=NULL, then a table is returned with the MEM for var1, its standard error, and test statistic. Note again that all MEMs are in the metric of tie probabilities, not log-odds. If a moderator is specified, a list is returned with the following elements:

Note

Syntax is loosely based on the margins package by Thomas Leeper and Stata's margins commands. See ergm.AME to compute average marginal effects. Currently only considers two-ways interactions.

Author(s)

Scott Duxbury, Associate Professor, University of North Carolina–Chapel Hill, Department of Sociology.

References

Duxbury, Scott W. 2023. "The Problem of Scaling in Exponential Random Graph Models." Sociological Methods & Research.

Duxbury, Scott W., and Jenna Wertsching. 2023. "Scaling Bias in Pooled Exponential Random Graph Models." Social Networks.

Duxbury, Scott W. 2025. "Marginal Substructural Effects for Exponential Random Graph Models." Working Paper.

Long, J. Scott, and Sarah Mustillo. 2018. "Using Predictions and Marginal Effects to Compare Groups in Regression Models for Binary Outcomes." Sociological Methods and Research

Mize, Trenton D. 2019. "Best Practices for Estimating, Interpreting, and Presenting Nonlinear Interaction Effects." Sociological Science

See Also

ergm.AME ergm.mma margins

Examples

library(ergm)


data("faux.dixon.high")


set.seed(21093)

my.ergm<-ergm(faux.dixon.high~edges+
                nodeicov("grade")+
                nodeocov("grade")+
                nodeifactor("sex")+
                nodeofactor("sex")+
                absdiff("grade")+
                nodematch("sex")+
                mutual)

#main effect
main.eff<-ergm.MEM(my.ergm,"mutual")

#main effect of "mutual" when sender and receiver effects for sex == 1
ergm.MEM(my.ergm,"mutual",
              at.controls=c("nodeifactor.sex.2","nodeofactor.sex.2"),
              control_vals=c(1,1))


##with moderator
sex.inter<-ergm.MEM(my.ergm,"nodeifactor.sex.2","nodeofactor.sex.2","nodematch.sex")

##with moderator at specific levels
grade.inter<-ergm.MEM(my.ergm,"nodeicov.grade","nodeocov.grade","absdiff.grade",
          at.2=c(9,12))

##when moderator changes from mean to mean +sd
tie.probs<-edge.prob2(my.ergm)
m<-mean(tie.probs$nodeocov.grade)
m.sd<-m+sd(tie.probs$nodeocov.grade)

grade.inter.at.means<-ergm.MEM(my.ergm,"nodeicov.grade","nodeocov.grade",
                            "absdiff.grade",at.2=c(m,m.sd))

Function to compute marginal substructural effects in ERGM.

Description

ERGM function to compute marginal substructural effects in ERGM, as described by Duxbury (2025). Intended for use with endogenous substructural terms in ERGMs. Also provides utilities to test interactions between substructural terms and exogenous covariates. See ergm.AME for average marginal effects and ergm.MEM for marginal effects at means.

Usage

ergm.MSE(model,
         substructural_effect,
         higher_order_term=NULL,
         lower_order_term=NULL,
         at.lower_order_term=NULL,
         estimate="aMSE",
         var2=NULL,
         inter=NULL,
         at.2=NULL,
         at.controls=NULL,
         control_vals=NULL,
         return_Jac=FALSE)

Arguments

Details

Computes the marginal substructural effect for a specified substructural term. Formally, the MSE for a unit is given by

MSE_{ij}=Pr(Y_{ij}=1|-y_{ij},\delta ^+_{ij}(y)=1,x_{ij})-Pr(Y_{ij}=0|-y_{ij},\delta ^+_{ij}(y)=0,x_{ij})

where \delta ^+_{ij}(y) is the substructural effect of interest. The estimate argument determines whether the MSE should be taken holding controls at observed values (when set to "aMSE"), holding controls at means ("MSEm"), or by combining the estimates from multiple substructures (when set to "aTSE").

The terms provided in the lower_order_terms argument will be held constant at a value of 1 when estimating the MSE, unless alternative values are provided with the at.lower_order_term argument. If the higher_order_term argument is provided, the specified term will be held at a value of 0 when estimating the marginal substructural effect

When an endogenous network term is specified as an interaction with an exogenous term, the MSE for each level of the interaction can be obtained by providing the var2 and inter argumnets. This returns the MSE at different levels of var2 along with a test of the differences between the MSEs. If at.controls and control_vals are provided, the MEM is calculated while holding specified control variables at fixed values provided in control_vals, rather than at their means

Value

A table containing the MSE estimate and variance estimates. If inter and var2 are provided, a list is returned containing:

Note

Syntax is loosely based on the margins package by Thomas Leeper and Stata's margins commands. See ergm.AME to compute average marginal effects. Currently only considers two-ways interactions.

Author(s)

Scott Duxbury, Associate Professor, University of North Carolina–Chapel Hill, Department of Sociology.

References

Duxbury, Scott W. 2023. "The Problem of Scaling in Exponential Random Graph Models." Sociological Methods & Research.

Duxbury, Scott W., and Jenna Wertsching. 2023. "Scaling Bias in Pooled Exponential Random Graph Models." Social Networks.

Duxbury, Scott W. 2025. "Marginal Substructural Effects for Exponential Random Graph Models." Working Paper.

Long, J. Scott, and Sarah Mustillo. 2018. "Using Predictions and Marginal Effects to Compare Groups in Regression Models for Binary Outcomes." Sociological Methods and Research

Mize, Trenton D. 2019. "Best Practices for Estimating, Interpreting, and Presenting Nonlinear Interaction Effects." Sociological Science

See Also

ergm.AME ergm.mma ergm.msma ergm.MEM margins

Examples

library(ergm)


data("faux.dixon.high")


set.seed(21093)

my.ergm<-ergm(faux.dixon.high~edges+
                nodeicov("grade")+
                nodeocov("grade")+
                nodeifactor("sex")+
                nodeofactor("sex")+
                absdiff("grade")+
                nodematch("sex")+
                mutual+
                gwidegree(.5,fixed=TRUE))

#MSE at means
ergm.MSE(my.ergm,
          substructural_effect="mutual",
          lower_order_term="gwideg.fixed.0.5",
          estimate="MSEm")

#total effect of both endogenous terms
ergm.MSE(my.ergm,
          substructural_effect="mutual",
          lower_order_term="gwideg.fixed.0.5",
          estimate="tMSEm")

Function to conduct marginal effects mediation analysis in ERGM.

Description

ergm.mma is a function to conduct mediation analysis in ERGM using marginal effects. It computes the total, direct, and indirect average marginal effects for two nested ERGMs fit to the same data. Can be used with discrete or continuous mediators and for multiple mediator analyses. Currently accepts ergm, btergm, mtergm, ergm.count, mlergm, and ergm.multi objects.

Usage

ergm.mma(restricted.model,
          full.model,
          direct.effect,
          mediator,
          at.controls=NULL,
          control_vals=NULL,
          ME="AME")

Arguments

Details

ergm.mma conducts marginal effects mediation analysis for nested ERGMs fit to the same network by computing the change in average marginal effects between models. The AMEs are estimated on the scale of tie probabilities, not the linear component (log-odds). Standard errors are computed using the Delta method.

A few notes on using ergm.mma:

• ergm.mma default specification uses the AME, which can be computationally intensive in large networks or high dimensional models. If run times are an issue, try specifying ME="MEM".

• ergm.mma can be applied to discrete mediators or multiple mediator analysis.

Value

Returns a table including the point estimates and standard errors for total, direct, and indirect effects. A single indirect effect is reported for joint mediation analyses. All marginal effects are computed on the scale of tie probabilities, not the linear component (log-odds).

Note

Note that ergm.mma may have restrictive run times in large networks or high dimensional models.

Author(s)

Scott Duxbury, Associate Professor, University of North Carolina–Chapel Hill, Department of Sociology.

References

Duxbury, Scott W. 2023. "The Problem of Scaling in Exponential Random Graph Models." Sociological Methods & Research.

See Also

ergm.AME ergm.mod.mma

Examples

library(ergm)


data("faux.mesa.high")

faux.mesa.high

set.seed(21093)

my.ergm1<-ergm(faux.mesa.high~edges+
            nodecov("Grade")+
            nodefactor("Race")+
            nodefactor("Sex")+
            nodematch("Grade")+
            nodematch("Sex")+
            nodematch("Race"),
            estimate = "MLE")


set.seed(21093)

my.ergm2<-ergm(faux.mesa.high~edges+
                nodecov("Grade")+
                nodefactor("Race")+
                nodefactor("Sex")+
                nodematch("Grade")+
                nodematch("Sex")+
                nodematch("Race")+
               gwesp(.5,fixed=TRUE))


###gwesp as single mediator
ergm.mma(my.ergm1,my.ergm2,mediator="gwesp.fixed.0.5",
             direct.effect="nodecov.Grade")


###multiple mediators

set.seed(21093)

my.ergm3<-ergm(faux.mesa.high~edges+
                 nodecov("Grade")+
                 nodefactor("Race")+
                 nodefactor("Sex")+
                 nodematch("Grade")+
                 nodematch("Sex")+
                 nodematch("Race")+
                 gwdsp(1,fixed=TRUE)+
                 gwesp(.5,fixed=TRUE),
                 #increase MC sample to facilitate convergence
               control = control.ergm(MCMC.samplesize=5000)
)

##joint mediation for gwdsp and gwesp
ergm.mma(my.ergm2,my.ergm3,mediator=c("gwdsp.fixed.1","gwesp.fixed.0.5"),
         direct.effect=names(my.ergm3$coef[8]))

Function to assess mediated moderation using marginal effects in ERGM.

Description

ergm.mod.mma is a function to asssess mediated moderation in ERGM using average marginal effects (AME), e.g. when the main effect is a part of an interaction. If joint=TRUE, the function computes the total, partial, and indirect effects for all parts of the interaction. If int.eff=TRUE, the function computes the same values, but only for the moderating effect (e.g., only the moderated portion). Both joint=TRUE and int.eff=TRUE can be set simultaneously. Currently accepts ergm, btergm, mtergm, ergm.count, mlergm, and ergm.multi objects.

Usage

ergm.mod.mma(restricted.model,
             full.model,
             var1,
             var2,
             inter,
             mediator,
             at.2=NULL,
             joint=FALSE,
             int.eff=FALSE,
             at.controls=NULL,
             control_vals=NULL)

Arguments

Details

ergm.mod.mma conducts mediation analyses using marginal effects when the main effect is part of an interaction. There are three ways to construe the mediating pathways. First, a researcher may be interested in whether a mediator variable mediates the main effect in an interaction, net of the moderator. To assess this, use ergm.mma for var1. This will compute the AME when the effect of the moderator is zero. Second, a researcher may be interested in the total or composite effect of an interaction, including the moderator and main effect. To assess this, set joint=TRUE. This computes the indirect effect for the AME at every level of at.2. The third scenario is when a researcher is interested in only the interaction effect. The interaction effect is defined here as the difference in AMEs between levels of a moderator (e.g., levels of at.2). Thus, the indirect effect is the third difference, or the difference in second differences between the restricted and full models. An example is whether triad closure mediates the effect of matched nodal characteristics, net of the main effect for nodal attributes (e.g., net of nodefactor/nodecov). To assess this, set int.eff=TRUE. Both joint=TRUE and int.eff=TRUE can be specified at the same time, but at least one must be specified for the function to work.

Value

Returns a list object containing the total, partial, and indirect AMEs at each level of at.2. If joint=TRUE is specified, returns:

If int.eff=TRUE is specified, returns a list with elements:

If both int.eff=TRUE and joint=TRUE, returns a list with elements:

Author(s)

Scott Duxbury, Associate Professor, University of North Carolina–Chapel Hill, Department of Sociology.

References

Duxbury, Scott W. 2023. "The Problem of Scaling in Exponential Random Graph Models." Sociological Methods & Research.

See Also

ergm.AME ergm.MEM ergm.mma

Examples

library(ergm)


data("faux.dixon.high")

faux.dixon.high


my.ergm<-ergm(faux.dixon.high~edges+
                nodeifactor("sex")+
                nodeofactor("sex")+
                nodematch("sex"))

my.ergmb<-ergm(faux.dixon.high~edges+
                nodeifactor("sex")+
                nodeofactor("sex")+
                nodematch("sex")+
                mutual)

summary(my.ergmb)


sex.mod.med<-ergm.mod.mma(my.ergm,my.ergmb,var1="nodeifactor.sex.2",var2="nodeofactor.sex.2",
             inter="nodematch.sex",mediator="mutual",int.eff = TRUE,joint=TRUE)

Function to compare marginal substructrual effects between nested ERGMs.

Description

ergm.msma tests the difference in a marginal substructural effect between two ERGMs fit to the same network that differ only in their specification. It computes the total, direct, and indirect marginal substructural effects. Can be used with discrete or continuous mediators and for multiple mediator analyses. Currently accepts ergm, btergm, mtergm, ergm.count, mlergm, and ergm.multi objects.

Usage

ergm.msma(restricted.model,
                    full.model,
                    direct_substructural_effect,
                    higher_order_term=NULL,
                    lower_order_term=NULL,
                    at.lower_order_term=NULL,
                    mediator,
                    at.controls=NULL,
                    control_vals=NULL,
                    estimate="aMSE")

Arguments

Details

ergm.msma calculates the change in a marginal substructural effect between two models fit to the same data. Formally, define two models Mod^1 and Mod^2 that differ by the inclusion of one or more mediating variables. For a substructural network term of interest given by the change statistic \delta ^+_{ij}(y), the ergm.msma provides the following quantities:

MSE^{Mod^1}(\delta ^{+}_{ij}(y))

MSE^{Mod^2}(\delta ^{+}_{ij}(y))

MSE^{Mod^1}(\delta ^{+}_{ij}(y))-MSE^{Mod^2}(\delta ^{+}_{ij}(y))

Where MSE^{Mod^1}(\delta ^{+}_{ij}(y)) is the total effect corresponding to the marginal substructural effect of \delta ^{+}_{ij}(y) operating through all indirect pathways, MSE^{Mod^2}(\delta ^{+}_{ij}(y)) is the direct effect of \delta ^+_{ij}(y) on tie formation, and MSE^{Mod^1}(\delta ^{+}_{ij}(y))-MSE^{Mod^2}(\delta ^{+}_{ij}(y)) is the portion of the total effect explained by controlling for a confounding variable.

Value

Returns a table including the point estimates and standard errors for total, direct, and indirect effects. A single indirect effect is reported for joint mediation analyses. All marginal substructural effects are computed on the scale of tie probabilities, not the linear component (log-odds).

Note

Note that ergm.msma may have restrictive run times in large networks or high dimensional models.

Author(s)

Scott Duxbury, Associate Professor, University of North Carolina–Chapel Hill, Department of Sociology.

References

Duxbury, Scott W. 2023. "The Problem of Scaling in Exponential Random Graph Models." Sociological Methods & Research.

Duxbury, Scott W., and Jenna Wertsching. 2023. "Scaling Bias in Pooled Exponential Random Graph Models." Social Networks.

Duxbury, Scott W. 2025. "Marginal Substructural Effects for Exponential Random Graph Models." Working Paper.

See Also

ergm.AME ergm.mod.mma ergm.mma ergm.MSE ergm.MEM

Examples

library(ergm)


data("faux.mesa.high")

faux.mesa.high

#does sociality explain triadic effects?

  #model without sociality effects
my.ergm1<-ergm(faux.mesa.high~edges+
                nodematch("Grade")+
                nodematch("Sex")+
                nodematch("Race")+
                gwesp(.5,fixed=TRUE),
               control = control.ergm(MCMLE.termination="Hummel",
                                      MCMLE.effectiveSize = NULL,
                                      MCMC.samplesize = 5000,
                                      MCMLE.maxit=120))


  #model with sociality effects
my.ergm2<-ergm(faux.mesa.high~edges+
                nodecov("Grade")+
                nodefactor("Race")+
                nodefactor("Sex")+
                nodematch("Grade")+
                nodematch("Sex")+
                nodematch("Race")+
                 gwesp(.5,fixed=TRUE),
                control = control.ergm(MCMLE.termination="Hummel",
                                      MCMLE.effectiveSize = NULL,
                                      MCMC.samplesize = 5000,
                                      MCMLE.maxit=120))


###sociality effects as mediators
ergm.msma(my.ergm1,
            my.ergm2,
            direct_substructural_effect="gwesp.fixed.0.5",
            mediator=c("nodecov.Grade","nodefactor.Sex.M","nodefactor.Race.White",
            "nodefactor.Race.Other","nodefactor.Race.Hisp","nodefactor.Race.NatAm"),
            estimate="aMSE")

Function to diagnose multicollinearity in ERGM.

Description

Computes the variance inflation factor from the covariance matrix of the ERGM estimator.

Usage

vif.ergm(my.ergm)

Arguments

Details

Computes the variance inflation factor using the covariance matrix of the ERGM estimator. Values above 20 indicate the onset of moderate collinearity problems, values above 100 indicate that strong collinearity likely exists and may be problematizing the convergence of the Markov chain to the stationarity distribution. High VIFs alongside a near-singular Hessian matrix is a clear indicator of multicollinearity. Consider changing model specification in such cases.

Value

Returns a matrix of VIFs for each model parameter. Higher values indicate that the variable in one column of the data matrix is highly correlated with a linear combination of the remaining model covariates. High VIFs can also arise from a large bivariate correlation.

Author(s)

Scott Duxbury, Associate Professor, University of North Carolina–Chapel Hill, Department of Sociology.

References

Duxbury, Scott W. 2021. "Diagnosing Multicollinearity in Exponential Random Graph Models" Sociological Methods and Research.

Examples

set.seed(21093)

library(ergm)
data("faux.mesa.high")

my.ergm2<-ergm(faux.mesa.high~edges+
                nodecov("Grade")+
                nodefactor("Race")+
                nodefactor("Sex")+
                nodematch("Grade")+
                nodematch("Sex")+
                nodematch("Race"))

vif.ergm(my.ergm2)

#to compute the tolerance instead of the VIF

tol<-1/(vif.ergm(my.ergm2))

#to compute R squared
r.sq<-1-tol