Logistic Regression for Network Data

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Description

netlogit performs a logistic regression of the network variable in y on the network variables in set x. The resulting fits (and coefficients) are then tested against the indicated null hypothesis.

Usage

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netlogit(y, x, intercept=TRUE, mode="digraph", diag=FALSE,
    nullhyp=c("qap", "qapspp", "qapy", "qapx", "qapallx", 
    "cugtie", "cugden", "cuguman", "classical"), test.statistic = 
    c("z-value","beta"), tol=1e-7, reps=1000)

Arguments

y

dependent network variable. NAs are allowed, and the data should be dichotomous.

x

the stack of independent network variables. Note that NAs are permitted, as is dichotomous data.

intercept

logical; should an intercept term be fitted?

mode

string indicating the type of graph being evaluated. "digraph" indicates that edges should be interpreted as directed; "graph" indicates that edges are undirected. mode is set to "digraph" by default.

diag

boolean indicating whether or not the diagonal should be treated as valid data. Set this true if and only if the data can contain loops. diag is FALSE by default.

nullhyp

string indicating the particular null hypothesis against which to test the observed estimands.

test.statistic

string indicating the test statistic to be used for the Monte Carlo procedures.

tol

tolerance parameter for qr.solve.

reps

integer indicating the number of draws to use for quantile estimation. (Relevant to the null hypothesis test only – the analysis itself is unaffected by this parameter.) Note that, as for all Monte Carlo procedures, convergence is slower for more extreme quantiles. By default, reps=1000.

Details

netlogit is primarily a front-end to the built-in glm.fit routine. netlogit handles vectorization, sets up glm options, and deals with null hypothesis testing; the actual fitting is taken care of by glm.fit.

Logistic network regression using is directly analogous to standard logistic regression elementwise on the appropriately vectorized adjacency matrices of the networks involved. As such, it is often a more appropriate model for fitting dichotomous response networks than is linear network regression.

Because of the frequent presence of row/column/block autocorrelation in network data, classical hull hypothesis tests (and associated standard errors) are generally suspect. Further, it is sometimes of interest to compare fitted parameter values to those arising from various baseline models (e.g., uniform random graphs conditional on certain observed statistics). The tests supported by netlogit are as follows:

classical

tests based on classical asymptotics.

cug

conditional uniform graph test (see cugtest) controlling for order.

cugden

conditional uniform graph test, controlling for order and density.

cugtie

conditional uniform graph test, controlling for order and tie distribution.

qap

QAP permutation test (see qaptest); currently identical to qapspp.

qapallx

QAP permutation test, using independent x-permutations.

qapspp

QAP permutation test, using Dekker's “semi-partialling plus” procedure.

qapx

QAP permutation test, using (single) x-permutations.

qapy

QAP permutation test, using y-permutations.

Note that interpretation of quantiles for single coefficients can be complex in the presence of multicollinearity or third variable effects. Although qapspp is known to be robust to these conditions in the OLS case, there are no equivalent results for logistic regression. Caution is thus advised.

The statistic to be employed in the above tests may be selected via test.statistic. By default, the z-statistic (rather than estimated coefficient) is used, as this is more approximately pivotal; coefficient-based tests are not recommended for QAP null hypotheses, although they are provided here for legacy purposes.

Reasonable printing and summarizing of netlogit objects is provided by print.netlogit and summary.netlogit, respectively. No plot methods exist at this time.

Value

An object of class netlogit

Author(s)

Carter T. Butts buttsc@uci.edu

References

Butts, C.T., and Carley, K.M. (2001). “Multivariate Methods for Interstructural Analysis.” CASOS working paper, Carnegie Mellon University.

See Also

glm, netlm

Examples

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## Not run: 
#Create some input graphs
x<-rgraph(20,4)

#Create a response structure
y.l<-x[1,,]+4*x[2,,]+2*x[3,,]   #Note that the fourth graph is 
                                #unrelated
y.p<-apply(y.l,c(1,2),function(a){1/(1+exp(-a))})
y<-rgraph(20,tprob=y.p)

#Fit a netlogit model
nl<-netlogit(y,x,reps=100)

#Examine the results
summary(nl)

## End(Not run)

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