This document describes the ways to specify nodal
attributes or functions of nodal attributes and which levels for
categorical factors to include. For the helper functions to
facilitate this, see
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Term nodal attribute arguments, typically called
on are interpreted as follows:
Extract the vertex attribute with this name.
Extract the vertex attributes and paste them together, separated by dots if the term expects categorical attributes and (typically) combine into a covariate matrix if it expects quantitative attributes.
The function is called on the LHS network and
additional arguments to
ergm_get_vattr(), expected to return a
vector or matrix of appropriate dimension. (Shorter vectors and
matrix columns will be recycled as needed.)
The expression on the RHS of the formula is
evaluated in an environment of the vertex attributes of the
network, expected to return a vector or matrix of appropriate
dimension. (Shorter vectors and matrix columns will be recycled as
needed.) Within this expression, the network itself accessible as
.nw. For example,
nodecov(~abs(Grade-mean(Grade))/network.size(.)) would return the
absolute difference of each actor's "Grade" attribute from its
network-wide mean, divided by the network size.
AsIsobject created by
Use as is, checking only for correct length and type.
Any of these arguments may also be wrapped in or piped through
COLLAPSE_SMALLEST(attr, n, into) or,
attr %>% COLLAPSE_SMALLEST(n, into), a convenience function that will
transform the attribute by collapsing the smallest
into one, naming it
into. Note that
into must be of the same
type (numeric, character, etc.) as the vertex attribute in
The name the nodal attribute receives in the statistic can be
overridden by setting a an
For categorical attributes, to select which levels are of interest
and their ordering, use the argument
levels. Selection of nodes (from
the appropriate vector of nodal indices) is likewise handled as the
selection of levels, using the argument
nodes. These arguments are interpreted
Use the given list of levels as is.
Used for indexing of a list of
all possible levels (typically, unique values of the attribute) in
default older (typically lexicographic), i.e.,
sort(unique(attr))[levels]. In particular,
retain all levels. Negative values exclude. Another special value
LARGEST, which will refer to the most frequent category, so,
say, to set such a category as the baseline, pass
levels=-LARGEST. In addition,
LARGEST(n) will refer to the
SMALLEST works analogously. Note that if there
are ties in frequencies, they will be broken arbitrarily. To
specify numeric or logical levels literally, wrap in
Retain all possible levels; usually equivalent to
Use as is.
The function is called on the list of unique values of the attribute, the values of the attribute themselves, and the network itself, depending on its arity. Its return value is interpreted as above.
The expression on the RHS of the formula is
evaluated in an environment in which the network itself is
.nw, the list of unique values of the attribute as
. or as
.levels, and the attribute vector itself as
.attr. Its return value is interpreted as above.
For mixing effects (i.e.,
level2= arguments), a
matrix can be used to select elements of the mixing matrix, either
by specifying a logical (
FALSE) matrix of the same
dimension as the mixing matrix to select the corresponding cells or
a two-column numeric matrix indicating giving the coordinates of
cells to be used.
nodes, and others often have a default that is sensible for the
term in question.
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library(magrittr) # for %>% data(faux.mesa.high) # Activity by grade with a baseline grade excluded: summary(faux.mesa.high~nodefactor(~Grade)) # Name overrides: summary(faux.mesa.high~nodefactor("Form"~Grade)) # Only for terms that don't use the LHS. summary(faux.mesa.high~nodefactor(~structure(Grade,name="Form"))) # Retain all levels: summary(faux.mesa.high~nodefactor(~Grade, levels=TRUE)) # or levels=NULL # Use the largest grade as baseline (also Grade 7): summary(faux.mesa.high~nodefactor(~Grade, levels=-LARGEST)) # Activity by grade with no baseline smallest two grades (11 and # 12) collapsed into a new category, labelled 0: table(faux.mesa.high %v% "Grade") summary(faux.mesa.high~nodefactor((~Grade) %>% COLLAPSE_SMALLEST(2, 0), levels=TRUE)) # Mixing between lower and upper grades: summary(faux.mesa.high~mm(~Grade>=10)) # Mixing between grades 7 and 8 only: summary(faux.mesa.high~mm("Grade", levels=I(c(7,8)))) # or summary(faux.mesa.high~mm("Grade", levels=1:2)) # or using levels2 (see ? mm) to filter the combinations of levels, summary(faux.mesa.high~mm("Grade", levels2=~sapply(.levels, function(l) l[]%in%c(7,8) && l[]%in%c(7,8)))) # Here are some less complex ways to specify levels2. This is the # full list of combinations of sexes in an undirected network: summary(faux.mesa.high~mm("Sex", levels2=TRUE)) # Select only the second combination: summary(faux.mesa.high~mm("Sex", levels2=2)) # Equivalently, summary(faux.mesa.high~mm("Sex", levels2=-c(1,3))) # or summary(faux.mesa.high~mm("Sex", levels2=c(FALSE,TRUE,FALSE))) # Select all *but* the second one: summary(faux.mesa.high~mm("Sex", levels2=-2)) # Select via a mixing matrix: (Network is undirected and # attributes are the same on both sides, so we can use either M or # its transpose.) (M <- matrix(c(FALSE,TRUE,FALSE,FALSE),2,2)) summary(faux.mesa.high~mm("Sex", levels2=M)+mm("Sex", levels2=t(M))) # Select via an index of a cell: idx <- cbind(1,2) summary(faux.mesa.high~mm("Sex", levels2=idx)) # mm() term allows two-sided attribute formulas with different attributes: summary(faux.mesa.high~mm(Grade~Race, levels2=TRUE)) # It is possible to have collapsing functions in the formula; note # the parentheses around "~Race": this is because a formula # operator (~) has lower precedence than pipe (|>): summary(faux.mesa.high~mm(Grade~(~Race) %>% COLLAPSE_SMALLEST(3,"BWO"), levels2=TRUE)) # Some terms, such as nodecov(), accept matrices of nodal # covariates. An certain R quirk means that columns whose # expressions are not typical variable names have their names # dropped and need to be adjusted. Consider, for example, the # linear and quadratic effects of grade: Grade <- faux.mesa.high %v% "Grade" colnames(cbind(Grade, Grade^2)) # Second column name missing. colnames(cbind(Grade, Grade2=Grade^2)) # Can be set manually, colnames(cbind(Grade, `Grade^2`=Grade^2)) # even to non-variable-names. colnames(cbind(Grade, Grade^2, deparse.level=2)) # Alternatively, deparse.level=2 forces naming. rm(Grade) # Therefore, the nodal attribute names are set as follows: summary(faux.mesa.high~nodecov(~cbind(Grade, Grade^2))) # column names dropped with a warning summary(faux.mesa.high~nodecov(~cbind(Grade, Grade2=Grade^2))) # column names set manually summary(faux.mesa.high~nodecov(~cbind(Grade, Grade^2, deparse.level=2))) # using deparse.level=2 # Activity by grade with a random covariate. Note that setting an attribute "name" gives it a name: randomcov <- structure(I(rbinom(network.size(faux.mesa.high),1,0.5)), name="random") summary(faux.mesa.high~nodefactor(I(randomcov)))
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