EstimateIsing {IsingSampler}

non-regularized estimation methods for the Ising Model

Description

This function can be used for several non-regularized estimation methods of the Ising Model. See details.

Usage

EstimateIsing(data, responses, beta = 1, method = c("uni", "pl",
                 "bi", "ll"), adj = matrix(1, ncol(data), ncol(data)),
                 ...)
EstimateIsingUni(data, responses, beta = 1, adj = matrix(1, ncol(data),
                 ncol(data)), min_sum = -Inf, thresholding = FALSE, alpha = 0.01, 
                 AND = TRUE, ...)
EstimateIsingBi(data, responses, beta = 1, ...)
EstimateIsingPL(data, responses, beta = 1, ...)
EstimateIsingLL(data, responses, beta = 1, adj = matrix(1, ncol(data),
                 ncol(data)), ...)

Arguments

data

Data frame with binary responses to estimate the Ising model over

responses

Vector of length two indicating the response coding (usually c(0L, 1L) pr c(-1L, 1L))

beta

Inverse temperature parameter

method

The method to be used. pl uses pseudolikelihood estimation, uni sequential univariate regressions, bi bivariate regressions and ll estimates the Ising model as a loglinear model.

adj

Adjacency matrix of the Ising model.

min_sum

The minimum sum score that is artifically possible in the dataset. Defaults to -Inf. Set this only if you know a lower sum score is not possible in the data, for example due to selection bias.

thresholding

Logical, should the model be thresholded for significance?

alpha

Alpha level used in thresholding

AND

Logical, should an AND-rule (both regressions need to be significant) or OR-rule (one of the regressions needs to be significant) be used?

...

Arguments sent to estimator functions

Details

The following algorithms can be used (see Epskamp, Maris, Waldorp, Borsboom; in press).

pl

Estimates the Ising model by maximizing the pseudolikelihood (Besag, 1975).

uni

Estimates 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.

bi

Estimates 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.

ll

Estimates the Ising model by phrasing it as a loglinear model with at most pairwise interactions. Uses loglin.

Value

A list containing the estimation results:

graph

The estimated network

thresholds

The estimated thresholds

results

The results object used in the analysis

Author(s)

Sacha Epskamp ([e-mail])

References

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.

Examples

# 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)])