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p2: MCMC estimates for the p2 model

Description

Estimates p2 model parameters with the adaptive random walk algorithm as described in Zijlstra, Van Duijn and Snijders (2009) <doi: 10.1348/000711007X255336>.

Usage

p2(net, sender = NULL, receiver = NULL, density = NULL, reciprocity = NULL, 
burnin = NULL, sample = NULL, adapt = NULL, seed = NULL)

Value

Returns a matrix with MCMC means, standard deviations, quantiles and estimated effective sample sizes for p2 parameters.

Arguments

net

Directed dichotomous n*n network (digraph).

sender

Optional sender covariates of lenght n.

receiver

Optinal receiver covariates of length n.

density

Optional density covariates of dimensions n*n.

reciprocity

Optional symmetric reciprocity covariates of dimensions n*n.

burnin

Optional specification of number of burn-in iterations (default is 10000).

sample

Optional specification of number of MCMC samples (default is 40000).

adapt

Optional number of adaptive sequenses (default is 100).

seed

Optonal specification of random seed (delfault is 1).

Author

Bonne J.H. Zijlstra

References

Zijlstra, B.J.H., Duijn, M.A.J. van, and Snijders, T.A.B. (2009). MCMC estimation for the $p_2$ network regression model with crossed random effects. British Journal of Mathematical and Statistical Psychology, 62, 143-166.

Examples

# create a very small network with covariates for illustrative purposes
S <- c(1,0,1,0,1,1,0,1,0,1)
REC <- (S*-1)+1
D1 <- matrix(c(0,1,0,1,0,1,0,1,0,1,
              0,0,0,1,0,1,0,1,0,1,
              1,1,0,0,1,0,0,0,0,0,
              1,1,1,0,1,0,0,0,0,1,
              1,0,1,0,0,1,1,0,1,0,
              0,0,0,0,0,0,1,1,1,1,
              0,0,0,0,0,1,0,1,0,1,
              1,0,0,0,0,1,1,0,1,1,
              0,1,0,1,0,1,0,1,0,0,
              1,0,1,1,1,0,0,0,0,0), ncol=10)
D2 <- abs(matrix(rep(S,10), byrow = FALSE, ncol= 10) -
            matrix(rep(REC,10), byrow = TRUE, ncol= 10))
R <- D1*t(D1)
Y <- matrix(c(0,1,1,1,1,1,0,0,1,1,
              0,0,0,1,1,1,0,0,1,0,
              1,1,0,1,1,1,0,0,1,1,
              1,1,1,0,1,1,0,1,1,0,
              1,1,1,1,0,1,1,0,1,1,
              0,1,1,1,1,0,1,1,1,0,
              1,0,1,0,1,1,0,1,0,1,
              0,1,1,1,0,1,1,0,1,1,
              1,0,1,0,1,0,1,1,0,1,
              1,1,1,0,0,1,1,1,1,0), ncol=10) 

# estimate p2 model
p2(Y,sender= ~ S, receiver =  ~ REC, density = ~ D1 + D2, reciprocity= ~ R,
   burnin = 100, sample = 400, adapt = 10)
# Notice: burn-in, sample size and number of adaptive sequenses are 
# much smaller than recommended to keep computation time low.
# recommended code: 
if (FALSE) {
p2(Y,sender= ~ S, receiver =  ~ REC, density = ~ D1+ D2, reciprocity= ~ R)
}