ergm: ergm.mple – R documentation

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ergm.mple

Find a maximizer to the psuedolikelihood function

Description

The ergm.mple function finds a maximizer to the psuedolikelihood function (MPLE). It is the default method for finding the ERGM starting coefficient values. It is normally called internally the ergm process and not directly by the user. Generally ergmMPLE would be called by users instead.

ergm.pl is an even more internal workhorse function that prepares many of the components needed by ergm.mple for the regression rountines that are used to find the MPLE estimated ergm. It should not be called directly by the user.

Usage

ergm.mple(
  nw,
  fd,
  m,
  init = NULL,
  MPLEtype = "glm",
  family = "binomial",
  save.glm = TRUE,
  save.xmat = TRUE,
  control = NULL,
  proposal = NULL,
  verbose = FALSE,
  ...
)

ergm.pl(nw, fd, m, theta.offset = NULL, control, verbose = FALSE)

Arguments

`nw`	response network.
`fd`	An `rlebdm` with informative dyads.
`m`	the model, as returned by `ergm_model`
`init`	a vector a vector of initial theta coefficients
`MPLEtype`	the method for MPL estimation as "penalized", "glm" or "logitreg"; default="glm"
`family`	the family to use in the R native routine `glm`; only applicable if "glm" is the 'MPLEtype'; default="binomial"
`save.glm`	whether the mple fit and the null mple fit should be returned (T or F); if false, NULL is returned for both; default==TRUE
`control`	a list of MCMC related parameters; recognized components include: samplesize : the number of networks to sample Clist.miss : see 'Clist.miss' above; some of the code uses this Clist.miss,
`proposal`	an `ergm_proposal()` object.
`verbose`	whether this and the C routines should be verbose (T or F); default=FALSE
`...`	additional parameters passed from within; all will be ignored
`theta.offset`	a numeric vector of length equal to the number of statistics of the model, specifying (positionally) the coefficients of the offset statistics; elements corresponding to free parameters are ignored.

Details

According to Hunter et al. (2008): "The maximizer of the pseudolikelihood may thus easily be found (at least in principle) by using logistic regression as a computational device." In order for this to work, the predictors of the logistic regression model must be calculated. These are the change statistics as described in Section 3.2 of Hunter et al. (2008), put into matrix form so that each pair of nodes is one row whose values are the vector of change statistics for that node pair. The ergm.pl function computes these change statistics and the ergm.mple function implements the logistic regression using R's glm function. Generally, neither ergm.mple nor ergm.pl should be called by users if the logistic regression output is desired; instead, use the ergmMPLE function.

In the case where the ERGM is a dyadic independence model, the MPLE is the same as the MLE. However, in general this is not the case and, as van Duijn et al. (2009) warn, the statistical properties of MPLEs in general are somewhat mysterious.

MPLE values are used even in the case of dyadic dependence models as starting points for the MCMC algorithm.

Value

ergm.mple returns an ergm object as a list containing several items; for details see the return list in the ergm

ergm.pl returns a list containing:

xmat : the compressed and possibly sampled matrix of change statistics
xmat.full : as xmat but with offset terms
zy : the corresponding vector of responses, i.e. tie values
foffset : combined effect of offset terms
wend : the vector of weights for xmat and zy
numobs : the number of dyads

References

Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris and Martina (2008). "ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks." Journal of Statistical Software, 24(3), pp. 1-29. https://www.jstatsoft.org/article/view/v024i03

van Duijn MAJ, Gile K, Handcock MS (2009). "Comparison of Maximum Pseudo Likelihood and Maximum Likelihood Estimation of Exponential Family Random Graph Models." Social Networks, 31, pp. 52-62.