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Understanding the time course of interventions - amemory strategy example
March, 2018
Charles Driver
Max Planck Institute for Human Development
The study
Change in associative and recognition memory across the adult age range,particularly with regards to strategy use.
Longitudinal study with 5 waves – though actually 8 waves!
Within wave, participants shown two lists of 26 word pairs, and tested onrecognition of individual words (items) and pairs of words (associations).
book running
The study
Change in associative and recognition memory across the adult age range,particularly with regards to strategy use.
Longitudinal study with 5 waves – though actually 8 waves!
Within wave, participants shown two lists of 26 word pairs, and tested onrecognition of individual words (items) and pairs of words (associations).
book running
The study
Change in associative and recognition memory across the adult age range,particularly with regards to strategy use.
Longitudinal study with 5 waves – though actually 8 waves!
Within wave, participants shown two lists of 26 word pairs, and tested onrecognition of individual words (items) and pairs of words (associations).
book running
The study
Change in associative and recognition memory across the adult age range,particularly with regards to strategy use.
Longitudinal study with 5 waves – though actually 8 waves!
Within wave, participants shown two lists of 26 word pairs, and tested onrecognition of individual words (items) and pairs of words (associations).
book running
Longitudinal timeline
0 50 100 150 200 250
01
23
45
6Observations
Subject
Yea
rs fr
om s
tudy
sta
rt
Before each of the 3 waves with the short, 2 week interval, deep encodingintervention:
Participants asked to generate, for each pair, a sentence relating the twowords to each other during the study portion, and use that sentence to aidrecognition of words and pairs.
Individual variation in timing too...
Longitudinal timeline
0 50 100 150 200 250
01
23
45
6Observations
Subject
Yea
rs fr
om s
tudy
sta
rt
Before each of the 3 waves with the short, 2 week interval, deep encodingintervention:
Participants asked to generate, for each pair, a sentence relating the twowords to each other during the study portion, and use that sentence to aidrecognition of words and pairs.
Individual variation in timing too...
Longitudinal timeline
0 50 100 150 200 250
01
23
45
6Observations
Subject
Yea
rs fr
om s
tudy
sta
rt
Before each of the 3 waves with the short, 2 week interval, deep encodingintervention:
Participants asked to generate, for each pair, a sentence relating the twowords to each other during the study portion, and use that sentence to aidrecognition of words and pairs.
Individual variation in timing too...
Longitudinal timeline
0 50 100 150 200 250
01
23
45
6Observations
Subject
Yea
rs fr
om s
tudy
sta
rt
Before each of the 3 waves with the short, 2 week interval, deep encodingintervention:
Participants asked to generate, for each pair, a sentence relating the twowords to each other during the study portion, and use that sentence to aidrecognition of words and pairs.
Individual variation in timing too...
Research questions
Does the intervention have lasting effects?
How do the covariates moderate the findings?
Research questions
Does the intervention have lasting effects?
How do the covariates moderate the findings?
Research questions
Does the intervention have lasting effects?
How do the covariates moderate the findings?
Descriptive plots
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0 asfa
Years
asfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0 ashr
Years
ashr
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0 itfa
Years
itfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0 ithr
Years
ithr
Descriptive plots
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0 asfa
Years
asfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0 ashr
Years
ashr
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0 itfa
Years
itfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0 ithr
Years
ithr
Modelling - hierarchical Bayesian continuous time dynamic model.
Subject level latent dynamics driven by stochastic differential equation:
dη(t) =
(Aη(t) + b + Mχ(t)
)dt + GdW(t) (1)
Observations for each subject are described by:
y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)
Possible via:
wide, SEM approach.long, Kalman-filter.
Frequentist SEM allows individual variation in intercepts,
With Bayesian formulation, everything can vary.
Modelling - hierarchical Bayesian continuous time dynamic model.
Subject level latent dynamics driven by stochastic differential equation:
dη(t) =
(Aη(t) + b + Mχ(t)
)dt + GdW(t) (1)
Observations for each subject are described by:
y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)
Possible via:
wide, SEM approach.long, Kalman-filter.
Frequentist SEM allows individual variation in intercepts,
With Bayesian formulation, everything can vary.
Modelling - hierarchical Bayesian continuous time dynamic model.
Subject level latent dynamics driven by stochastic differential equation:
dη(t) =
(Aη(t) + b + Mχ(t)
)dt + GdW(t) (1)
Observations for each subject are described by:
y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)
Possible via:
wide, SEM approach.long, Kalman-filter.
Frequentist SEM allows individual variation in intercepts,
With Bayesian formulation, everything can vary.
Modelling - hierarchical Bayesian continuous time dynamic model.
Subject level latent dynamics driven by stochastic differential equation:
dη(t) =
(Aη(t) + b + Mχ(t)
)dt + GdW(t) (1)
Observations for each subject are described by:
y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)
Possible via:
wide, SEM approach.long, Kalman-filter.
Frequentist SEM allows individual variation in intercepts,
With Bayesian formulation, everything can vary.
Modelling - hierarchical Bayesian continuous time dynamic model.
Subject level latent dynamics driven by stochastic differential equation:
dη(t) =
(Aη(t) + b + Mχ(t)
)dt + GdW(t) (1)
Observations for each subject are described by:
y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)
Possible via:wide, SEM approach.
long, Kalman-filter.
Frequentist SEM allows individual variation in intercepts,
With Bayesian formulation, everything can vary.
Modelling - hierarchical Bayesian continuous time dynamic model.
Subject level latent dynamics driven by stochastic differential equation:
dη(t) =
(Aη(t) + b + Mχ(t)
)dt + GdW(t) (1)
Observations for each subject are described by:
y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)
Possible via:wide, SEM approach.long, Kalman-filter.
Frequentist SEM allows individual variation in intercepts,
With Bayesian formulation, everything can vary.
Modelling - hierarchical Bayesian continuous time dynamic model.
Subject level latent dynamics driven by stochastic differential equation:
dη(t) =
(Aη(t) + b + Mχ(t)
)dt + GdW(t) (1)
Observations for each subject are described by:
y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)
Possible via:wide, SEM approach.long, Kalman-filter.
Frequentist SEM allows individual variation in intercepts,
With Bayesian formulation, everything can vary.
Modelling - hierarchical Bayesian continuous time dynamic model.
Subject level latent dynamics driven by stochastic differential equation:
dη(t) =
(Aη(t) + b + Mχ(t)
)dt + GdW(t) (1)
Observations for each subject are described by:
y(t) = Λη(t) + τ + ε(t) where ε(t) ∼ N(0c ,Θ) (2)
Possible via:wide, SEM approach.long, Kalman-filter.
Frequentist SEM allows individual variation in intercepts,
With Bayesian formulation, everything can vary.
Modelling – take 2
Four latent memory factors asfa, ashr, itfa, ithr, each measured by twonoisy indicators per wave.
Change over time in these latent factors is modelled with an initialintercept, a linear slope, and a stochastic portion to account formeaningful but unpredictable (according to our model) change.
On top of this, we estimate an intervention process, and the effect of thisprocess on each of the four memory factors.
0 1 2 3 4 5
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Subject 1, Age 75, Sex F, WkMz 1.55, METSz -0.81
Time
asfa
Modelling – take 2
Four latent memory factors asfa, ashr, itfa, ithr, each measured by twonoisy indicators per wave.
Change over time in these latent factors is modelled with an initialintercept, a linear slope, and a stochastic portion to account formeaningful but unpredictable (according to our model) change.
On top of this, we estimate an intervention process, and the effect of thisprocess on each of the four memory factors.
0 1 2 3 4 5
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Subject 1, Age 75, Sex F, WkMz 1.55, METSz -0.81
Time
asfa
Modelling – take 2
Four latent memory factors asfa, ashr, itfa, ithr, each measured by twonoisy indicators per wave.
Change over time in these latent factors is modelled with an initialintercept, a linear slope, and a stochastic portion to account formeaningful but unpredictable (according to our model) change.
On top of this, we estimate an intervention process, and the effect of thisprocess on each of the four memory factors.
0 1 2 3 4 5
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Subject 1, Age 75, Sex F, WkMz 1.55, METSz -0.81
Time
asfa
Modelling – take 2
Four latent memory factors asfa, ashr, itfa, ithr, each measured by twonoisy indicators per wave.
Change over time in these latent factors is modelled with an initialintercept, a linear slope, and a stochastic portion to account formeaningful but unpredictable (according to our model) change.
On top of this, we estimate an intervention process, and the effect of thisprocess on each of the four memory factors.
0 1 2 3 4 5
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Subject 1, Age 75, Sex F, WkMz 1.55, METSz -0.81
Time
asfa
What do we gain with such an approach to interventions?
Continuous time accounts for variability in time interval betweenobservations.
Intervention as dynamic process allows estimating unknown shape /persistence parameters.
Hierarchical approach accounts for, allows understanding of, individualvariability.
What do we gain with such an approach to interventions?
Continuous time accounts for variability in time interval betweenobservations.
Intervention as dynamic process allows estimating unknown shape /persistence parameters.
Hierarchical approach accounts for, allows understanding of, individualvariability.
What do we gain with such an approach to interventions?
Continuous time accounts for variability in time interval betweenobservations.
Intervention as dynamic process allows estimating unknown shape /persistence parameters.
Hierarchical approach accounts for, allows understanding of, individualvariability.
What do we gain with such an approach to interventions?
Continuous time accounts for variability in time interval betweenobservations.
Intervention as dynamic process allows estimating unknown shape /persistence parameters.
Hierarchical approach accounts for, allows understanding of, individualvariability.
Results
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
asfa
Years
asfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
ashr
Years
ashr
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
itfa
Years
itfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
ithr
Years
ithr
Sig. intervention improvement for asfa, ashr, itfa.
Unclear if intervention effect persists across years – probably not in general.
Intervention gives greater gains for worse performers.
Results
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
asfa
Years
asfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
ashr
Years
ashr
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
itfa
Years
itfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
ithr
Years
ithr
Sig. intervention improvement for asfa, ashr, itfa.
Unclear if intervention effect persists across years – probably not in general.
Intervention gives greater gains for worse performers.
Results
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
asfa
Years
asfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
ashr
Years
ashr
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
itfa
Years
itfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
ithr
Years
ithr
Sig. intervention improvement for asfa, ashr, itfa.
Unclear if intervention effect persists across years – probably not in general.
Intervention gives greater gains for worse performers.
Results
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
asfa
Years
asfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
ashr
Years
ashr
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
itfa
Years
itfa
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
ithr
Years
ithr
Sig. intervention improvement for asfa, ashr, itfa.
Unclear if intervention effect persists across years – probably not in general.
Intervention gives greater gains for worse performers.
Individual differences - age effects
20 30 40 50 60 70
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
AgeT1
Effect
TD_asfa_intTD_ashr_intTD_itfa_intTD_ithr_int
20 30 40 50 60 70
−0.2
−0.1
0.0
0.1
0.2
0.3
AgeT1
Effect
slope_asfaslope__ashrslope__itfaslope__ithr
20 30 40 50 60 70
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
AgeT1
Effect
manifestmeans_asfamanifestmeans_ashrmanifestmeans_itfamanifestmeans_ithr
20 30 40 50 60 70
0.6
0.8
1.0
1.2
AgeT1
Effect
manifestvar_asfamanifestvar_ashrmanifestvar_itfamanifestvar_ithr
20 30 40 50 60 70
−10
−8−6
−4−2
02
AgeT1
Effect
dr_memInt
20 30 40 50 60 70
−4−2
02
4
AgeT1
Effect
TD_memInt2TD_memInt3
Individual differences - age effects
20 30 40 50 60 70
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
AgeT1
Effect
TD_asfa_intTD_ashr_intTD_itfa_intTD_ithr_int
20 30 40 50 60 70−0.2
−0.1
0.0
0.1
0.2
0.3
AgeT1
Effect
slope_asfaslope__ashrslope__itfaslope__ithr
20 30 40 50 60 70
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
AgeT1
Effect
manifestmeans_asfamanifestmeans_ashrmanifestmeans_itfamanifestmeans_ithr
20 30 40 50 60 70
0.6
0.8
1.0
1.2
AgeT1
Effect
manifestvar_asfamanifestvar_ashrmanifestvar_itfamanifestvar_ithr
20 30 40 50 60 70
−10
−8−6
−4−2
02
AgeT1
Effect
dr_memInt
20 30 40 50 60 70
−4−2
02
4
AgeT1
Effect
TD_memInt2TD_memInt3
Discussion points - different shapes of intervention effect
0 5 10 15 20
0.0
0.2
0.4
0.6
0.8
1.0
Basic impulse effect
Time
Stat
e
Base process
0 5 10 15 20
0.0
0.5
1.0
1.5
2.0
2.5
Persistent level change
Time
Stat
e
Base processInput process
0 5 10 15 20
0.0
0.5
1.0
1.5
Dissipative impulse
Time
Stat
e
Base processInput process
0 5 10 15 20
-0.5
0.0
0.5
1.0
Oscillatory dissipation
Time
Stat
e
Base processInput processMediating input process
Discussion points - interventions on a trend
0 5 10 15 20
01
23
45
6
Time
Stat
e
Process without interventionProcess with interventionIntervention
Discussion points - system identification
0 5 10 15 20
−0.
50.
00.
51.
01.
52.
0
Natural state
Time
Sta
te
Process 1Process 2
0 5 10 15 20−
0.5
0.0
0.5
1.0
1.5
2.0
State with interventions
Time
Sta
te
Process 1Process 2
Discussion points - absolute model fit
Fits are better than saturated covariance structure.
Are there formalised approaches for model fit with person specific meanand or covariance?
Is absolute fit actually important?
Discussion points - absolute model fit
Fits are better than saturated covariance structure.
Are there formalised approaches for model fit with person specific meanand or covariance?
Is absolute fit actually important?
Discussion points - absolute model fit
Fits are better than saturated covariance structure.
Are there formalised approaches for model fit with person specific meanand or covariance?
Is absolute fit actually important?
Summary
The effect of interventions can change in time, and across people.
Analyses and plots via ctsem R package.
Chapter: Understanding the time course of interventions with continuoustime dynamic models.
Thanks!
Summary
The effect of interventions can change in time, and across people.
Analyses and plots via ctsem R package.
Chapter: Understanding the time course of interventions with continuoustime dynamic models.
Thanks!
Summary
The effect of interventions can change in time, and across people.
Analyses and plots via ctsem R package.
Chapter: Understanding the time course of interventions with continuoustime dynamic models.
Thanks!
Summary
The effect of interventions can change in time, and across people.
Analyses and plots via ctsem R package.
Chapter: Understanding the time course of interventions with continuoustime dynamic models.
Thanks!
Summary
The effect of interventions can change in time, and across people.
Analyses and plots via ctsem R package.
Chapter: Understanding the time course of interventions with continuoustime dynamic models.
Thanks!
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