The present work was motivated by the analysis of a large database belonging to Stimulus, an independent French consulting firm specialized in wellbeing and occupational health. Stimulus has developed and made available for companies an online tool to collect data on stress levels and psychosocial risk factors, and in the future to develop a useful preventative intervention strategy.

A method developed by Cooper & Clarke, involving a quantitative risk assessment approach to prioritize psychosocial risks in the workplace [9], is currently often used. To identify stressors related to high stress level, they suggest calculating a “risk level indicator” to measure the impact of a given stressor on stress: Risk=Exposure(E)×Consequences(C) (1)

Here, E is the mean value of the stressor (exposure) and C (consequences) the proportion of variance of stress level explained by the given stressor (r²) obtained from a simple linear regression.

However, the relevance of this indicator is questionable, despite its ease of use. The “risk level indicator” (1) represents neither a statistical risk measure, nor an impact measure. Indeed, the r² is obtained from a simple linear regression between stress (the outcome) and a given stressor, where the impact of the other stressors is ignored. In short, this would imply that acting on a given stressor to reduce stress levels does not impact the other stressors, which is not entirely reasonable.

We illustrate this (Fig 1) with two examples of variation of stress level (y) following exposure to a given stressor (x).

In the left-hand panel, we show the case of two stressors x₁ and x₂ with the same variability, as well as the same correlation with y, whereas the average exposure for x₂ is higher than for x₁ (E₂ > E₁). It follows that x₁ and x₂ have the same risk, since increasing (or decreasing) x₁ or x₂ equally would have the same influence on y. However, according to Cooper’s index, x₂ should have a higher risk than x₁, which is not true. In the right-hand panel, we show the case of two stressors x₁ and x₂ with the same average exposure level (E₁ = E₂), where variability and correlation with y are different (x₁ is more correlated with y than x₂). Therefore, x₂ has a higher risk than x₁ because y, given x₂, has more variability than y, given x₁. However, according to Cooper’s index, x₁ should have a higher risk than x₂, which is not true here.

The mean value of a stressor may be considered as a performance index. However, it is not related to any effect on stress. The slope of the regression line would be a better indicator than the correlation; however, a simple regression is not pertinent here. In the next section, we show that structural equation modeling can provide an adequate solution.

To obtain insight into data on stressors and stress level, correlation analyses were conducted using structural equation modeling (SEM), which has the advantage of providing global measures of fit for latent (subjective or unobserved) variable models [15,16]. The SEM approach is based on conceptual models, and defined by two sets of equations: the inner (or structural) model, and the outer (or measurement) model. The structural model specifies relationships between latent constructs (block of stressors), whereas the measurement model specifies relationships between a latent construct and its manifest variables (stressors), as illustrated in Fig 2. Structural equation models help to assess whether or not hypothesized relationships between variables are valid for the study population, as it enables the specified relationships to be tested against the observed pattern of correlation between variables.

In fact, we hypothesize in the underlying conceptual model, developed with experts at Stimulus, that all stressor blocks are closely related (i.e., correlated), and that changes in one would be negatively associated with stress level.

To predict the impact of the 5 job stressors blocks (exogenous constructs) on the stress block (endogenous construct), we used PLS-PM over other SEM approaches, for two main reasons. First, it allows the development of a system of weights via several indices, when the blocks of stressors are strongly correlated, which was the case with our data. Second, PLS-PM is a better choice when the Gaussian distribution assumption is not valid, which is the case for stressors (6-point Likert scale). PLS-PM uses an iterative algorithm; after convergence, latent variable scores are obtained for each observation, and structural coefficients are estimated using multiple regression.

This approach appears to be a useful tool for psychosocial risk management policy for the workplace, and comes with two advantages. First, it allows us to build a relevant scale for stress level using the 25 items in the PSM25 questionnaire, rather than using an equally-weighted scale. Second, it gives a ranking of the five blocks of stressors according to their predictive impact on stress level, using path coefficient values.

However, in order to directly prioritize stressors impacting stress level, we considered constructing a system of levers to identify stressors which decision makers should maintain or act on in priority, to reduce stress level. To achieve this, we suggest using importance-performance analysis (IPA) [17], where weights and path coefficients estimated in the PLS model are used to calculate item importance.

IPA is an easily understandable graphical tool presented as a grid divided into four quadrants. The horizontal axis shows the item’s performance, and the vertical axis its importance. The four quadrants are as follows. A is the top-left quadrant (“Concentrate Management Here”), B the top-right (“Keep up the Good Work”), C bottom-left (“Low Priority”) and D bottom-right (“Possible Overkill”).

Of most interest are items in quadrants A and B, as these are relatively “more important” than those in quadrants C and D. Therefore, an item with a lower performance and a higher importance falls into quadrant A, indicating that decision makers should devote further resources to this particular attribute, so as to improve its performance.

An item's performance is defined as its observed mean score over the 10 000 individual responses to this item. Its importance is calculated with the formula (2) in which the importance of a given item is the product of the absolute value of the outer weight and the path coefficient of the latent variable in which the item belongs, obtained from the PLS-PM: Importance(kthitem)=100×|Outer weight(kthitem ofjthblock)|×Path coefficient(jthblock,stress) (2)

The study was approved by the French Data Protection Authority “La Commission Nationale de l’Informatique et des Libertés” (CNIL, #1839949 v 0).

To evaluate the homogeneity (or unidimensionality) of the six blocks, eigenvalues of the correlation matrix between manifest variables (stressors) belonging to the same block were calculated [18]. Table 1 gives the values of the first eigenvalue corresponding to each block, as well as Cronbach's α. Since the first eigenvalue is dominant and Cronbach's α is high; we may conclude as to the unidimensionality of each block, which can thus be summarized as a single latent variable. The PLS-PM approach, together with the two measurement tools, were validated in the four following steps.

First, correlations between the five blocks of stressors (work context, job control, relationships, tasks and recognition), given in Table 2, show that they were mutually positively and strongly related. For this reason mainly, PLS-PM is an appropriate SEM approach to deal with collinearity issues. Indeed, the structural model should be tested for potential collinearity that might bias the results of the underlying multiple regression analysis.

Second, the measurement model allowed us to confirm the validity of the six latent constructs. As for the total stress and total stressors, the outer weights were statistically significant, indicating the relevance of the latent variables. Thus, the measurement model quality is satisfactory. Furthermore, normalized outer weights of items belonging to the stress block could potentially be used to define a more relevant stress scale, using the PSM25 questionnaire. This is a more relevant scale than that with all 25 items equally weighted as described above in the Stress measurement paragraph.

Third, the structural model allowed us to evaluate the strength and significance of the path coefficients for the relationships (structural paths) hypothesized between the constructs. The path coefficient values (Fig 3), indicate similar, negative impact of each of the five stressor constructs on the stress construct.

Finally, the assessment of the model’s quality shows the good ability of the model to predict the endogenous construct “stress” (R² = 0.40), indicating that the five blocks of stressors explain 40% of the variance of the stress construct (Fig 3).

We performed PLS-PM as described above, using a 10 000 employees dataset. A randomly drawn subsample of 5 000 employees was used to develop the models, and the remaining 5 000 employees' data served for the validation step. Analyses were performed using the PLS-PM package from the XLSTAT software (https://www.xlstat.com/en/).

The IPA plot of importance according to performance values for each of 58 stressors is shown in Fig 4 and S4 Table. Sets of stressors in each of the quadrants A and B were identified, and detailed below.

In terms of the most important items, for the most part the five following items were identified in quadrant A, where improvement in performance is the most pressing, and upon which management should concentrate its efforts:

Of the most important items, for the most part the following six items were identified in quadrant B, where efforts should be maintained:

These results from the analyzed data suggest that, for organizational strategies to prevent and manage stress, decision-makers should act in priority on the level of the 5 “stressors to improve", and should maintain the level of the 6 “stressors to maintain”, because otherwise the stress level will increase.

IPA’s robustness against changes in the scale used to categorize the answers to the 58 items related to stressors, was tested as follows. Instead of using the 6-point Likert scale for individuals’ answers to each of the 58 items, we dichotomized the answers as follows:

Results (not shown here) demonstrate a similar distribution of the items in the four quadrants. In particular, the items to improve (from quadrant A) and the items to maintain (from quadrant B) were similar. This indicates the robustness of the IPA results.

Although several models are available to identify risk factors impacting stress level, none are based on a solid theoretical base. These models were developed using empirical field studies. However, it is very important to be able to take into account interactions between the various risk factors for stress, identified through epidemiological studies. The PLS-PM approach allows us to predict stress levels using five strongly correlated blocks built from 58 stressors, and to understand concepts that are difficult to formalize. Using path coefficients, this approach allows us to prioritize the five stressor's latent variable constructs based on their ability to predict stress's latent variable construct.

The IPA approach allows the direct identification of stressors requiring priority attention for managerial action to reduce workplace stress levels, using an indirect computation of item importance coming from the PLS-PM results. Based on a plot of item importance in relation to measured performance, IPA provides a useful and easily understandable graphical guide as to how the quadrants differ from one another. As a result, it allows decision-makers to identify areas in which they must reallocate resources [20] in future organizational strategies to prevent and manage stress. Furthermore, the rather similar distribution of items on the IPA plot observed using dichotomized responses as opposed to the initial 6-point Likert-scale indicates the robustness of the IPA results.

The use of data from Stimulus provided a two-fold advantage in this study. First, the high quality of data collection, thanks to the large set of study questionnaires filled out during routine visits with company occupational physicians. Second, being able to use such a large dataset (10 000 employees) meant powerful statistical results could be obtained.

As several studies suggest that women suffer more stress than men [21–23], we performed stratified analyses, separately for men (49.6% of the employees) and women (50.4%), and found similar division over the 4 quadrants in the IPA analysis. This means that there is no need to adjust for gender, which would require more complex computations [24]. Other characteristics, either at individual level or at company level, were not considered in our analyses. In fact, Stimulus database involved data from hundreds of companies, but with many characteristics, such as profession or type of company, considered confidential.

As correlation does not imply causality, a causal analysis should also be performed to determine the stressors on which to act in order to reduce psychosocial disorders associated with high stress level. Bühlmann proposes an analysis based on causal graphs [25] which can be used to supplement the previous approach in finding stressors on which to act in priority to reduce stress levels. This causal model could be validated using longitudinal data collected after putting in place a strategy for intervention against work-related stress prevention.