non-regularized estimation methods for the Ising Model
This function can be used for several non-regularized estimation methods of the Ising Model. See details.
EstimateIsing(data, responses, beta = 1, method = c("pl", "uni",
"bi", "ll"), adj = matrix(1, ncol(data), ncol(data)),
...)
EstimateIsingUni(data, responses, beta = 1, adj = matrix(1, ncol(data),
ncol(data)), ...)
EstimateIsingBi(data, responses, beta = 1, ...)
EstimateIsingPL(data, responses, beta = 1, ...)
EstimateIsingLL(data, responses, beta = 1, adj = matrix(1, ncol(data),
ncol(data)), ...)data |
Data frame with binary responses to estimate the Ising model over |
responses |
Vector of length two indicating the response coding (usually |
beta |
Inverse temperature parameter |
method |
The method to be used. |
adj |
Adjacency matrix of the Ising model. |
... |
Arguments sent to estimator functions |
The following algorithms can be used (see Epskamp, Maris, Waldorp, Borsboom; in press).
plEstimates the Ising model by maximizing the pseudolikelihood (Besag, 1975).
uniEstimates the Ising model by computing univariate logistic regressions of each node on all other nodes. This leads to a single estimate for each threshold and two estimates for each network parameter. The two estimates are averaged to produce the final network. Uses glm.
biEstimates the Ising model using multinomial logistic regression of each pair of nodes on all other nodes. This leads to a single estimate of each network parameter and $p$ estimates of each threshold parameter. Uses multinom.
llEstimates the Ising model by phrasing it as a loglinear model with at most pairwise interactions. Uses loglin.
A list containing the estimation results:
graph |
The estimated network |
thresholds |
The estimated thresholds |
results |
The results object used in the analysis |
Sacha Epskamp (mail@sachaepskamp.com)
Epskamp, S., Maris, G., Waldorp, L. J., and Borsboom, D. (in press). Network Psychometrics. To appear in: Irwing, P., Hughes, D., and Booth, T. (Eds.), Handbook of Psychometrics. New York: Wiley.
Besag, J. (1975), Statistical analysis of non-lattice data. The statistician, 24, 179-195.
# Input: N <- 5 # Number of nodes nSample <- 500 # Number of samples # Ising parameters: Graph <- matrix(sample(0:1,N^2,TRUE,prob = c(0.7, 0.3)),N,N) * rnorm(N^2) Graph <- Graph + t(Graph) diag(Graph) <- 0 Thresholds <- rep(0,N) Beta <- 1 # Response options (0,1 or -1,1): Resp <- c(0L,1L) Data <- IsingSampler(nSample,Graph, Thresholds) # Pseudolikelihood: resPL <- EstimateIsing(Data, method = "pl") cor(Graph[upper.tri(Graph)], resPL$graph[upper.tri(resPL$graph)]) # Univariate logistic regressions: resUni <- EstimateIsing(Data, method = "uni") cor(Graph[upper.tri(Graph)], resUni$graph[upper.tri(resUni$graph)]) # bivariate logistic regressions: resBi <- EstimateIsing(Data, method = "bi") cor(Graph[upper.tri(Graph)], resBi$graph[upper.tri(resBi$graph)]) # Loglinear model: resLL <- EstimateIsing(Data, method = "ll") cor(Graph[upper.tri(Graph)], resLL$graph[upper.tri(resLL$graph)])
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