What's for dynr: A package for linear ... - modeling.uconn.edu...nonlinear DYNamic modeling in R Lu...

MakeDynr

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Why

Dynr Facts

ModelingFramework

Estimation

Example 1:Linear SDE

Example 2:NonlinearDiscrete-time

Example 3:Regime-switchingNonlinearODE

Take-homeMessage

References

What’s for dynr: A package for linear andnonlinear DYNamic modeling in R

Lu Ou1, Michael D. Hunter2, and Sy-Miin Chow1

Pennsylvania State University: Human Development and Family Studies1

University of Oklahoma Health Sciences Center: Pediatrics2

[email protected]

Modern Modeling Methods (M3)Storrs, CT; May 25, 2016

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What’s in a name?

BicameRal Extended Kalman Filter with Iterated Smoothing(BREKFIS)

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Overview

1 Why

2 Dynr Facts

3 Modeling Framework

4 Estimation

5 Example 1: Linear SDE

6 Example 2: Nonlinear Discrete-time

7 Example 3: Regime-switching Nonlinear ODE

8 Take-home Message

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Why dynr?Why make a new package for this?

� OpenMx (Neale et al., in press) (linear only)

� ctsem (Driver, Oud, & Voelkle, 2015) (linear, continuoustime only)

� MATLAB (single subject)

� MKFM6 (Dolan, 2005) (linear only)

� dlm (Petris, 2010) (slow)

� SsfPack (Koopman, Shephard, & Doornik, 1999) (singlesubject)

� MPlus 8 (not available yet, linear only)

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Why dynr?Why make a new package for this?

� Linear and nonlinear models

� Multiple subjects

� Intuitive interface

� Fast

� Great reporting

� Combine dynamics for continuous and categorical latentvariables

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Why dynamics?

� Goal of psychology (Hockenbury & Hockenbury, 2010)� To understand behavior and mental processes

� Behavior unfolds in time.

� Mental processes are fundamentally time-oriented

� Action across time is the study of dynamics.

� Development occurs within people and across time.

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Why differential equations?

� Common language of many sciences

� Hypothesize rules that govern individual systems over time� Rules: actions, reactions, forces, influences� Individual: people are generally heterogeneous

� Discrete-time methods are differential equations in discretetime.

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1 Dynr fits discrete- and continuous-time dynamicmodels to multivariate longitudinal/time-series data.

2 Dynr handles linear and nonlinear dynamic modelswith an easy-to-use interface.

� Dynr allows model specification in matrix and formulaforms.

� Dynr allows automatic differentiation.

3 Dynr deals with dynamic models withregime-switching properties.

� e.g., Markov switching autoregressive (MSAR);Markov switching Kalman Filter (MSKF)

� Caveat: Only linear measurement

4 Dynr computes in C and runs fast.

5 Dynr provides ready-to-present results through LaTexequations and plots.

What can dynr do? Dynr Facts 1-5

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� https://quantdev.ssri.psu.edu/

avada_resources/dynr/

� In the next week or so, on CRAN!

Where can I get dynr?

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https://quantdev.ssri.psu.edu/avada_resources/dynr/


MakeDynr

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� Gather data with dynr.data()

� Prepare recipes with� prep.measurement()� prep.*Dynamics()� prep.initial()� prep.noise()� prep.regimes() (optional)

� Mix recipes and data into a model withdynr.model()

� Cook model with dynr.cook()

� Serve results with� summary()� plot()� dynr.ggplot()� plotFormula()� printex()

dynr preparation

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Modeling Framework

� Dynamic Model (prep.*Dynamics())� Discrete-time

xi (ti,j) = Fθf ,i (xi (ti,j−1)) + ζi (ti,j), ζi (ti,j) ∼ N(0,Σζ)� Continuous-time Ordinary and Stochastic Differential

Equation (ODE & SDE)dxi (t) = Fθf ,i (xi (t), t)dt + Gθf ,i (t)dw(t)

� Measurement Model (prep.measurement())yi (ti ,j) = µ + Λxi (ti ,j) + εi (ti ,j), εi (ti ,j) ∼ N(0,Σy )

� Initial condition (prep.initial())x1(t1,j) ∼ N(x0,P0)

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What are regime-switchingdynamic models?

� A regime–switching longitudinal model consists of severallatent (unobserved) classes–or “regimes.” Within eachclass, a submodel is used to described the distinct changepatterns associated with the class.

� Each “regime” can be thought of as one of the stages orphases of a dynamic process.

� Individuals can switch between classes or regimes overtime.

� The changes that unfold within a regime are continuous innature.

� Markov-switching, hidden markov models, latent transitionanalysis, probabilistic functions of Markov chains (Petrie,1969)

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Initial regime probabilitiesTransition probabilities

Multinomial logistic regression models are used to represent theinitial regime probabilities and describe each individual i ’stransition in class membership from time t-1 to time t as

Pr(Si1 = k|xi1,θ)∆= πk,i1 =

exp(ak1 + b′k1xi1)∑Ks1=1 exp(as1 + b′s1xi1)

,

Pr(Sit = k|Si ,t−1 = j , xit ,θ)∆= πjk,it =

exp(akt + b′ktxit)∑Kst=1 exp(ast + b′stxit)

Sit = individual i ’s class membership at time t

K = the number of regimes

akt = the logit intercept for the kth regime at time t

xit = a vector of covariates for person i at time t

bkt = a vector of logit slopes for the kth regime at time t

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Extended Kalman Filter

� Prediction (Discrete Time)

x̂t|t−1 = F (t, x̂t−1|t−1)

Pt|t−1 =∂F (t, x̂(t))

∂x̂Pt−1|t−1

∂F (t, x̂(t))

∂x̂

T

+ Q

� Prediction (Continuous Time)

d x̂

dt= F (t, x̂t−1|t−1)

DP(t) =∂F (t, x̂(t))

∂x̂P(t) + P(t)(

∂F (t, x̂(t))

∂x̂)T + Q(t)

� Solve these differential equations using Runge-Kutta oradaptive ODE solver.

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Linear Harmonic Oscillator

� fit to data from broad domains within psychology

� resilience of older adults (Boker, Montpetit, Hunter, &Bergeman, 2010)

� coupling of smoking and drinking behavior in adolescents(Boker & Graham, 1998)

� response of widows to the loss of their spouse (Bisconti,Bergeman, & Boker, 2004, 2006)

� fluctuations and self-regulation of emotions (S. Chow,Ram, Boker, Fujita, & Clore, 2005)

� mother-infant synchrony during playful, face-to-faceinteractions (Zentall, Boker, & Braungart-Rieker, 2006)

� coupling of weather and mood in patients with bipolardisorder (Boker, Leibenluft, Deboeck, Virk, & Postolache,2008)

� dynamics of romantic partners (Steele & Ferrer, 2011)

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Damped and Forced Harmonic Oscillator

� As a second-order system

d2x

dt2= −kx − c

dx

dt+ ζ (1)

� As a vector of first-order systems( dxdtd2xdt2

)=

(0 1−k −c

)(xdxdt

)+

(0ζ

)(2)

� The Measurement Model

y =(

1 0)( x

dxdt

)+ ε (3)

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Linear Harmonic OscillatorExample code

# measurement

# this is the factor loadings matrix

#Lambda in SEM notation or C in OpenMx notation

meas <- prep.measurement(

# starting values and fixed values

values.load=matrix(c(1, 0), 1, 2),

# parameter names or fixed

params.load=matrix(c('fixed', 'fixed'), 1, 2),

state.names=c("Position","Velocity"),

obs.names=c("y1"))

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# define the differential equation

dynamics <- prep.matrixDynamics(

values.dyn=matrix(c(0, -0.1, 1, -0.2), 2, 2),

params.dyn=matrix(

c('fixed', 'spring', 'fixed', 'friction'),

2, 2), #uses params 'spring' and 'friction'

isContinuousTime=TRUE)

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# Prepare for cooking

# put all the recipes together

model <- dynr.model(dynamics=dynamics,

measurement=meas,

noise=ecov, initial=initial, data=data,

outfile="LinearSDE.c")

# Look with LaTeX

printex(model)

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Linear SDE: printex {dynr}The measurement model is given by:[

y1(t)]

=[1 0

] [Position(t)Velocity(t)

]+ ε,

ε ∼ N( [

0.00],[mnoise

] )The dynamic model is given by:[dPosition(t)dVelocity(t)

]= (

[0 1

spring friction

] [Position(t)Velocity(t)

])dt + dw(t),

dw(t) ∼ N([0.00

0.00

],

[0 00 dnoise

])The initial condition of the dynamic model is given by:[

Position(0)Velocity(0)

]∼ N

([inipos1

],

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# Cook

# Estimate free parameters

res <- dynr.cook(model)

# Examine results

summary(res)

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summary

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Output: plot {dynr}plot(res, model)

111111111

11111111111111111111

11111111111111111111111

11111111111111

1

11111111

1

1111111111111111111111111111111111111111111111111

1

1111111111111111111

111

1111111111111

1

1

1111

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11111111111111111111111111111111111111111111111111111

11111

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111

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1111111111111

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11111111111111111111111111111

1111

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11111111

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11111

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1111111111111111111111111111111111111111111111111111111111111111111111111

1

1

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11111

1111

11111111111111111111

1111111111

11111111111

1

11111111111111111

11111111111111111111

111

111111111

1

111

1

1111111111

1

11111111111111111111111111

111111111111111111111

11111111111

11111111111111111111

111111

11111

11111111111111111111111111

11

1

1

1111111111111111111111111

111

1

1

1111

11111

111111111111111111111111

11111111111111111111111111

1111

11

11111111

1111

1

11111111111111

1111111111111111111111

11111111111111111111

1

111111111111111

1

1111111111111111

11111111111111111111111122

222222

2222222222222222222222

22222222222222222222222222222222222

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22

222222222

2222

222222222222222222222222222222222222222222222222222222

2222222

22

22222222222222222222222222222222222222222222

2

2222

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22222

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22222

2

22

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1

−4

0

4

0 250 500 750 1000time

Sm

ooth

ed S

tate

Val

ues

variable 1 2state1 state2

Dynamic Model without Noise

d(Position(t)) = (Velocity(t))dt

d(Velocity(t)) = (−0.25 × Position(t) + −0.62 × Velocity(t))dt

Measurement Model without Noise

y1 = Position34 / 51

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Example 2: MotivationData from the Affective Dynamics and Individual Differencesstudy (Emotions and Dynamic Systems Laboratory, 2010).Participants provided daily affect ratings 5 times a day atrandom intervals over 30 days.

−2.5

0.0

2.5

5.0

0 10 20 30time

valu

e

state Uncoupling Coupling

variable Positive Emotion Negative Emotion

Observed Positive and Negative Affects

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Regime-switching NonlinearDynamic Factor Analysis Model

PEit = aPPEi ,t−1 + bPN,citNEi ,t−1 + ζPE ,it

NEit = aNNEi ,t−1 + bNP,citPEi ,t−1 + ζNE ,it (4)

bPN,cit =

{0 if cit = 0

bPN0

(exp(abs(NEi,t−1))

1+exp(abs(NEi,t−1))

)if cit = 1,

bNP,Sit =

{0 if cit = 0

bNP0

(exp(abs(PEi,t−1))

1+exp(abs(PEi,t−1))

)if cit = 1,

(5)

(S.-M. Chow & Zhang, 2013). Model adapted from an earlier model presented by(S.-M. Chow, Tang, Yuan, Song, & Zhu, 2011).

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Regime-switching NonlinearDynamic Factor Analysis Model

� Dynr fits discrete-time dynamic models too.

� Dynr allows specification of nonlinear dynamicmodels in formula forms.

� Dynr deals with dynamic models withregime-switching properties.

� Dynr provides ready-to-present results throughLaTex equations and plots.

Dynr Facts

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Output: dynr.ggplot {dynr}

1 2

−2

−1

0

1

2

0 100 200 300 0 100 200 300timeS

mo

oth

ed

Sta

te V

alu

es

variable PE NE

regime Coupled (nonlinear) Decoupled (linear)

Results from RS Nonlinear DFA model

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Regime-switchingPredator and Prey Model

The dynamic model is given by:

Regime 1:

d(prey)

dt= a× prey − b × prey × predator ,

d(predator)

dt= −c × predator + d × prey × predator ,

Regime 2:

d(prey)

dt= a× prey − e × prey2

− b × prey × predator ,

d(predator)

dt= f × predator − c × predator2

+ d × prey × predator

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One-regime Predator-and-preyModel

1

2

3

0 1 2 3 4 5time

valu

e

variable

prey

predator

0

1

2

3

0 1 2 3 4 5time

valu

e

variable

x

y

0.5

1.0

1.5

2.0

0 1 2 3prey

pred

ator

5

10

15

20id

−1

0

1

2

3

−1 0 1 2 3 4x

y

5

10

15

20id

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One-regime extension ofthe Predator-and-prey Model

0

1

2

3

0 1 2 3 4 5time

valu

e

variable

prey

predator

−1

0

1

2

3

0 1 2 3 4 5time

valu

e

variable

x

y

0.8

1.2

1.6

2.0

0 1 2 3prey

pred

ator

5

10

15

20id

0

1

2

3

4

−2 0 2 4x

y

5

10

15

20id

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0

1

2

3

0 1 2 3 4 5time

valu

e

variable

prey

predator

−1

0

1

2

3

0 1 2 3 4 5time

valu

e

variable

x

y

1.0

1.5

2.0

0 1 2 3prey

pred

ator

5

10

15

20id

−1

0

1

2

3

−2 0 2 4x

y

5

10

15

20id

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� Dynr fits nonlinear ODE models withregime-switching properties.

� Dynr allows for automatic differentiation.

� Dynr provides ready-to-present results throughLaTex equations and plots.

Dynr Facts

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1 Dynr fits discrete- and continuous-time dynamicmodels to multivariate longitudinal/time-series data.

2 Dynr handles linear and nonlinear dynamic modelswith an easy-to-use interface.

� Dynr allows model specification in matrix and formulaforms.

� Dynr allows automatic differentiation.

3 Dynr deals with dynamic models withregime-switching properties.

� e.g., Markov switching autoregressive (MSAR);Markov switching Kalman Filter (MSKF)

� Caveat: Only linear measurement

4 Dynr computes in C and runs fast.

5 Dynr provides ready-to-present results through LaTexequations and plots.

What can dynr do? Dynr Facts 1-5

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� https://quantdev.ssri.psu.edu/

avada_resources/dynr/

� In the next week or so, on CRAN!

Where can I get dynr?

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MakeDynr

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Take-homeMessage

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� Gather data with dynr.data()

� Prepare recipes with� prep.measurement()� prep.dynamics()� prep.initial()� prep.noise()� prep.regimes() (optional)

� Mix recipes and data into a model withdynr.model()

� Cook model with dynr.cook()

� Serve results with� summary()� plot()� dynr.ggplot()� plotFormula()� printex()

dynr preparation

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Thank you for your attention!

� NIH grants R01GM105004, R01HD07699

� NSF grant BCS-0826844

� Sukruth Reddy, Zhaohua Lu, Timothy Brick, Meng Chen, PeifengYin

� The QuantDev Group

Acknowledgements

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References

Bisconti, T. L., Bergeman, C. S., & Boker, S. M. (2004). Emotionalwell-being in recently bereaved widows: A dynamical systemsapproach. Journal of Gerontology, 59B, 158-167.

Bisconti, T. L., Bergeman, C. S., & Boker, S. M. (2006). Socialsupport as a predictor of variability: An examination of theadjustment trajectories of recent widows. Psychology andAging, 21, 590-599.

Boker, S. M., & Graham, J. (1998). A dynamical systems analysis ofadolescent substance abuse. Multivariate BehavioralResearch, 33, 479-507. doi: 10.1207/s15327906mbr3304\ 3

Boker, S. M., Leibenluft, E., Deboeck, P. R., Virk, G., & Postolache,T. T. (2008). Mood oscillations and coupling between moodand weather in patients with rapid cycling bipolar disorder.International Journal of Child Health and HumanDevelopment, 1(2), 181-203.

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MakeDynr

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Why

Dynr Facts

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Estimation




Take-homeMessage

References

Boker, S. M., Montpetit, M. A., Hunter, M. D., & Bergeman, C. S.(2010). Modeling resilience with differential equations. InP. C. M. Molenaar & K. Newell (Eds.), Individual pathwaysof change: Statistical models for analyzing learning anddevelopment (p. 183-206). Washington, D.C.: AmericanPsychological Association. doi: 10.1037/12140-011

Chow, S., Ram, N., Boker, S. M., Fujita, F., & Clore, G. (2005).Emotion as a thermostat: Representing emotion regulationusing a damped oscillator model. Emotion, 5, 208-225.

Chow, S.-M., Tang, N., Yuan, Y., Song, X., & Zhu, H. (2011).Bayesian estimation of semiparametric nonlinear dynamicfactor analysis models using the Dirichlet process prior.British Journal of Mathematical and Statistical Psychology,64(1), 69–106.

Chow, S.-M., & Zhang, G. (2013). Nonlinear regime-switchingstate-space (RSSS) models. Psychometrika, 78(4), 740–768.

Dolan, C. V. (2005). MKFM6: Multi-group, multi-subject stationarytime series modeling based on the kalman filter. Retrievedfrom http://users/fmg.uva.nl/cdolan/

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http://users/fmg.uva.nl/cdolan/

MakeDynr

Ou, Hunter,Chow

Why

Dynr Facts

ModelingFramework

Estimation




Take-homeMessage

References

Driver, C. C., Oud, J. H. L., & Voelkle, M. C. (2015). Continuoustime structural equation modelling with R package ctsem.Journal of Statistical Software.

Emotions and Dynamic Systems Laboratory. (2010). The affectivedynamics and individual differences (ADID) study:Developing non-stationary and network-based methods formodeling the perception and physiology of emotions.Unpublished manual.

Koopman, S. J., Shephard, N., & Doornik, J. A. (1999). Statisticalalgorithms for models in state space using SsfPack 2.2.Econometrics Journal, 2(1), 113-166. doi:10.1111/1368-423X.00023

Neale, M. C., Hunter, M. D., Pritikin, J. N., Zahery, M., Brick, T. R.,Kirkpatrick, R. M., . . . Boker, S. M. (in press). OpenMx2.0: Extended structural equation and statistical modeling.Psychometrika. doi: 10.1007/s11336-014-9435-8

Petrie, T. (1969). Probabilistic functions of finite state markovchains. Annals of Mathematical Statistics, 40, 97-115.

Petris, G. (2010). A R package for dynamic linear models. Journal ofStatistical Software, 36(12), 1-16.

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MakeDynr

Ou, Hunter,Chow

Why

Dynr Facts

ModelingFramework

Estimation




Take-homeMessage

References

Steele, J. S., & Ferrer, E. (2011). Latent differential equationmodeling of self-regulatory and coregulatory affectiveprocesses. Multivariate Behavioral Research, 46(6), 956-984.doi: 10.1080/00273171.2011.625305

Zentall, S. R., Boker, S. M., & Braungart-Rieker, J. M. (2006, June).Mother-infant synchrony: A dynamical systems approach. InProceedings of the Fifth International Conference onDevelopment and Learning.

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