Time-series Analysis - Network Analysis 2017• Onepersonmeasuredmultipletimes: N= 1time-series....

Introduction N = 1: Graphical VAR N > 1: Multi-level VAR SVAR / GIMME Cross-sectional Conclusion

Time-series AnalysisNetwork Analysis 2017

Sacha Epskamp

11-12-2017


Psychological Data

Subject Time Item 1 Item 2 Item 3Subject 1 Time 1 2 2 4Subject 2 Time 1 4 1 2Subject 3 Time 1 1 3 0

• Multiple people measured once: cross-sectional analysis


Psychological Data

Subject Time Item 1 Item 2 Item 3Subject 1 Time 1 2 2 4Subject 1 Time 2 2 4 4Subject 1 Time 3 1 4 3

• Multiple people measured once: cross-sectional analysis• One person measured multiple times: N = 1 time-series


Psychological Data

Subject Time Item 1 Item 2 Item 3Subject 1 Time 1 2 2 4Subject 1 Time 2 2 4 4Subject 1 Time 3 1 4 3Subject 2 Time 1 4 1 2Subject 2 Time 2 3 1 2Subject 2 Time 3 3 2 1Subject 3 Time 1 1 3 0Subject 3 Time 2 4 0 1Subject 3 Time 3 0 3 3

• Multiple people measured once: cross-sectional analysis• One person measured multiple times: N = 1 time-series• Multiple people measured multiple times: N > 1 time-series


Cross-sectional Analysis

A1

A2

A3

A4

A5

C1

C2

C3

C4

C5

E1E2

E3

E4

E5

N1

N2

N3

N4

N5

O1

O2

O3

O4

O5

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

AgreeablenessA1: Am indifferent to the feelings of others.A2: Inquire about others' well−being.A3: Know how to comfort others.A4: Love children.A5: Make people feel at ease.

ConscientiousnessC1: Am exacting in my work.C2: Continue until everything is perfect.C3: Do things according to a plan.C4: Do things in a half−way manner.C5: Waste my time.

ExtraversionE1: Don't talk a lot.E2: Find it difficult to approach others.E3: Know how to captivate people.E4: Make friends easily.E5: Take charge.

NeuroticismN1: Get angry easily.N2: Get irritated easily.N3: Have frequent mood swings.N4: Often feel blue.N5: Panic easily.

OpennessO1: Am full of ideas.O2: Avoid difficult reading material.O3: Carry the conversation to a higher level.O4: Spend time reflecting on things.O5: Will not probe deeply into a subject.

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

AgreeablenessA1: Am indifferent to the feelings of others.A2: Inquire about others' well−being.A3: Know how to comfort others.A4: Love children.A5: Make people feel at ease.

ConscientiousnessC1: Am exacting in my work.C2: Continue until everything is perfect.C3: Do things according to a plan.C4: Do things in a half−way manner.C5: Waste my time.

ExtraversionE1: Don't talk a lot.E2: Find it difficult to approach others.E3: Know how to captivate people.E4: Make friends easily.E5: Take charge.

NeuroticismN1: Get angry easily.N2: Get irritated easily.N3: Have frequent mood swings.N4: Often feel blue.N5: Panic easily.

OpennessO1: Am full of ideas.O2: Avoid difficult reading material.O3: Carry the conversation to a higher level.O4: Spend time reflecting on things.O5: Will not probe deeply into a subject.

• Concentration network: unique variance between two variables


N = 1 Time-series Analysis

relaxed

sad

nervous

concentration

tired

rumination

bodilydiscomfort

(b) Temporal network − Patient 1

relaxed

sad

nervous

concentration

tired

rumination

bodilydiscomfort

(a) Contemporaneous network − Patient 1

• Contemporaneous network: conditional concentration given t − 1• Temporal network: regression coefficients between t − 1 and t


N > 1 Time-series Analysis

Outgoing

Energetic

Adventurous

Happy

Exercise

Temporal

Outgoing

Energetic

Adventurous

Happy

Exercise

Contemporaneous

Outgoing

Energetic

Adventurous

Happy

Exercise

Between−subjects

• Between-subjects network: concentration network betweenstationary means

• Two-step multilevel VAR


The Psychosystems Ecosystem

Cross−sectional

Longitudinal

Binary

ContinuousOrdinal

Yes

No

Yes No

Yes

No

Yes

No

Yes

No

Mixed

Yes

No

Type ofdata

Scale ofmeasurement

Multiplepersons?

Regularize?

Gaussian?

qgraphcor_auto() cor()

hugehuge.npn()

Regularize?

qgraphgraph = 'pcor'qgraph

graph = 'glasso'

IsingSamplerEstimateIsing()

IsingFit

Binarize

mlVAR

GraphicalVAR

bootnet

lvnet

mgm

NetworkCom−parnisonTest

Stationary?


N = 1: Graphical VAR


Time-series Data

• One person measured several times in a short period• Cases can not reasonably be assumed to be independent

• Knowing someone’s level of fatigue at a time point helps predicthis or her level of fatigue at the next time point.

• Likelihood not easy to compute without three assumptions:• The time-series factorize according to a graph• The model does not change over time• The first measurement is exogenous


Y1(p) Y2

(p) Y3(p) Y4

(p) Y5(p)

lag−0

Y1(p) Y2

(p) Y3(p) Y4

(p) Y5(p)

lag−1

Y1(p) Y2

(p) Y3(p) Y4

(p) Y5(p)

lag−2

• We will use the lag-1 factorization


Graphical Vector Auto-regression (VAR)

YYY t | yyy t−1 ∼ N (BBByyy t−1,ΘΘΘ)

• Variables assumed centered• BBB encodes the temporal network

• Temporal prediction• ΘΘΘ−1 encodes the contemporaneous network

• GGM• Graphical VAR model

• Wild, B., Eichler, M., Friederich, H. C., Hartmann, M., Zipfel, S., &Herzog, W. (2010). A graphical vector autoregressive modellingapproach to the analysis of electronic diary data. BMC medicalresearch methodology, 10(1), 28.


Temporal effects

• The temporal network shows that one variable predicts anothervariable in the next measurement occasion

• Granger causality• Only temporal network from (graphical) VAR needed in

predicting new responses


Contemporaneous effects

• The contemporaneous network shows that two variables predictone-another after taking temporal information into account

• Contains effects faster than the time-window of measurement• Somatic arousal → anticipation of panic attack → anxiety

• The temporal network can be seen as a correction fordependent measurements in estimating the GGM


Exercising

Energetic

Temporal network

Exercising

Energetic

Contemporaneous network


• Estimation straightforward using multiple regression• For model selection, we use the graphical VAR model

• Wild et al. (2010). A graphical vector autoregressive modellingapproach to the analysis of electronic diary data. BMC MedicalResearch Methodology 10 (1): 28.

• Estimation via LASSO regularization, using EBIC to selectoptimal tuning parameter

• Abegaz & Wit (2013). Sparse Time Series Chain GraphicalModels for Reconstructing Genetic Networks. Biostatistics:kxt005.

• Rothman, Elizaveta, & Zhu (2010). Sparse MultivariateRegression with Covariance Estimation. Journal ofComputational and Graphical Statistics 19 (4): 947–62.

• We implemented these methods in the R packagegraphicalVAR

• Also implemented in sparseTSCGM


Assumptions• Stationarity

• Plausible when data is obtained in short time-span, lessplausible if data is obtained in longer time-span

• Stationary means• Can be assessed by regressing each time-series on time itself as

predictor• Detrending is possible: for example one can remove a linear

trend (see practical)• Stationary network model(s)

• Short intro to time-varying networks this afternoon• Equidistant measurements

• With multiple measurments per day, by default violated due tonights

• Remove nights, or model nights as missing observations• Continuous time modeling poses promising ways to deal with

non-equidistant measurements


Personalized Networks in Clinical Practice

relaxed

sad

nervous

concentrationtired

rumination bodilydiscomfort

(a) Temporal network − Patient 1

relaxed

sad

nervous

concentrationtired

rumination bodilydiscomfort

(b) Contemporaneous network − Patient 1

• Contemporaneous network: conditional concentration given t − 1• Temporal network: regression coefficients between t − 1 and t


N > 1: Multi-level VAR


Multi-level VAR

• Each subject is assumed to have their own temporal andcontemporaneous VAR model

• VAR parameters come from distribution• Fixed effect• Random effect

• Bringmann, L. F., Vissers, N., Wichers, M., Geschwind, N.,Kuppens, P., Peeters, F., ... & Tuerlinckx, F. (2013). Anetwork approach to psychopathology: new insights intoclinical longitudinal data. PloS one, 8(4), e60188.


Multi-level VAR

Adding superscript p for subject. Level 1 model:

YYY (p)t | yyy(p)t = N

(µµµ(p) +BBB(p)

(yyy (p)t−1 −µµµ

(p)),ΘΘΘ(p)

)Level 2 model: [

µµµ(p)

Vec(BBB(p)

)] ∼ N (fff ,ΩΩΩ) .fff encodes fixed effects and ΩΩΩ the distribution of random effects.


µ1

β11

β12

µ2

β21

β22

Y1 Y2

1 1


Each Parameter has a Distribution

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

0

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

dnor

m(x

, mea

ns[i]

, SD

s[i])


Individual Networks

0.15

0.15

−0.16

0.2

0.28

−0.58

Y1 Y2

1 1

Bob 0.06

0.07

−0.1

0.22

0.29

−0.54

Y1 Y2

1 1

Alice


Random Effects

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

BobAlice

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

dnor

m(x

, mea

ns[i]

, SD

s[i])


Fixed Effects

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

Mean

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

dnor

m(x

, mea

ns[i]

, SD

s[i])


Fixed Effects

0.07

−0.14

0.17

0.18 0.34

−0.6

Y1 Y2

1 1


Individual Differences

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

95% interval

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

x

dnor

m(x

, mea

ns[i]

, SD

s[i])

dnor

m(x

, mea

ns[i]

, SD

s[i])


Parameter correlation Matrix

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1


Parameter Correlation Matrix

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

1

0.01

−0.54

0.21

−0.18

0.46

0.01

1

−0.24

−0.66

0.77

0.06

−0.54

−0.24

1

−0.12

0.34

−0.75

0.21

−0.66

−0.12

1

−0.76

0.1

−0.18

0.77

0.34

−0.76

1

−0.18

0.46

0.06

−0.75

0.1

−0.18

1


Stability

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

1

0.01

−0.54

0.21

−0.18

0.46

0.01

1

−0.24

−0.66

0.77

0.06

−0.54

−0.24

1

−0.12

0.34

−0.75

0.21

−0.66

−0.12

1

−0.76

0.1

−0.18

0.77

0.34

−0.76

1

−0.18

0.46

0.06

−0.75

0.1

−0.18

1


Connectivity

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

1

0.01

−0.54

0.21

−0.18

0.46

0.01

1

−0.24

−0.66

0.77

0.06

−0.54

−0.24

1

−0.12

0.34

−0.75

0.21

−0.66

−0.12

1

−0.76

0.1

−0.18

0.77

0.34

−0.76

1

−0.18

0.46

0.06

−0.75

0.1

−0.18

1


Between-subject Effects

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

1

0.01

−0.54

0.21

−0.18

0.46

0.01

1

−0.24

−0.66

0.77

0.06

−0.54

−0.24

1

−0.12

0.34

−0.75

0.21

−0.66

−0.12

1

−0.76

0.1

−0.18

0.77

0.34

−0.76

1

−0.18

0.46

0.06

−0.75

0.1

−0.18

1


Between-subjects Network

The random effects variance-covariance matrix can be divided infour blocks:

[RRRµµµRRRBBB

]∼ N

(000,[

ΩΩΩµµµ ΩΩΩµµµBBBΩΩΩBBBµµµ ΩΩΩBBB

]).

• Block ΩΩΩµµµ encodes the between-subject relationships betweenmeans

• These can be used to estimate a GGM• Between-subjects network of partial correlations


Typingspeed

Spellingerrors

Within−subjects

Typingspeed

Spellingerrors

Between−subjects

Example based on Hamaker, E. L. (2012). Why Researchers ShouldThink ‘Within-Person’: A Paradigmatic Rationale. Handbook ofResearch Methods for Studying Daily Life. The Guilford Press NewYork, NY, 43–61.


Physicalactivity

Heartrate

Within−subjects

Physicalactivity

Heartrate

Between−subjects

Example kindly provided by Ellen Hamaker and based on Hoffman,L. (2015). Longitudinal analysis: Modeling within-person fluctuationand change. New York, NY, USA: Routledge.


Temporal Estimation• Multi-variate multi-level MLE regression estimation is

complicated and not yet well implemented in open sourcesoftware

• lme4 packages implements univariate multi-level regression• Douglas Bates, Martin Maechler, Ben Bolker, Steve Walker

(2015). Fitting Linear Mixed-Effects Models Using lme4.Journal of Statistical Software, 67(1), 1-48.doi:10.18637/jss.v067.i01

• lmer function

• A multi-level VAR model can be estimated by sequentiallyestimating univariate models

• Estimate all incoming edges per node• Bringmann et al. (2013). A network approach to

psychopathology: new insights into clinical time-series data.PloS one, 8(4), e60188.

doi:10.18637/jss.v067.i01


µ1

β11

β12

µ2

β21

β22

Y1 Y2

1 1

µ1

β11

β12

µ2

β21

β22

Y1 Y2

1 1


Temporal Estimation

• Correlated estimation:• Needs to integrate out a high-dimensional distribution over

parameters• Only feasible for up to ~6 nodes• Does not estimate all parameter covariances

• Not all parameters together in the same model

• Orthogonal estimation• Alternatively, parameter covariances can be fixed to zero• Fast, and works for high dimensions (e.g., 20 nodes)• But, does not return any parameter correlation


Correlated Estimation

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1


Orthogonal Estimation

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1

Y1 Y2

1 1


Between-subject Estimation

• Between subject effects can be obtained by centering predictorsand adding the person-means as level 2 predictors

• Hamaker, E. L., & Grasman, R. P. (2015). To center or not tocenter? Investigating inertia with a multilevel autoregressivemodel. Frontiers in psychology, 5, 1492.

• This can be seen as node-wise estimation of a GGM• Thus, an estimate for the between-subjects GGM can be

obtained by averaging the level-2 predictive effects standardizedwith the residual variances


Contemporaneous Estimation

• Contemporaneous networks need to be estimated post-hoc byinvestigating the residuals

• Either inverting the sample variance-covariance matrix ofresiduals:

• Fixed• Unique

• Or as a second multi-level model using nodewise estimation ofa GGM:

• Correlated• Orthogonal


• Mplus 8 contains dynamic structural equation models• statmodel.com/download/DSEM.pdf

• Multi-level VAR is a special case• statmodel.com/download/usersguide/Chapter9.pdf,

example 9.32• Contemporaneous and between-subject networks are not

obtained by default, can be computed from the Bayesiansamples (BPARAMETERS option)

• Automated wrapper to come in mlVAR (implemented in develversion)

statmodel.com/download/DSEM.pdfstatmodel.com/download/usersguide/Chapter9.pdf


Empirical Example 1

• Two datasets• Original: 26 subjects, 51 measurements on average, 1323 total

observations• Replication: 65 subjects, 35.5 measurements on average, 2309

total observations

• 16 indicators of neuroticism, extroversion, conscientiousness• Orthogonal estimation of temporal and contemporaneous

effects• Only significant effects shown

• Alpha = 0.05 and using the “or” rule


Fixed effects

Outgoing

Energetic

Adventurous

Happy

Exercise

Maximum: 0.2

Temporal

Outgoing

Energetic

Adventurous

Happy

Exercise

Maximum: 0.5

Contemporaneous

Outgoing

Energetic

Adventurous

Happy

Exercise

Maximum: 0.5

Between−subjects


Individual Differences

Outgoing

Energetic

Adventurous

Happy

Exercise

Maximum: 0.18

Temporal

Outgoing

Energetic

Adventurous

Happy

Exercise

Maximum: 0.01

Contemporaneous


1

2

34

5

6

7

89

1011

12

13

1415

16

17

Maximum: 0.17

Temporal

1

2

34

5

6

7

89

1011

12

13

1415

16

17

Maximum: 0.55

Contemporaneous

1

2

34

5

6

7

89

1011

12

13

1415

16

17

●

●

●

●

NeuroticismConscientiousnessExtraversionExercise

●

●

●

●

NeuroticismConscientiousnessExtraversionExercise

Maximum: 0.55

Between−subjects

1 = “Worried”; 2 = “Organized”; 3 = “Ambitious”; 4 = “Depressed”; 5 =“Outgoing”; 6 = “Self-Conscious”; 7 = “Self-Disciplined”; 8 = “Energetic”; 9 =“Frustrated”; 10 = “Focused”; 11 = “Guilty”; 12 = “Adventurous”; 13 =“Happy”; 14 = “Control”; 15 = “Achieved”; 16 = “Angry”; 17 = “Exercise.”


Empirical Example 2

• Re-analysis of original Bringmann example• Bringmann, L. F., Vissers, N., Wichers, M., Geschwind, N., Kuppens,

P., Peeters, F., Borsboom, D., & Tuerlinckx, F. (2013). A networkapproach to psychopathology: new insights into clinical longitudinaldata. PloS one, 8(4), e60188.

• Geschwind, N., Peeters, F., Drukker, M., van Os, J., & Wichers, M.(2011). Mindfulness training increases momentary positive emotionsand reward experience in adults vulnerable to depression: arandomized controlled trial. Journal of consulting and clinicalpsychology, 79(5), 618-628.

• Re-analysis using three software packages• Two-step multi-level VAR (mlVAR)• LASSO regularization (graphicalVAR)• Bayesian multivariate estimation (Mlus 8, generated by mlVAR)

• arxiv.org/abs/1609.04156

arxiv.org/abs/1609.04156


cheerful

pleasant

worry

fearful

sad

relaxed

Temporal

cheerful

pleasant

worry

fearful

sad

relaxed

Contemporaneous

cheerful

pleasant

worry

fearful

sad

relaxed

Between−subjects

mlVAR estimation


cheerful

pleasant

worry

fearful

sad

relaxed

Temporal

cheerful

pleasant

worry

fearful

sad

relaxed

Contemporaneous

cheerful

pleasant

worry

fearful

sad

relaxed

Between−subjects

graphicalVAR estimation


cheerful

pleasant

worry

fearful

sad

relaxed

Temporal

cheerful

pleasant

worry

fearful

sad

relaxed

Contemporaneous

cheerful

pleasant

worry

fearful

sad

relaxed

Between−subjects

Mplus estimation


Pre-print online at http://arxiv.org/abs/1609.04156

http://arxiv.org/abs/1609.04156


Structural VAR & GIMME


Structural VAR• Another option for modeling N = 1 data including

contemporaneous effects is structural VAR• Models contemporaneous effects as a directed network• Contemporaneous directed model does not need to be assumed

acyiclic: cycles potentially identified• If the temporal network is not empty (autoregressions), lagged

variables act as exogenous predictors identifying cycles• Rigdon, E. E. (1995). A necessary and sufficient identification rule

for structural models estimated in practice. Multivariate BehavioralResearch, 30(3), 359-383.

• Equivalent to graphical VAR• Temporal edges in GVAR may be induced by a chain connecting

a temporal and contemporaneous edge in SVAR• Contemporaneous edges in GVAR may be induced by a

contemporaneous collider• Can be estimated by performing stepwise model search (e.g.,

using SEM)


Structural VAR Graphical VAR

Example

At−1

Bt−1

At

Bt

At−1

Bt−1

At

Bt

Pros Causally interpretable; allowscausal modeling of contempora-neous effects; temporal networkestimation takes contemporane-ous effects into account; cycliceffects are identified with auto-regressions.

Well identified; well defined satu-rated model; allows sparse mod-eling of contemporaneous ef-fects; latent variables result inclusters of undirected edges.

Cons Potentially poorly identified;multiple solutions possible;strong reliance on the assump-tion of no latent variables;strong interpretation of thedirection of effect.

Potentially spurious edges inboth the temporal and contem-poraneous networks; No direc-tion of effect in contemporane-ous network. Limited softwarefor confirmatory estimation.


Group iterative multiple model estimation (GIMME)

• The GIMME algorithm is designed to estimate structural VARmodels for N > 1 data

• Gates, K. M., & Molenaar, P. C. (2012). Group search algorithmrecovers effective connectivity maps for individuals in homogeneousand heterogeneous samples. Neuroimage, 63(1), 310-319.

• Estimates a structural VAR model per subject, checks whichedges are common at group levels and include those edges inall subjects

• Shows which edges are common in all participants and whichedges differ between participants

• Information borrowed from other subjects in terms of structure,not in terms of parameters

• No multi-level modeling!• gimme package in R (http://gimme.web.unc.edu/)

http://gimme.web.unc.edu/


Lane, S. T., & Gates, K. M. (2017). Automated Selection of RobustIndividual-Level Structural Equation Models for Time Series Data. StructuralEquation Modeling: A Multidisciplinary Journal, 1-15.


Cross-sectional data revisited


• Only under extremely unrealistic assumptions are parametersestimated from cross-sectional data the same as parametersyou would estimate from time-series data

• Molenaar, P. C. (2004). A manifesto on psychology as idiographicscience: Bringing the person back into scientific psychology, this timeforever. Measurement, 2(4), 201-218.

• More and more critisism towards cross-sectional analysisbecause of this

• “[T]he utility of cross-sectional psychopathology networksfundamentally relies on the assumption of ergodicity: that thebetween-person structure at one time is the same as thewithin-person structure over time (Molenaar, 2004)” —- Forbes et al.(in press)

• “We think it is time to investigate networks at the proper level ofinvestigation (ie, at the intraindividual level). As long as we keepinvestigating cross-sectional group-level networks, the results willremain compatible with a traditional disease model, will not beinformative of symptom interactions within individuals, and willobscure scientific reasoning” — Bos & Wanders (2016)


“If both [cross-sectional GGM and temporal VAR] result in similar conclusions,this would greatly facilitate future research and clinical applications (...). If not,then cross-sectional symptom networks are unlikely to reflect causal symptomdynamics, as postulated by this network theory.”

a: first observation network (n = 104); person-mean network (n = 104); c: thedynamic network (n = 104 × 50)

• Bos, F. M., Snippe, E., de Vos, S., Hartmann, J. A., Simons, C. J., van derKrieke, L., De Jonge, P. & Wichers, M. (2017). Can We Jump fromCross-Sectional to Dynamic Interpretations of Networks? Implications for theNetwork Perspective in Psychiatry. Psychotherapy and Psychosomatics, 86(3),175-177.


But what is a cross-sectional network really?

• See arxiv.org/abs/1609.04156 (current revision draft inDropbox) for a methodological investigation

• Mathematically, if VAR models generated the data,cross-sectional networks are a complicated function ofwithin-subject effects (temporal and contemporaneous) andbetween-subject effects

• Simulations show that cross-sectional networks mostly retrievewithin-subject or between-subject edges, depending on whichhas more variance

• Hypothesis: the variance can be assumed dominant dependingon the type of questions asked

• Clinical interviews, questions relating to a long period of time,questions relating to within-person constants: between-subjectsvariance likely to be dominant

• Questions such as “Did you experience more or less than youraverage ...” potentially feature dominant within-subjectsvariance



Isvoranu, A. M., Borsboom, D., van Os, J. & Guloksuz, S. (2016). A NetworkApproach to Environmental Impact in Psychotic Disorder: Brief TheoreticalFramework. Schizophrenia Bulletin, 42(4), 870-873.


Repeated measures

• With repeated measures, within-person centering all data,pooling and estimating a GGM on the pooled data leads to anetwork that can be interpreted as within-subjects network

• Assuming no auto-regressions; arxiv.org/abs/1609.04156• Described among other developments in recent tutorial paper

• Costantini, G., Richetin, J., Preti, E., Casini, E., Epskamp, S., &Perugini, M. (2017). Stability and variability of personality networks.A tutorial on recent developments in network psychometrics.Personality and Individual Differences.



Conclusion


Conclusion

• Temporal ordering of data can be taken into account• graphical VAR

• Contemporaneous network (GGM)• Temporal network (VAR)• Between-subjects network (GGM)

• structural VAR estimates contemporaneous effects as a directednetwork

• Multi-level modeling or GIMME can be used when there aremultiple subjects


Limitations and Future Directions

• A lot of problems with VAR models• Multivariate normality• Stationarity• Lag interval• Model complexity (lag-2, day effects, etcetera)

• A lot of potential problems with multi-level estimation• Multivariate estimation• Modeling random contemporaneous effects• Parameter variance-covariances• Model selection

• Possibly move away from multi-level• LASSO variants?


The Limit of Observational Data

• Network structures are only hypothesis generating• Highlighting potential causal pathways

• Observational data can never confirm causality• Mixture of experimental and observational data needed

• We need to completely rethink the modeling framework to doso


The Psychosystems Ecosystem

Cross−sectional

Longitudinal

Binary

ContinuousOrdinal

Yes

No

Yes No

Yes

No

Yes

No

Yes

No

Mixed

Yes

No

Type ofdata

Scale ofmeasurement

Multiplepersons?

Regularize?

Gaussian?

qgraphcor_auto() cor()

hugehuge.npn()

Regularize?

qgraphgraph = 'pcor'qgraph

graph = 'glasso'

IsingSamplerEstimateIsing()

IsingFit

Binarize

mlVAR

GraphicalVAR

bootnet

lvnet

mgm

NetworkCom−parnisonTest

Stationary?


Thank you for your attention!

IntroductionIntroduction

N=1: Graphical VARn=1

N > 1: Multi-level VARMulti-level VAREstimation

SVAR / GIMMESVAR / GIMME

Cross-sectionalCross-sectional

ConclusionConclusion

Time-series Analysis - Network Analysis 2017• Onepersonmeasuredmultipletimes: N= 1time-series....

Documents

Transcript of Time-series Analysis - Network Analysis 2017• Onepersonmeasuredmultipletimes: N= 1time-series....