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.
ergm.mple(nw, fd, m, init = NULL, MPLEtype = "glm",
family = "binomial", maxMPLEsamplesize = 1e+06, save.glm = TRUE,
theta1 = NULL, control = NULL, proposal = NULL, verbose = FALSE,
...)ergm.pl(nw, fd, m, theta.offset = NULL, maxMPLEsamplesize = 1e+06,
control, verbose = FALSE)
response network.
An rlebdm with informative dyads.
the model, as returned by ergm_model
a vector a vector of initial theta coefficients
the method for MPL estimation as "penalized", "glm" or "logitreg"; default="glm"
the family to use in the R native routine
glm; only applicable if "glm" is the 'MPLEtype';
default="binomial"
the sample size to use for endogenous sampling in the psuedo-likelihood computation; default=1e6
whether the mple fit and the null mple fit should be returned (T or F); if false, NULL is returned for both; default==TRUE
the independence theta; if specified and non-NULL, this is ignored except to return its value in the returned ergm; default=NULL, in which case 'theta1' is computed
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,
an ergm_proposal() object.
whether this and the C routines should be verbose (T or F); default=FALSE
additional parameters passed from within; all will be ignored
a logical vector specifying which of the model coefficients are offset, i.e. fixed
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
zy : the corresponding vector of responses, i.e. tie values
foffset : ??
wend : the vector of weights for 'xmat' and 'zy'
numobs : the number of dyads
xmat.full: the 'xmat' before sampling; if no sampling is needed, this is NULL
zy.full : the 'zy' before sampling; if no sampling is needed, this is NULL
foffset.full : ??
theta.offset : a numeric vector whose ith entry tells whether the the ith curved coefficient?? was offset/fixed; -Inf implies the coefficient was fixed, 0 otherwise; if the model hasn't any curved terms, the first entry of this vector is one of log(Clist$nedges/(Clist$ndyads-Clist$nedges)) log(1/(Clist$ndyads-1)) depending on 'Clist$nedges'
maxMPLEsamplesize: the 'maxMPLEsamplesize' inputted to
ergm.pl
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.
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. http://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.