## Optimal Time Lags in Longitudinal Studies on Social Stress at Work

Several cross-sectional meta-analyses revealed that stressors and strains correlate at a moderate or even high level (e.g. Burnout; Alarcon, 2011), whereas longitudinal meta-analyses showed that cross-lagged effects of prior stressors on later strain (while statistically controlling for prior strain) are low or not existent (e.g. Dormann & Haun, 2011; Ford, Matthews, Wooldridge, Mishra, Kakar, & Strahan, 2014; Nielsen & Einarsen, 2012). This contradictory finding has been explained by referring to the selection of “not optimal“ time lags in panel studies. Dormann and Griffin (revisions pending) derived optimal time lags on the basis of differential equation models. They concluded that long time lags are rarely justified when it is aimed at empirically investigating psychological stress.

Until now, there is a lack of systematic studies that determine the effect sizes of stressors on strains across a range of different time lags. Furthermore, there are only very few studies that applied short (a few weeks) or very short (a day) time lags. Our intention is to analyse such time-varying effects in the area of social stress, i.e., stress that arises during social interactions among employees. We will go above and beyond extant research inasmuch as prior research has not been dealing with subordinates as particular sources of social stress for supervisors. Theoretically, our assumption of stressful subordinates is based on the stress-as-offense-to-self model (SOS model; Semmer, Jakobshagen, Meier & Elfering, 2007). According to the SOS model, self-esteem represents an important personal resource for resilience. Research will focus on the dynamic aspects of the stress-crossover processes among supervisors and their subordinates, as well as the immediate, short-term, and mid-term consequences of such crossover processes. The consequences we will investigate are health and performance outcomes.

The goal of the research project thus is systematically investigating effects of subordinate-related social stressors across different time lags. Two questions shall be solved. On the one hand, we are interested in the time lag for which effects become particularly strong. On the other hand, we aim at identifying those personal characteristics of supervisors (resilience factors), which moderate the time period across which strain remains at elevated levels. For this purpose, we will use new statistical developments, which provide estimates of so-called drift parameters (Voelkle et al., 2012). Drift parameters express the change of variables and the change of relations among variables across time. These drift parameters will be empirically estimated using differential equation of the kind (cf. Waelde, 2012, Kap. 10)

d**x**(t) =(**Ax**(t) + **b**)dt + **G**dB(t).

In this equation **x**(t) represents a V × 1 vector containing the V variables of the research model, **A** is the V × V drift matrix, **b** is a V × 1 vector containing the regression constants across continuous time, **G** is the Cholesky triangle matrix and dB(t) is the stochastic process across time, for which dB(t) expresses the increment in the Brownian motion. The matrix exponential of **A** can then be further investigated to identify the optimal time lag (Dormann & Griffin, revisions pending), which is important because using an optimal time lag increases the probability to empirically validate actual causal relations among stressors and strains.

To empirically investigate the research questions a diary design will be employed in the dissertation project. The analyses of cross-lagged affects will be carried out at the within-person level (Level 1 in terms of hierarchical linear models) as well as at the between-person level (Level 2).

The goal of the postdoc project is to analyse data from a just finished research project (emotional stress at work, N = 100 dual earner couples, T = 40 measurement occasions with varying time lags between 15 minutes and 12 days). We aim at extending current methods of dynamic modelling in two ways. On the one hand, the varying time lags between and with persons have to be appropriately modelled.

On the other hand, possible circadian processes shall be adequately modeled using stochastic differential equations. Since the data are already available, the postdoctoral candidate shall be able to achieve international publications within a relatively short time period.

**References**

Alarcon, G. M. (2011). A meta-analysis of burnout with job demands, resources, and attitudes. *Journal of Vocational Behavior, 79*, 549-562.

D

ormann, C. & Haun, S. (2011). *Longitudinal effects of stress at work: A meta-analysis.* 26th Annual Conference Program of the APA Division 14 Society for Industrial and Organizational Psychology (SIOP), April 14-16, 2011, Chicago, IL [Abstracts]; Apr 2011; 40.

Dormann, C. & Griffin, M. (revisions pending). *Optimal time intervals in longitudinal studies.*

Ford, M. T., Matthews, R. A., Wooldridge, J. D., Mishra, V., Kakar, U. M., & Strahan, S. R. (2014). How do occupational stressor-strain effects vary with time? A review and meta-analysis of the relevance of time lags in longitudinal studies. *Work & Stress, 28*(1), 9-30.

Nielsen, M. B., & Einarsen, S. (2012). Outcomes of exposure to workplace bullying: A meta-analytic review. *Work & Stress, 26*(4), 309-332.

Nylund, K. L., Asparouhov, T. & Muthén, B. O (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo Simulation Study. *Structural Equation Modeling, 14*(4), 535-569.

Semmer, N. K., Jakobshagen, N., Meier, L., & Elfering, A. (2007). Occupational stress research: The „stress-as-offense-to-self“ perspective. In J. Houdmont & S. McIntyre (eds.), *Occupational Health* Psychology: European Perspectives on Research, Education and Practice (Vol. 2) (pp. 43-60). Maia, Portugal: ISMAI Publications.

Voelkle, M. C., Oud, J. H. L., Davidov, E., & Schmidt, P. (2012). A SEM approach to continuous time modeling of panel data: Relating authoritarism and anomia. *Psychological Methods, 17*, 176-192.

Wälde, K. (2014).*Stress and Coping: An Economic Approach*. Mimeo Johannes-Gutenberg-University Mainz, www.waelde.com/pub.