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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,

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SLIDE 1

CoTi TiMA

Christian Dormann University of Mainz, Germany & University of South Australia, Adelaide cdormann@uni-mainz.de

  • Temporal Dynamics of Wellbeing

&

  • 26. Feb. 2015 University of Sheffield,

Exploring Big Data to Examine Employee Health and Wellbeing: A Seminar Series

Continuous Time Meta-Analysis

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SLIDE 2

CoTiMa

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

  • C. Dormann

Slide 2

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 lags1)
  • Simpler (but still a bit complex): Continuous time meta-analysis2)
1) Voelkle & Oud (2013) 2) Dormann (submitted)

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

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SLIDE 3

CoTiMa

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

  • C. Dormann

Slide 3

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 Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

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SLIDE 4

CoTiMa

  • C. Dormann

Slide 4

Common Analysis of Panel Data

it1

r

Y0X0

Xt1 Xt0 Yt1 Yt0

dt1 ct1 rt1 eXt1 eYt1 it2

Xt2 Yt2

dt2 ct2 rt2 eXt2 eYt2

A = i r c d ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-5
SLIDE 5

CoTiMA

  • C. Dormann

Slide 5

  • 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,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-6
SLIDE 6

CoTiMA

  • C. Dormann

Slide 6

  • 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,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

‘true’ = ‘true’ =

  • time-independent or

time-independent or

  • time-

time-scaleable scaleable

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SLIDE 7

CoTiMA

  • C. Dormann

Slide 7

  • 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,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

How to figure out whether ‘grey’ or ‘black’ interventions are more effective?

‘true’ = ‘true’ =

  • time-independent or

time-independent or

  • time-

time-scaleable scaleable

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SLIDE 8

CoTiMa

  • C. Dormann

Slide 8

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)
  • Instead of estimating discrete effects (B)

=> simultaneous estimation of continuous (A) & discrete (B) effects => continuous (A) effects can be compared across studies (B not)

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

A = i r c d ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

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SLIDE 9

CoTiMa

  • C. Dormann

Slide 9

How the Problem is Solved

E = irow A ⊗ I + I⊗ A

( )−1 e A ⊗I + I⊗ A ( )⋅Δt − I

⎡ ⎣ ⎢ ⎤ ⎦ ⎥rowQ ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ B = eA⋅Δt

Auto & Cross Effects (A) => Autoregressive & Cross-lagged Effects (B) Diffusion Effects (Q) => Error (Co-)Variances (E)

mxAlgebra(expm(DRIFT * lag), name = ”B”) 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,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-10
SLIDE 10

CoTiMa

  • C. Dormann

Slide 10

Sum Up: What we then get

.825 .078 .118 .747 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = e −.200 .100 .150 −.300 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ×1 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥. .996 .002 .003 .994 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = e −.200 .100 .150 −.300 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ × 1 52.18 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥.

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

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SLIDE 11

CoTiMa

  • C. Dormann

Slide 11

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,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-12
SLIDE 12

CoTiMa

  • C. Dormann

Slide 12

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,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

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SLIDE 13

CoTiMa

  • C. Dormann

Slide 13

The Relation Between Team Cohesiveness & Team Performance

  • Yet unclear (Mathieu et al., 2015):
  • possible reciprocity in the cohesion–performance relationship,
  • similarity/comparability of reciprocal causal relationships
  • Meta-analysis by Mathieu et al. (2015; k = 17 studies, N = 737 teams)

cohesion–performance relations from only panel studies analyzed at the team-level not adjusted for unreliability (sporadically available; different performance measures; often reported at individual level) Correlation-based meta-analysis (Cheung, 2015): sample size-weighted correlations as input to a CLP- SEM analysis Strategy to deal with differences in time lags & multiple time lags: selected correlations from 2 out of several measurements or averaged correlations (e.g., Wave 3+4 & 6+7) Results:

  • all cohesion–performance correlations >0 (p < .05) but high variation across studies
  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-14
SLIDE 14

CoTiMa

  • C. Dormann

Slide 14

The Relation Between Team Cohesiveness & Team Performance

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-15
SLIDE 15

CoTiMa

  • C. Dormann

Slide 15

The Relation Between Team Cohesiveness & Team Performance

  • Meta-analysis by Mathieu et al. (2015)

Problems (not fixed in CoTiMA):

  • temporal alignment of cohesion team performance not necessarily consistent (e.g. performance =

aggregate of multiple scores obtained after cohesion was measured).

  • first measurement occasion occurred early in the lifecycles of some teams yet around the midpoint
  • f many others

Problems (fixed in CoTiMA):

  • Studies excluded which were not strict longitudinal (e.g., several morning/afternoon measures

aggregated; different measures at different waves): Fullagar et al. (2008); Lee et al. (2002):

  • Further studies excluded:

Casey-Campbell (2005): Data overlap with Martens et. al. (2007) Marsh (1996): did not converge ‘Strange’ longitudinal patterns Cobb (1999): team ‘cohesion’ was gone after 20min (rtt = .02) Rittman et al. (2003): Design like Cobb (1999); (performance rtt = .05) Mohammad et al: (performance rtt = .01)

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-16
SLIDE 16

CoTiMa

The Relation Between Team Cohesiveness & Team Performance

  • Results (continuous time estimates)

Study Auto Effect Cohesion SE Cohesion => Perform. SE Perf. => Cohesion SE Auto Effect Perform. SE Heterogeneity Model Primary Studies Bakeman & Helmreich (1975)

  • 0.141

0.095

  • 0.002

0.039 0.136 0.077

  • 0.016

0.031 Carron & Ball (1977)

  • 0.042

0.013

  • 0.005

0.024 0.052 0.014

  • 0.014

0.025 Landers et al. (1982)

  • 0.020

0.020 0.011 0.025 0.019 0.020

  • 0.016

0.025 Williams & Hacker (1982)

  • 0.167

0.135 0.032 0.132 0.165 0.144

  • 0.073

0.140 Greene (1989)

  • 0.020

0.007 0.005 0.005 0.012 0.006

  • 0.012

0.005 Chang & Bordia (2001)

  • 0.106

0.148 0.320 0.310 0.015 0.181

  • 0.532

0.389 Martens et al. (2007)

  • 0.204

0.028 0.081 0.027 0.075 0.028

  • 0.194

0.027 DeOrtentiis et al. (2013)

  • 0.130

0.048

  • 0.015

0.040 0.004 0.038

  • 0.089

0.032 Mathieu et al. (2015) Sample I

  • 0.149

0.037 0.028 0.031 0.054 0.035

  • 0.102

0.029 Mathieu et al. (2015) Sample II

  • 0.177

0.040 0.016 0.028 0.056 0.036

  • 0.085

0.025 LL (df) 642.346 (117) Study Auto Effect Cohesion SE Cohesion => Perform. SE Perf. => Cohesion SE Auto Effect Perform. SE Heterogeneity Model Primary Studies Bakeman & Helmreich (1975)

  • 0.141

0.095

  • 0.002

0.039 0.136 0.077

  • 0.016

0.031 Carron & Ball (1977)

  • 0.042

0.013

  • 0.005

0.024 0.052 0.014

  • 0.014

0.025 Landers et al. (1982)

  • 0.020

0.020 0.011 0.025 0.019 0.020

  • 0.016

0.025 Williams & Hacker (1982)

  • 0.167

0.135 0.032 0.132 0.165 0.144

  • 0.073

0.140 Greene (1989)

  • 0.020

0.007 0.005 0.005 0.012 0.006

  • 0.012

0.005 Chang & Bordia (2001)

  • 0.106

0.148 0.320 0.310 0.015 0.181

  • 0.532

0.389 Martens et al. (2007)

  • 0.204

0.028 0.081 0.027 0.075 0.028

  • 0.194

0.027 DeOrtentiis et al. (2013)

  • 0.130

0.048

  • 0.015

0.040 0.004 0.038

  • 0.089

0.032 Mathieu et al. (2015) Sample I

  • 0.149

0.037 0.028 0.031 0.054 0.035

  • 0.102

0.029 Mathieu et al. (2015) Sample II

  • 0.177

0.040 0.016 0.028 0.056 0.036

  • 0.085

0.025 LL (df) 642.346 (117)

  • C. Dormann

Slide 16

Study Auto Effect Cohesion SE Cohesion => Perform. SE Perf. => Cohesion SE Auto Effect Perform. SE Heterogeneity Model Primary Studies Bakeman & Helmreich (1975)

  • 0.141

0.095

  • 0.002

0.039 0.136 0.077

  • 0.016

0.031 Carron & Ball (1977)

  • 0.042

0.013

  • 0.005

0.024 0.052 0.014

  • 0.014

0.025 Landers et al. (1982)

  • 0.020

0.020 0.011 0.025 0.019 0.020

  • 0.016

0.025 Williams & Hacker (1982)

  • 0.167

0.135 0.032 0.132 0.165 0.144

  • 0.073

0.140 Greene (1989)

  • 0.020

0.007 0.005 0.005 0.012 0.006

  • 0.012

0.005 Chang & Bordia (2001)

  • 0.106

0.148 0.320 0.310 0.015 0.181

  • 0.532

0.389 Martens et al. (2007)

  • 0.204

0.028 0.081 0.027 0.075 0.028

  • 0.194

0.027 DeOrtentiis et al. (2013)

  • 0.130

0.048

  • 0.015

0.040 0.004 0.038

  • 0.089

0.032 Mathieu et al. (2015) Sample I

  • 0.149

0.037 0.028 0.031 0.054 0.035

  • 0.102

0.029 Mathieu et al. (2015) Sample II

  • 0.177

0.040 0.016 0.028 0.056 0.036

  • 0.085

0.025 LL (df) 642.346 (117) Study Auto Effect Cohesion SE Cohesion => Perform. SE Perf. => Cohesion SE Auto Effect Perform. SE Heterogeneity Model Primary Studies Bakeman & Helmreich (1975)

  • 0.141

0.095

  • 0.002

0.039 0.136 0.077

  • 0.016

0.031 Carron & Ball (1977)

  • 0.042

0.013

  • 0.005

0.024 0.052 0.014

  • 0.014

0.025 Landers et al. (1982)

  • 0.020

0.020 0.011 0.025 0.019 0.020

  • 0.016

0.025 Williams & Hacker (1982)

  • 0.167

0.135 0.032 0.132 0.165 0.144

  • 0.073

0.140 Greene (1989)

  • 0.020

0.007 0.005 0.005 0.012 0.006

  • 0.012

0.005 Chang & Bordia (2001)

  • 0.106

0.148 0.320 0.310 0.015 0.181

  • 0.532

0.389 Martens et al. (2007)

  • 0.204

0.028 0.081 0.027 0.075 0.028

  • 0.194

0.027 DeOrtentiis et al. (2013)

  • 0.130

0.048

  • 0.015

0.040 0.004 0.038

  • 0.089

0.032 Mathieu et al. (2015) Sample I

  • 0.149

0.037 0.028 0.031 0.054 0.035

  • 0.102

0.029 Mathieu et al. (2015) Sample II

  • 0.177

0.040 0.016 0.028 0.056 0.036

  • 0.085

0.025 LL (df) 642.346 (117)

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-17
SLIDE 17

CoTiMa

The Relation Between Team Cohesiveness & Team Performance

  • Results
  • C. Dormann

Slide 17

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-18
SLIDE 18

CoTiMa

The Relation Between Team Cohesiveness & Team Performance

  • Cohesion => P

Cohesion => Performance: erformance: Discrete lagged effects (based on continuous drift)

  • C. Dormann

Slide 18

weeks

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-19
SLIDE 19

CoTiMa

The Relation Between Team Cohesiveness & Team Performance

  • Performance => Cohesion:

erformance => Cohesion: Discrete lagged effects (based on continuous drift)

  • C. Dormann

Slide 19

weeks

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-20
SLIDE 20

CoTiMa

Conclusions

  • Extant approaches to meta-analysis of panel studies: Ignored time or used 2 (most) or 3 (rarely) categories
  • Advantages of CoTiMA

Time is modelled (implicitly; not not explicitly as a ‘cause’) Multiple waves are easy to handle (a single drift matrix is estimated, e.g., Martens et al., 2007), Multiple operationalizations of constructs can used as indicators of a latent factor

  • Applications to primary data (individuals)

Individually varying time intervals could be modelled time is used as information – there is no such thing as ‘missing data’ (no sparsely populated spreadsheet) Package for R: ctsem (cf. https://cran.r-project.org/web/packages/ctsem/ctsem.pdf) Reference: Driver, C. C., Oud, J. H. L., & Voelkle, M. C. (in press). Continuous Time Structural Equation Modeling with R Package ctsem. Journal of Statistical Software.

  • C. Dormann

Slide 20

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-21
SLIDE 21

CoTiMa

Conclusions

We still do very little about possible mutual influence

  • f group cohesion and performance in the general

working population despite 40 years of longitudinal research.

  • C. Dormann

Slide 21

A study that I would recommend:

  • Focus on general working population
  • Interdependent teams & mutual task
  • Interval of 8 weeks (some in between measures)
  • Focus on task instead of social cohesion
  • Performance measure of the mutual task
  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-22
SLIDE 22

CoTiMa

  • C. Dormann

Slide 22

A 2-study CoTiMA in a Nutshell (1/1)

require(OpenMx) empcov1 <- matrix(c(1.0000, 0.4234, 0.5599, 0.5679, 0.4234, 1.0000, 0.4234, 0.5271, 0.5599, 0.4234, 1.0000, 0.5274, 0.5679, 0.5271, 0.5274, 1.0000), 4, 4, dimnames=list(c('X0', 'Y0', 'X1', 'Y1'), c('X0', 'Y0', 'X1', 'Y1'))) Avalues1ct <- matrix(data = 0, 8, 8) Avalues1ct[3:4,1:2] <-.20 diag(Avalues1ct[5:8,1:4]) <- rep(1, 4) Alabels1ct <- matrix(data = as.logical(NA), nrow=8, ncol=8) Alabels1ct[3:4,1:2] <- c("B1L1[1,1]", "B1L1[2,1]", "B1L1[1,2]", "B1L1[2,2]") Afree1ct <- matrix(data = as.logical("F"), nrow=8, ncol=8) Svalues1ct <- matrix(data = 0, nrow=8, ncol=8) Svalues1ct[1:2,1:2] <- c(1.0, .68, .68, 1.0) Svalues1ct[3:4,3:4] <- c(0.3, .00, .00, 0.3) Slabels1ct <- matrix(data = as.logical(NA), nrow=8, ncol=8) Slabels1ct[1:2,1:2] <- c("phi111", "phi112", "phi112", "phi122") Slabels1ct[3:4,3:4] <- c("E1L1[1,1]", "E1L1[2,1]", "E1L1[3,1]", "E1L1[4,1]") Sfree1ct <- matrix(data = as.logical("F"), nrow=8, ncol=8) Sfree1ct[1:2,1:2] <- as.logical("T") Fvalues1a <- matrix(data = 0, nrow=4, ncol=4) Fvalues1b <- diag(4) Fvalues1ct <- cbind(Fvalues1a, Fvalues1b) FnamesLatObs1ct <- c("X0_", "Y0_", "X1_", "Y1_", "X0", "Y0", "X1", "Y1") FnamesObs1ct <- c("X0", "Y0", "X1", "Y1") DRIFTvalues1 <- matrix( c(-.56, .38, .67, -.74), 2, 2, byrow=TRUE) DRIFTfree1 <- matrix(data = as.logical("T"), nrow=2, ncol=2) DRIFTlabels1 <- matrix( c("A111", "A112", "A121", "A122"), 2, 2,byrow=TRUE) Qvalues1 <- matrix( c(.70, -.29, -.29, .74), 2, 2, byrow=TRUE) Qfree1 <- matrix(data = as.logical("T"), nrow=2, ncol=2) Qlabels1 <- matrix( c("Q111", "Q112", "Q112", "Q122"), 2, 2 ,byrow=TRUE) IdentMatrix <- mxMatrix(type="Iden", nrow=2, ncol=2, free=FALSE, name="II") DRIFTHatch <- mxAlgebra(DRIFT %x% II + II %x% DRIFT, name = "DRIFTHATCH") primaryStudyMxModel1ct <- mxModel(name="primaryStudy1ct", mxData(empcov1, type="cov", numObs=1000), mxMatrix(values=Avalues1ct, free=Afree1ct, labels=Alabels1ct, name="A"), mxMatrix(values=Svalues1ct, free=Sfree1ct, labels=Slabels1ct, name="S"), mxMatrix(values=Fvalues1ct, free=FALSE, dimnames=list(FnamesObs1ct, FnamesLatObs1ct), name="F"), mxMatrix(type="Full", labels=DRIFTlabels1, values=DRIFTvalues1, free=DRIFTfree1, name="DRIFT"), mxMatrix(type="Full", labels= Qlabels1, values= Qvalues1, free= Qfree1, name="Q"), mxAlgebra(omxExponential(DRIFT %x% 2), name = "B1L1"), mxAlgebra(solve(DRIFTHATCH) %*% (omxExponential(DRIFTHATCH %x% 2)-II %x% II) %*% rvectorize(Q), name = "E1L1"), IdentMatrix, DRIFTHatch, mxExpectationRAM(A="A",S="S",F="F"), mxFitFunctionML() ) primaryStudyMxModel1ctFit <- mxRun(primaryStudyMxModel1ct) summary(primaryStudyMxModel1ctFit) primaryStudyMxModel1ctFit$matrices

Setting up Study 1 Testing Study 1

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis

slide-23
SLIDE 23

CoTiMa

  • C. Dormann

Slide 23

A 2-study CoTiMA in a Nutshell (2/2)

empcov2 <- matrix(c(1.0000, 0.5158, 0.7299, 0.6360, 0.5158, 1.0000, 0.5275, 0.7142, 0.7299, 0.5275, 1.0000, 0.5498, 0.6360, 0.7142, 0.5498, 1.0000), 4, 4, dimnames=list(c('X0', 'Y0', 'X1', 'Y1'), c('X0', 'Y0', 'X1', 'Y1'))) Alabels2ct <- sub("B1", "B2", Alabels1ct) Slabels2ct <- sub("E1", "E2", Slabels1ct) Slabels2ct <- sub("phi1", "phi2", Slabels2ct) DRIFTlabels2 <- sub("A1", "A2", DRIFTlabels1) Qlabels2 <- sub("Q1", "Q2", Qlabels1) primaryStudyMxModel2ct <- mxModel(name="primaryStudy2ct", mxData(observed=empcov2, type="cov", numObs=1000), mxMatrix(values=Avalues1ct, free=Afree1ct, labels=Alabels2ct, name="A"), mxMatrix(values=Svalues1ct, free=Sfree1ct, labels=Slabels2ct, name="S"), mxMatrix(values=Fvalues1ct, free=FALSE, dimnames=list(FnamesObs1ct, FnamesLatObs1ct), name="F"), mxMatrix(labels=DRIFTlabels2, values= DRIFTvalues1, free= DRIFTfree1, name="DRIFT"), mxMatrix(labels=Qlabels2, values= Qvalues1, free= Qfree1, name="Q"), mxAlgebra(omxExponential(1 %x% DRIFT), name = "B2L1"), mxAlgebra(solve(DRIFTHATCH) %*% (omxExponential(1 %x% DRIFTHATCH)-II %x% II) %*% rvectorize(Q), name = "E2L1"), IdentMatrix, DRIFTHatch, mxExpectationRAM(A="A",S="S",F="F"), mxFitFunctionML()) primaryStudyMxModel2ctFit <- mxRun(primaryStudyMxModel2ct) summary(primaryStudyMxModel2ctFit) funMGhet <- mxAlgebra(expression=primaryStudy2ct.fitfunction + primaryStudy1ct.fitfunction, name="minus2llhet" )
  • bjHet <- mxFitFunctionAlgebra( "minus2llhet" )
CoTiMAhet <- mxModel(model="Heterogeneity CoTiMA", primaryStudyMxModel2ct, primaryStudyMxModel1ct, funMGhet, objHet ) CoTiMAhetFit <- mxRun(CoTiMAhet) summary(CoTiMAhetFit) DRIFTlabels2_12 <- DRIFTlabels2 DRIFTlabels2_12[1,2] <- "A112” primaryStudyMxModel2ctHD12 <- mxRename(mxModel(primaryStudyMxModel2ct), "primaryStudy2ctHD12") primaryStudyMxModel2ctHD12 <- mxModel(primaryStudyMxModel2ctHD12, mxMatrix(labels=DRIFTlabels2_12, values= DRIFTvalues1, free= DRIFTfree1, name="DRIFT")) funMGhomDRIFT <- mxAlgebra( expression=primaryStudy2ctHD12.fitfunction + primaryStudy1ct.fitfunction, name="minus2llhomDRIFT" )
  • bjHomDRIFT <- mxFitFunctionAlgebra( "minus2llhomDRIFT" )
CoTiMAhomDRIFTHD12 <- mxModel(model="Hom-DRIFT CoTiMA", primaryStudyMxModel2ctHD12, primaryStudyMxModel1ct, funMGhomDRIFT, objHomDRIFT) CoTiMAhomDRIFTHD12Fit <- mxRun(CoTiMAhomDRIFTHD12) summary(CoTiMAhomDRIFTHD12Fit) abs(CoTiMAhetFit$output$fit - CoTiMAhomDRIFTHD12Fit$output$fit) 1-pchisq(abs(CoTiMAhetFit$output$fit - CoTiMAhomDRIFTHD12Fit$output$fit), 1)

Setting up Study 2 Heterogeneity Model “Homogeneizing” Study 2 Homogeneity Model Comparing Model Fit

  • 26. Feb. 2015 University of Sheffield,

Big Data, Employee Health, and Wellbeing

Temporal Dynamics of Wellbeing & Continuous Time Meta-Analysis