Network Psychometrics

The origins of psychological networks can be traced back to the studies on the orientation of particles devised by Lenz (1920) and further investigated by Ising (1925), whose name gave rise to the Ising network model. More recently, the network model has been conceived as a network of mutually reinforcing elements connected by causal relations (Marsman, 2018; van der Maas et al., 2006) so that they can better explain how complex interactions among different psychological variables occur (Epskamp, Borsboom & Fried, 2018). The way psychological networks are designed differs from latent causal models, such as unidimensional item response theory and structural equation modelling, since they do not model the dependencies among the observable variables (Borsboom, 2008). Hence, while latent trait models will seek for a common cause representation of the psychological variable by creating for instance a separate dimension for role clarity and another for communication, psychological networks will explore the interactions between the elements of these two dimensions all together.

In order to create and consequently understand a psychological network two elements are needed: nodes, represented by the observable behaviors or the items of a psychological instrument, and edges, the associations formed among them. From a statistical viewpoint, the nodes can be considered as the main effects, and the edges, the pairwise interactions (Marsman, 2018).

While applied to research in organizational psychology, psychological networks can create an interconnected system of reinforcing organizational behaviors that are able to show how different variables influence one another and which ones are more central for explaining the psychological trait under investigation. Even though the organizational psychology research tipically makes use of nonexperimental designs, psychological networks may suggest potential causal structures in a pathway. For example, workers might not rely on the organizational leadership, which in turn will impinge on the team morale and consequentely increase turnover intentions. This causal structure indicates that we would be able to predict turnover intentions by knowing the attitudes towards the leadership that could lead a worker to leave his or her organization. Nonetheless, we can also predict turnover intentions from team morale, making the knowledge on the attitudes towards leadership no longer necessary for the prediction of turnover intentions. As a result, the correlation estimated between leadership and turnover intentions is estimated to be zero, making these two variables conditionally independent from each other.

This property will be generalized to all relationships established among the items of a network, which will be calculated using partial correlation coefficients when data is assumed to be continuous or ordinal. Partial correlation networks are a subclass of undirected networks called Markov random field in which edges connect nodes by solid lines with no arrows, showing that the edge (x, y) is identical to the edge (y, x). The Figure 1 shows the graphical representation of a psychological network with items measuring engagement (Soane et al, 2012) and leadership transparency (Walumbwa et al, 2008) among leaders. The thickness of the edges represent the strengh of the association between two nodes, controlled by all other variables through partial correlation (Epskamp, Borsboom, Fried, 2018). The thicker an edge (solid line) is, the strongest the association between two nodes (circles).


Figure 1: A graphical representation of a psychological network showing relations among items measuring engagement and transparency

As can be seen in Figure 1, feeeling positive about the work (ENG01) is strongly related to sharing the same work values as other colleagues (ENG02), which in turn can motivate leaders to seek others’ opinions before making up their own minds (TRANSP03). As such, rather than test a few independent comparisons between the items of these two dimensions via regression models, a psychological network would assume that leadership develops from the complex interaction among all variables under measurement. It follows that the more variables a construct has, the greater the chance of identifying significant relations among them, making the application of psychological networks to the investigation of organizational climate an important methodological advance.

In addition to the estimation of psychological networks with the items of organizational climate, psychological networks seeks to analyze the predictability of the nodes, that is how much of the variance of a node can be predicted by the edges connected to it (Haslbeck & Waldorp, 2018). This analysis can confer weight to the edges and include information regarding interactions between variables from different dimensions, which would not be otherwise determined by traditional methods of data analysis. The importance of the nodes, or how influential in a network they are, can therefore be assessed via centrality indices of the network structure (Constantini et al,, 2015; Newman, 2010; Opsahl et al, 2010). The main three measures are strength, which shows how well a node is directly connected to other nodes, closeness, which shows how well a node is indirectly connected to other nodes, and betweenness, which quantifies the number of times a node acts as a bridge along the shortest path between two other nodes (Epskamp et al, 2018). Recent studies have revealed that strength is the most stable centrality index when cases are removed from the data set, while betweenness and closeness were not reliably estimated (Epskamp et al., 2017; Fried et al., 2018).

Figure 2 shows the three centrality indices for the aforementioned network relating the items of engagement and leadership transparency. The interpretation is quite straightforward as the farthest right an index is positioned, the highest the node centrality, with the leftmost values representing the least central nodes. Centrality measures are shown as standardized z-scores in most of the statistical packages in order to provide interpretability. As can be seen in Figure 1, sharing the same work values as other colleagues (ENG02) is the most important variable for explaining how leadership is perceived as it scores high in all of the three centrality measures. By being directly (strength) and indirectly (closeness) connected to other variables as well as representing a bridge variable (betweenness), ENG02 occupies a central position in the interactions among the variables in the network. For cross-sectional network models using small sample sizes, Epskamp, Borsboom and Fried (2017) recommend to calculate the stability of centrality indices and the accuracy of edge-weights. However, as this investigation makes use of a large data set, these estimates would render irrelevant. More information on how to calculate these measures can be found in the supplementary material.

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Figure 2: Centrality indices of a psychological network showing relations among items measuring engagement and transparency.

In psychological networks, the strength of the relationship between two variables is a parameter estimated from data. One of the most popular techniques for the estimation of network models based on continuous or ordinal data is the Gaussian graphical model, a pairwise Markov random field (PMRF) that calculates the partial correlation coefficient for the edges by conditioning on all other variables in the network. In order to enhance the prediction accuracy, interpretability and generalizability, a regularization technique called LASSO (least absolute shrinkage and selection operator) is further adopted, mainly when small samples are used (Epskamp, Borsboom, et al., 2017). By using LASSO, the usual sum of squared errors is minimized due a penalty that bound the total sum of the absolute values of the edges. As a result, some of the edge estimates are reduced to zero, while only a subset of covariates are selected in the final model. This type of network is called sparse, opposed to a dense network where each node is linked to every node in the network. The final step in the estimation process is choose a tuning parameter to control the amount of shrinkage and finally perform the model selection. The Extended Bayesian Information Criterion (EBIC; Chen & Chen, 2008), an extension of the Bayes Information Criteria, has been the algorithm used for model selection since it has worked well with the estimation of psychological networks based on dichotomous data, called Ising model (Foygel, Barber & Drton, 2015; van Burkulo et al., 2014), polytomous data (GGM) as well as for large number of covariates, as it has been applied in genetics research.