ergmMPLE {ergm}

ERGM Predictors and response for logistic regression calculation of MPLE

Description

Return the predictor matrix, response vector, and vector of weights that can be used to calculate the MPLE for an ERGM.

Usage

ergmMPLE(
  formula,
  constraints = ~.,
  obs.constraints = ~-observed,
  output = c("matrix", "array", "dyadlist", "fit"),
  expand.bipartite = FALSE,
  control = control.ergm(),
  verbose = FALSE,
  ...,
  basis = ergm.getnetwork(formula)
)

Arguments

formula, constraints, obs.constraints

An ERGM formula and (optional) constraint specification formulas. See ergm.

output

Character, partially matched. See Value.

expand.bipartite

Logical. Specifies whether the output matrices (or array slices) representing dyads for bipartite networks are represented as rectangular matrices with first mode vertices in rows and second mode in columns, or as square matrices with dimension equalling the total number of vertices, containing with structural NAs or 0s within each mode.

control

A list of control parameters for algorithm tuning, typically constructed with control.ergm(). Its documentation gives the the list of recognized control parameters and their meaning. The more generic utility snctrl() (StatNet ConTRoL) also provides argument completion for the available control functions and limited argument name checking.

verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.

...

Additional arguments, to be passed to lower-level functions.

basis

a value (usually a network) to override the LHS of the formula.

Details

The MPLE for an ERGM is calculated by first finding the matrix of change statistics. Each row of this matrix is associated with a particular pair (ordered or unordered, depending on whether the network is directed or undirected) of nodes, and the row equals the change in the vector of network statistics (as defined in formula) when that pair is toggled from a 0 (no edge) to a 1 (edge), holding all the rest of the network fixed. The MPLE results if we perform a logistic regression in which the predictor matrix is the matrix of change statistics and the response vector is the observed network (i.e., each entry is either 0 or 1, depending on whether the corresponding edge exists or not).

Using output="matrix", note that the result of the fit may be obtained from the glm function, as shown in the examples below.

Value

If output=="matrix" (the default), then only the response, predictor, and weights are returned; thus, the MPLE may be found by hand or the vector of change statistics may be used in some other way. To save space, the algorithm will automatically search for any duplicated rows in the predictor matrix (and corresponding response values). ergmMPLE function will return a list with three elements, response, predictor, and weights, respectively the response vector, the predictor matrix, and a vector of weights, which are really counts that tell how many times each corresponding response, predictor pair is repeated.

If output=="dyadlist", as "matrix", but rather than coalescing the duplicated rows, every relation in the network that is not fixed and is observed will have its own row in predictor and element in response and weights, and predictor matrix will have two additional rows at the start, tail and head, indicating to which dyad the row and the corresponding elements pertain.

If output=="array", a list with similarly named three elements is returned, but response is formatted into a sociomatrix; predictor is a 3-dimensional array of with cell predictor[t,h,k] containing the change score of term k for dyad (t,h); and weights is also formatted into a sociomatrix, with an element being 1 if it is to be added into the pseudolikelihood and 0 if it is not.

In particular, for a unipartite network, cells corresponding to self-loops, i.e., predictor[i,i,k] will be NA and weights[i,i] will be 0; and for a unipartite undirected network, lower triangle of each predictor[,,k] matrix will be set to NA, with the lower triangle of weights being set to 0.

To all of the above output types, attr(., "etamap") is attached containing the mapping and offset information.

If output=="fit", then ergmMPLE simply calls the ergm function with the estimate="MPLE" option set, returning an object of class ergm that gives the fitted pseudolikelihood model.

See Also

ergm, glm

Examples

data(faux.mesa.high)
formula <- faux.mesa.high ~ edges + nodematch("Sex") + nodefactor("Grade")
mplesetup <- ergmMPLE(formula)

# Obtain MPLE coefficients "by hand":
coef(glm(mplesetup$response ~ . - 1, data = data.frame(mplesetup$predictor),
         weights = mplesetup$weights, family="binomial"))

# Check that the coefficients agree with the output of the ergm function:
coef(ergmMPLE(formula, output="fit"))

# We can also format the predictor matrix into an array:
mplearray <- ergmMPLE(formula, output="array")

# The resulting matrices are big, so only print the first 8 actors:
mplearray$response[1:8,1:8]
mplearray$predictor[1:8,1:8,]
mplearray$weights[1:8,1:8]

# Constraints are handled:
faux.mesa.high%v%"block" <- seq_len(network.size(faux.mesa.high)) %/% 4
mplearray <- ergmMPLE(faux.mesa.high~edges, constraints=~blockdiag("block"), output="array")
mplearray$response[1:8,1:8]
mplearray$predictor[1:8,1:8,]
mplearray$weights[1:8,1:8]

# Or, a dyad list:
faux.mesa.high%v%"block" <- seq_len(network.size(faux.mesa.high)) %/% 4
mplearray <- ergmMPLE(faux.mesa.high~edges, constraints=~blockdiag("block"), output="dyadlist")
mplearray$response[1:8]
mplearray$predictor[1:8,]
mplearray$weights[1:8]

# Curved terms produce predictors on the canonical scale:
formula2 <- faux.mesa.high ~ gwesp
mplearray <- ergmMPLE(formula2, output="array")
# The resulting matrices are big, so only print the first 5 actors:
mplearray$response[1:5,1:5]
mplearray$predictor[1:5,1:5,1:3]
mplearray$weights[1:5,1:5]