# 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.

- Higher grades + faster learning
- Never study anything twice
- 100% sure, 100% understanding

### 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?

- 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:

- A unique study and practice tool
- Never study anything twice again
- Get the grades you hope for
- 100% sure, 100% understanding