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Networks - Epskamp, 2018

11 important questions on Networks - Epskamp, 2018

Of which components do psychological networks consist?

Psychological networks consist of nodes representing observed variables,
connected by edges representing statistical relationships.

Of which three steps does psychological research with networks consist?

estimate a statistical model on data, from which some parameters can be represented as a weighted network between observed variables.
analyze the weighted network structure using measures taken from graph theory to infer, for instance, the most central nodes.

assessing the accuracy of the network parameters and measures

What does it mean if the edges in a network represent partial correlations?

If the edges in a network represent partial correlations, it means they show the relationship between variables while conditioning for all other variables in the network.
this way, the direct relationship between variables is presented and no indirect effects are included.

What is a pairwise markov random field?

A PMRF is a network in which nodes represent variables, connected by undirected edges (edges with no arrowhead) indicating conditional dependence between two variables; two variables that are not connected are independent after conditioning on other variables.
When data are multivariate normal, such a conditional independence would correspond to a partial correlation being equal to zero.

What are the advantages of a pairwise random markov field, that a directed network does not have?

In cross-sectional observational data, causal networks (e.g., directed networks) are hard to estimate without stringent assumptions (e.g., no feedback loops).
In addition, directed networks suffer from a problem of many equivalent models (e.g., a network A → B is not statistically distinguishable from a network A ← B).

PMRFs, however, are well defined and have no equivalent models (i.e., for a given PMRF, there exists no other PMRF that describes exactly the same statistical independence relationships for the set of variables under consideration).

What pairwise markov random field model is appropriate if you have binary data, normal data, and a mix of binary and normal data?

The ising model is for binary data
for normal data, use the gaussian graphical model

edges can directlybe interpreted as partial correlation coefficients.

The GGM requires an estimate of the covariance matrix as input for which polychoric correlations can also be used in case the data are ordinal.
For continuous data that are not normally distributed, a transformation can be applied before estimating the GGM.

for mixed data, use mixed graphical models.

When estimating network models, what is a problem that frequently occurs?

in an unregularized network, the number of parameters to estimate grows quickly with the size of the network.

e.g. 55 for a 10 node network, and 1275 in a 50 node network

To estimate all parameters of the network, the number of datapoints generally needs to exceed the amount of parameters.

What is a solution to the problem small datasets impose on estimating the network?

Using lasso regularization when estimating the parameters.
the weighted sum of total absolute values of all weights is added to the loss function.
this forces the parameter estimation algorithm to set redundant parameters to zero.
As such, the LASSO returns a sparse (or, in substantive terms, conservative) network model: only a relatively small number of edges are used to explain the covariation structure in the data.

The LASSO utilizes a tuning parameter to control the degree to which regularization is applied, which can be tuned using the EBIC statistic.

What methods can be applied to gain insights into the accuracy of edge weights and the stability of centrality indices in the estimated network structure.

Estimation of the accuracy of edge-weights, by drawing bootstrapped CIs

investigating the stability of (the order of) centrality indices after observing only portions of the data
performing bootstrapped difference tests between edge-weights and centrality indices to test whether these differ significantly from each other.

Describe how can you assess the stability of edge weights.

Perform a non-parametric bootstrap on the data: sample with replacement to obtain bootstrapped samples.
a bootstrapped CI can be obtained by sorting the estimated weights and taking the xth and zth percentile positions.
the width of the bootstrapped ci's conveys the stability of the edge weights.
when LASSO regularization is used to estimate a network, the edge-weights are on average made smaller due to shrinkage, which biases the parametric bootstrap.

What is a typical way of assessing the importance of nodes in a network?

Computing centrality indices of the nodes. Examples are:

node strength, quantifying how well a node is directly connected to other nodes,
closeness, quantifying how well a node is indirectly connected to other nodes,

betweenness, quantifying how important a node is in the average path between two other nodes.

The question on the page originate from the summary of the following study material:

BDS: psychometrics

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Networks - Epskamp, 2018

11 important questions on Networks - Epskamp, 2018

Of which components do psychological networks consist?

Of which three steps does psychological research with networks consist?

What does it mean if the edges in a network represent partial correlations?

What is a pairwise markov random field?

What are the advantages of a pairwise random markov field, that a directed network does not have?

What pairwise markov random field model is appropriate if you have binary data, normal data, and a mix of binary and normal data?

When estimating network models, what is a problem that frequently occurs?

What is a solution to the problem small datasets impose on estimating the network?

What methods can be applied to gain insights into the accuracy of edge weights and the stability of centrality indices in the estimated network structure.

Describe how can you assess the stability of edge weights.

What is a typical way of assessing the importance of nodes in a network?

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