The item network and domain network of burnout in Chinese nurses

The item network and domain network were estimated via Gaussian graphical models (GGMs) [27]. GGMs are undirected networks in which the edges represent partial correlations between two nodes after conditioning on all other nodes in the network [28]. In the present study, the GGMs were calculated basing on nonparametric Spearman rho correlation matrices, and the nonparametric Spearman rho correlations among the items and domains are presented in Table S1 and Table S2 (in Supplemental Material). In the item network, the graphical least absolute shrinkage and selection operator (LASSO) algorithm was used to regularize the GGM [28]. This regularization procedure shrinks all edges and sets edges with small partial correlations to zero to obtain a parsimonious and sparse network, which is more stable and easier to interpret [28]. Meanwhile, the tuning parameter was set to 0.5 to adequately balance the sensitivity and specificity of picking out true edges [29]. Due to low variables (3 dimensions) but high samples (472 individuals), we used the unregularized model selection approach rather than regularization techniques to estimate the dimension network [30]. Visualizations of the item and domain networks were derived from the Fruchterman–Reingold algorithm, which locate nodes with stronger and numerous connections near the center of the network and weakly associated nodes on the periphery [31]. In the visualized networks, blue edges represent positive correlations and red edges represent negative correlations. Thicker edges indicate stronger correlations between the nodes.

Recent studies have shown that strength is the most reliable centrality index. The other centrality indices, such as betweenness and closeness, seem especially unsuitable for assessing the importance of nodes in psychological networks [32, 33]. Node strength is the sum of the absolute value of the edge weights attached to a node, and it may misinterpret the actual effect of nodes on the remaining network when there are negative edge weights in the network [34, 35]. Thus, we calculated the expected influence for both the item and dimension networks. This measure has replaced node strength in the most recent studies due to the evidence that it effectively considers both positive and negative edges within the network [35, 36]. Higher expected influence values indicate greater importance in the network [22]. The estimation, visualization, and centrality index of the item and dimension networks were carried out in the R-package qgraph [37]. In addition, we computed the predictability of each node in the item and dimension networks by using the R-package mgm [19]. Predictability is defined as the variance of a node, which is explained by all of its neighboring nodes, and this index could characterize the controllability of the network [19].

The spinglass algorithm was used to identify communities of items in the item network. It is based on the principle that the edges should connect nodes of the same community, whereas nodes belonging to different communities should not be connected [38]. It is important to note that an item can only be part of one community by using this procedure. Since the spinglass algorithm can yield different results in the same sample, we assessed the stability of the solution by running the algorithm 100 times and extracted the number of communities with the highest frequency. To complement the results, we also used the walktrap algorithm, which is based on the principle that adjacent nodes tend to belong to the same community [38]. This algorithm was shown to have high accuracy in simulation studies and was used in empirical network papers [39, 40].

We examined the robustness of the item and dimension networks by using the R-package bootnet [41, 42]. First, the accuracies of edge weights were evaluated by calculating the 95% confidence intervals (CI) using a non-parametric bootstrap approach (2000 bootstrap samples). Second, the stabilities of nodes’ expected influences were evaluated by computing the correlation stability (CS) coefficient, using a case-dropping bootstrap approach. The value of the CS coefficient should not be less than 0.25 and preferably should be more than 0.5 [42]. Third, bootstrapped difference tests (2000 bootstrap samples and α = 0.05) for edge weights and nodes’ expected influences were performed to evaluate whether two edge weights or two nodes’ expected influences differ significantly from each other.

The item network is shown in Fig. 1a. There were several obvious characteristics in this network. First, 53 (50.5%) among the 105 possible edges did not have zero values and all these edges had a positive value except for the one edge between E1 “I feel emotionally drained from my work” and R1 “I deal effectively with the problems of clients” (weight = − 0.04). Second, twelve edges with strongest regularized partial correlations existed between E1 “I feel emotionally drained from my work” and E2 “I feel used up at the end of the day” (weight = 0.45), between C1 “I have become more callous toward work since I took this job” and C2 “I have become less enthusiastic about my work” (weight = 0.33), between C2 “I have become less enthusiastic about my work” and C3 “I doubt the significance of my work” (weight = 0.31), between C3 “I doubt the significance of my work” and C4 “I have become more and more indifferent in the contribution of my job” (weight = 0.30), between R5 “I have accomplished many worthwhile things in this job” and R6 “I am confident that I can accomplish all tasks effectively” (weight = 0.29), between R3 “In my opinion, I am good at my job” and R4 “I feel very happy when I accomplish some tasks of my job” (weight = 0.28), between E3 “I feel tired when I get up in the morning and have to face another day at work” and E4 “Working with people all day is a real strain for me” (weight = 0.26), between R4 “I feel very happy when I accomplish some tasks of my job” and R5 “I have accomplished many worthwhile things in this job” (weight = 0.26), between R1 “I deal effectively with the problems of clients” and R2 “I feel that I am contributing to my company” (weight = 0.25), between R3 “In my opinion, I am good at my job” and R6 “I am confident that I can accomplish all tasks effectively” (weight = 0.24), between E4 “Working with people all day is a real strain for me” and E5 “I feel burned out from my work” (weight = 0.23), and between R2 “I feel that I am contributing to my company” and R3 “In my opinion, I am good at my job” (weight = 0.22). Third, node predictability is shown as a ring around the node in Fig. 1a. The value of node predictability ranged from 0.38 to 0.74 (see Table 2), with an average value of 0.64. This means that on average, 64% of the variance of the node can be explained by its neighbors in the item network. E1 “I feel emotionally drained from my work” (predictability = 0.74) and E5 “I feel burned out from my work” (predictability = 0.74) had the highest predictability: 74% of their variance can be explained by their neighboring nodes. R1 “I deal effectively with the problems of clients” (predictability = 0.38) had the lowest predictability: 38% of its variance can be explained by its neighboring nodes.

The z-score value of the expected influence for each node was computed to assess its relative importance in the item network (see Fig. 1b and Table 2). Three nodes with the highest expected influence were E5 “I feel burned out from my work” (z-scores = 0.99), R3 “In my opinion, I am good at my job” (z-scores = 0.94), and C1 “I have become more callous toward work since I took this job” (z-scores = 0.81). This indicates that these three nodes are the most associated nodes in the present network from a statistical point of view. The node with the lowest expected influence was R1 “I deal effectively with the problems of clients” (z-scores = − 2.53), which indicates that this node is the least associated node in the present network from a statistical point of view.

Bootstrap 95% confidence interval indicated that the estimation of edge weights was accurate (Fig. S1 in the Supplementary Material). In addition, the CS coefficient of nodes’ expected influences was 0.75, indicating that the estimation of nodes’ expected influence was adequately stable (Fig. S2 in the Supplementary Material). The bootstrapped difference test for edge weights showed that in the item network, a moderate proportion of the differences among edge weights was significant (Fig. S3 in the Supplementary Material). Moreover, the bootstrapped difference tests for nodes’ expected influences showed that in the item network, a small to moderate proportion of the differences among nodes’ expected influences was significant (Fig. S4 in the Supplementary Material).

The spinglass algorithm identified a mean of three communities of items corresponding to the three dimensions of MBI-GS, as proposed originally and confirmed by Maslach and her colleagues [3]. One community comprised items E1, E2, E3, E4, and E5, forming the dimension of “Emotional exhaustion”. One community was formed by items C1, C2, C3, and C4, and all of them constituted the dimension of “Cynicism”. The other community was formed by items R1, R2, R3, R4, R5, and R6 and was represented the dimension of “Reduced professional efficacy”. Meanwhile, the walktrap algorithm identified the same three communities as the spinglass algorithm.

The dimension network is shown in Fig. 2a. There were several obvious characteristics in the network. First, 2 (66.7%) edges among the 3 possible edges did not have zero values and these two edges had positive values. Second, the edge between “Emotional exhaustion” and “Cynicism” (weight = 0.65) had strong unregularized partial correlation, while the edge between “Cynicism” and “Reduced professional efficacy” (weight = 0.23) had relatively weak unregularized partial correlation. There was no unregularized partial correlation between “Emotional exhaustion” and “Reduced professional efficacy”. Third, node predictability is shown as a ring around the node in Fig. 2a. The node predictability of “Emotional exhaustion”, “Cynicism”, and “Reduced professional efficacy” was 0.56, 0.58, and 0.05 (see Table 2), respectively. This means that 56% of the variance of “Emotional exhaustion”, 58% of the variance of “Cynicism”, and 5% of the variance of “Reduced professional efficacy” can be explained by its neighbors in the dimension network.

The z-score value of the expected influence for each node was computed to assess its relative importance in the dimension network (see Fig. 2b and Table 2). “Cynicism” had the highest expected influence (z-scores = 0.89), which indicates that this node is the most associated node in the dimension network from a statistical point of view.

Bootstrap 95% confidence interval indicated that the estimation of edge weights was accurate (Fig. S5 in the Supplementary Material). In addition, the CS coefficient of nodes’ expected influences was 0.75, indicating that the estimations of node’s expected influence were adequately stable (Fig. S6 in the Supplementary Material). The bootstrapped difference test for edge weights showed that in the dimension network, difference between two edge weights was significant (Fig. S7 in the Supplementary Material). Moreover, the bootstrapped difference tests for nodes’ expected influences showed that in the dimension network, all differences among nodes’ expected influences were significant (Figs. S8 in the Supplementary Material).