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Temporal Dynamics of Wellbeing & C o Ti o TiMA Continuous Time Meta-Analysis Christian Dormann University of Mainz, Germany & University of South Australia, Adelaide cdormann@uni-mainz.de 26. Feb. 2015 University of Sheffield,

  1. Temporal Dynamics of Wellbeing & C o Ti o TiMA Continuous Time Meta-Analysis Christian Dormann University of Mainz, Germany & University of South Australia, Adelaide cdormann@uni-mainz.de 26. Feb. 2015 University of Sheffield, Exploring Big Data to Examine Employee Health and Wellbeing: A Seminar Series

  2. Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis CoTiMa Big Data, Temporal Dynamics & Analyses of Wellbeing (1) Big Data is there: Individuals’ work hours, work contents, environmental conditions, emotional strains, • behavioural responses & when they occur (time) are continuously recorded. The number of empirical studies on work-related wellbeing grows fast • (> 25.000 overall, > 1.500 in 2015, ~150 repeated measures in 2015) (2) Designing & suggesting (personalized) interventions requires understanding the causal relations. Repeatedly measured data across time is very useful. (3) Combining data/studies could yield extremely complex data structures: Endless numbers of variables and time points could combine into very sparsely populated spreadsheets. (4) New methods for causal analysis are required. They are there, but not yet well known. Continuous time structural equation modelling with individually varying time lags 1) • Simpler (but still a bit complex): Continuous time meta-analysis 2) • 1) Voelkle & Oud (2013) 2) Dormann (submitted) 26. Feb. 2015 University of Sheffield, C. Dormann Slide 2 Big Data, Employee Health, and Wellbeing

  3. Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis CoTiMa Overview (1) Problem: How to Meta-Analyse Time-Dependent Effect Sizes of Panel Studies? (2) Solution: Continuous Time Meta-Analysis (CoTiMA) of Structural Equation Models (3) Example: Group Cohesion & Group Performance: CoTiMA (4) Conclusions 26. Feb. 2015 University of Sheffield, C. Dormann Slide 3 Big Data, Employee Health, and Wellbeing

  4. Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis CoTiMa Common Analysis of Panel Data i t 1 i t 2 X t 0 X t 1 X t 2 c t 1 c t 2 e X t 1 e X t 2 r Y 0 X 0 r t 1 r t 2 Y t 0 Y t 1 Y t 2 d t 1 d t 2 e Y t 1 e Y t 2 ⎛ ⎞ i r A = ⎜ ⎟ ⎝ ⎠ c d 26. Feb. 2015 University of Sheffield, C. Dormann Slide 4 Big Data, Employee Health, and Wellbeing

  5. Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis CoTiMA Grey Sample: ‘true’ X –> Y = .30 Black Sample: ‘true’ X –> Y = .15 � � but � � � X –> X & Y –> Y < X –> X & Y –> Y � 26. Feb. 2015 University of Sheffield, C. Dormann Slide 5 Big Data, Employee Health, and Wellbeing

  6. Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis CoTiMA Grey Sample: ‘true’ X –> Y = .30 Black Sample: ‘true’ X –> Y = .15 � � but � � � X –> X & Y –> Y < X –> X & Y –> Y � ‘true’ = ‘true’ = • time-independent or time-independent or • time- time-scaleable scaleable 26. Feb. 2015 University of Sheffield, C. Dormann Slide 6 Big Data, Employee Health, and Wellbeing

  7. Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis CoTiMA Grey Sample: ‘true’ X –> Y = .30 Black Sample: ‘true’ X –> Y = .15 How to figure out � � whether ‘grey’ or but � � � ‘black’ interventions X –> X & Y –> Y < X –> X & Y –> Y � are more effective? ‘true’ = ‘true’ = • time-independent or time-independent or • time- time-scaleable scaleable 26. Feb. 2015 University of Sheffield, C. Dormann Slide 7 Big Data, Employee Health, and Wellbeing

  8. Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis CoTiMa How to Time-scale Cross-lagged (discrete) Effects:? Continuous Time Modelling using Stochastic Differential Equations • Assumption: X and Y mutually affect each other continuously over time • Instead of autoregressive & cross-lagged effects: auto effects & cross effects • autoregressive & cross-lagged effects -> Discrete Empirical Matrix (B) ⎛ ⎞ • auto & cross effects -> Continuous Drift Matrix (A) i r A = ⎜ ⎟ ⎝ ⎠ • Instead of estimating discrete effects (B) c d => simultaneous estimation of continuous (A) & discrete (B) effects => continuous (A) effects can be compared across studies (B not) 26. Feb. 2015 University of Sheffield, C. Dormann Slide 8 Big Data, Employee Health, and Wellbeing

  9. Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis CoTiMa How the Problem is Solved B = e A ⋅Δ t Auto & Cross Effects ( A ) => Autoregressive & Cross-lagged Effects ( B ) mxAlgebra(expm(DRIFT * lag), name = ”B”) ( ) ⋅Δ t − I ⎧ ⎫ ) − 1 e A ⊗ I + I ⊗ A ⎡ ⎤ ( Diffusion Effects ( Q ) => A ⊗ I + I ⊗ A ⎨ ⎬ E = irow ⎥ row Q ⎢ Error (Co-)Variances ( E ) ⎣ ⎦ ⎩ ⎭ mxAlgebra(DRIFT %x% I + I %x% DRIFT, name = "DHatch") mxAlgebra(solve(DHatch) %*% (expm(DHatch * lag) - I %x% I) %*% rvectorize(Q), name = ”E"), 26. Feb. 2015 University of Sheffield, C. Dormann Slide 9 Big Data, Employee Health, and Wellbeing

  10. Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis CoTiMa Sum Up: What we then get ⎡ ⎤ ⎛ ⎞ − .200 .100 ⎟ × 1 ⎢ ⎥ . ⎜ − .300 ⎛ ⎞ ⎝ ⎠ .150 ⎣ ⎦ .825 .078 ⎟ = e ⎜ ⎝ ⎠ .118 .747 ⎡ ⎤ ⎛ ⎞ − .200 1 .100 ⎟ × ⎢ ⎥ . ⎜ − .300 ⎛ ⎞ ⎝ ⎠ .150 52.18 ⎣ ⎦ .996 .002 ⎟ = e ⎜ ⎝ ⎠ .003 .994 26. Feb. 2015 University of Sheffield, C. Dormann Slide 10 Big Data, Employee Health, and Wellbeing

  11. Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis CoTiMa CoTiMA: Multi Group Analysis of Continous Time Models • The basic CoTiMA principle: When a set of primary studies When a set of primary studies reflects the same underlying causal mechanism, reflects the same underlying causal mechanism, the discrete par the discrete parameter estimates may v ameter estimates may vary across studies ary across studies, whereas the continuous drift par whereas the continuous drift parameters should be inv ameters should be invariant. ariant. • Invariance of drift parameters can be tested using multip group (multi sample) CT SEM • Even when drift parameters vary across studies, “forcing” them to be invariant yields the best single estimate of a population effect • Meta regression and other techniques can be applied to analyse possible predictors of drift parameters (moderators) • Further advantages: � Multiple operationalizations in primary studies may be used as indicators of a latent factor � Different numbers of waves are easy to handle (only one drift matrix per primary study) � Primary studies with missing variables could be included by means of phantom variables 26. Feb. 2015 University of Sheffield, C. Dormann Slide 11 Big Data, Employee Health, and Wellbeing

  12. Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis CoTiMa The Relation Between Team Cohesiveness & Team Performance • Team cohesion = degree of member integration or “bonding” in which members share a strong commitment to one another and the purpose of the team (Zaccaro et al., 2001). • Team cohesion = emergent state. Properties of the team that are typically dynamic in nature and vary as a function of team context, inputs, processes, and outcomes (Marks, Mathieu, & Zaccaro, 2001) • Cohesion can be both a consequence of previous performance levels as well as influence subsequent team performance. cohesive teams = more willing to work together cooperatively � cohesive teams = share a joint commitment to task accomplishment � > cooperation & commitment => task strategies, motivation, attention direction toward accomplishing goals (e.g., Beal et al., 2003; Casey-Campbell & Martens, 2009; Gully et al., 1995) performance: members feel greater affection for one another & joint pride (Schlenker, 1975) � performance: poor performance disappoints, demoralizes, & failures are attributed to other team � members (Jackson, 2011; Schlenker, 1975; Snyder et al.,1986). 26. Feb. 2015 University of Sheffield, C. Dormann Slide 12 Big Data, Employee Health, and Wellbeing

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