Todd D. Little University of Kansas Director, Quantitative Training Program
-
Upload
debra-brady -
Category
Documents
-
view
28 -
download
0
description
Transcript of Todd D. Little University of Kansas Director, Quantitative Training Program
1crmda.KU.edu
Todd D. LittleUniversity of Kansas
Director, Quantitative Training ProgramDirector, Center for Research Methods and Data Analysis
Director, Undergraduate Social and Behavioral Sciences Methodology MinorMember, Developmental Psychology Training Program
crmda.KU.eduColloquium presented 04-05-2013 @ Purdue University
Special Thanks to Noel A. Card, James P. Selig, & Kristopher Preacher
Representing Time in Longitudinal Research: Assessment Lag as Moderator
33
Overview
• Conceptualizing and Representing Time in Longitudinal Research• B = ƒ(age) vs. Δ = ƒ(time)
• The Accelerated Longitudinal Design
• Developmental-Lag Model
• The Lag as Moderator Model
crmda.KU.edu
4
Validity Threats in Longitudinal Work
• Threats to Validity – Maturation
• In pre-post experiment effects may be due to maturation not the treatment
• Most longitudinal studies, maturation is the focus.
– Regression to the mean• Only applicable with measurement error
– Instrumentation effects (factorial invariance)– Test-retest/practice effects (ugh)– Selection Effects
• Sample Selectivity vs. Selective Attrition
• Age, Cohort, and Time of Measurement are confounded– Sequential designs attempt to unconfound these.
crmda.KU.edu
6
Design Independent
Variables Confounded Effect
Cohort-Sequential
Age & Cohort
Age x Cohort Interaction is confounded with Time
Time- Sequential
Age & Time Age x Time Interaction is confounded with Cohort
Cross-Sequential
Cohort & Time
Cohort x Time Interaction is confounded with Age
What’s Confounded?
crmda.KU.edu
8
Accelerated Longitudinal Designs
Fall 6
Spr6
Fall7
Spr7
Fall8
Spr8
Fall9
Grade 6
Grade 7
Grade 8
Grade
crmda.KU.edu
9
Accelerated Growth Curve Model(L13.1.GC.LevelCUBIC.Accelerated)
Fall 6
Spr.6
Fall7
Spr.7
Fall8
Spr.8
Fall9
==
==
= ==
===
==
==
-4*
5*0*
-3*-3* 0*
5* -1*1*1*0*-1*-1* 1*
-3*-2*-1* 0*1*2*3*
1* 1*1*1*
1*
1*1*
a1
Inter-cept
Linear
a2
Quad-ratic
a3
Cubic
a4
Grade8
8=11*
0*
Grade7
7=11*
0*
= = = = = = =
crmda.KU.edu
10
Plot of Estimated Trends
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Fall 6 Spr 6 Fall 7 Spr 7 Fall 8 Spr 8 Fall 9
Positive Affect
Negative Affect
crmda.KU.edu
11
Appropriate Time and Intervals• Age in years, months, days.• Experiential time: Amount of time something is experienced
– Years of schooling, length of relationship, amount of practice– Calibrate on beginning of event, measure time experienced
• Episodic time: Time of onset of a life event– Toilet trained, driver license, puberty, birth of child, retirement– Early onset, on-time, late onset: used to classify or calibrate.– Time since onset or time from normative or expected occurrence.
• Measurement Intervals (rate and span)– How fast is the developmental process?– Intervals must be equal to or less than expected processes of change– Measurement occasions must span the expected period of change– Cyclical processes
• E.g., schooling studies at yearly intervals vs. half-year intervals
crmda.KU.edu
• Use 2-time point data with variable time-lags to measure a growth trajectory + practice effects (McArdle & Woodcock, 1997)
Developmental time-lag model
13crmda.KU.edu
T1 T2Age
1student
2345678
0 1 2Time
3 4 5 65;65;34;94;64;115;75;25;4
5;75;84;115;05;45;105;35;8
14crmda.KU.edu
T0 T1
1
T2 T3 T4 T5 T6
1
Intercept
12 3 4
Growth
0
1t t tY I B G A P Linear growth
56
11
11
111
17crmda.KU.edu
T0 T1
1
T2 T3 T4 T5 T6
1 1
Intercept
11
1
Practice
1
Growth
1t t tY I B G A P Constant Practice Effect
11
11
111 1
011
2 3 40
56
18crmda.KU.edu
T0 T1
1
T2 T3 T4 T5 T6
1 1
Intercept
.45 .35
PracticeGrowth
1t t tY I B G A P Exponential Practice Decline
11
11
111 112 3 4
05
6
.55.67
.870
19crmda.KU.edu
T0Y I1T1Y I G P 2T2Y I G P
3T3Y I G P
4 4TY I G P
5 5TY I G P
6 6TY I G P
The Equations for Each Time Point
T0Y I1 1.0T1Y I G P 2 .82T2Y I G P
3 .67T3Y I G P
4 4 .55TY I G P
5 5 .45TY I G P
6 6 .37TY I G P
Constant Practice Effect Declining Practice Effect
20crmda.KU.edu
• Summary– 2 measured time points are formatted according to
time-lag– This formatting allows a growth-curve to be fit,
measuring growth and practice effects
Developmental time-lag model
21crmda.KU.edu
22
Temporal Design
• Changes (and causes) take time to Unfold• The ability to detect an effect depends on the
measurement interval• The ability to model the shape of the effect
requires adequate sampling of time intervals.• The ability to model the optimal effect
requires knowing the shape in order to pick the optimal (peak) interval.
• Lag within Occasion: the Lag as Moderator Model
crmda.KU.edu
• One possible way to address the issue of lag choice is to treat lag as a moderator
• Following this approach lag is treated as a continuous variable that can vary across individuals
24
Lag as Moderator (LAM) Models
crmda.KU.edu
X1X2X3X4X5
Xn
Y1Y2
Y3Y4
Y5
Yn
T1 Tmin Tmax
•••
25
Variable Actual Assessments
T2
X6 Y6X7 Y7X8 Y8X9 Y9Xi YiXj Yj
crmda.KU.edu
• Xi is the focal predictor of outcome Yi
• Lagi can vary across persons
• b1 describes the effect of Xi on Yi when Lagi is zero
• b2 describes the effect of Lagi on Yi when Xi is zero
• b3 describes change in the Xi → Yi relationship as a function of Lagi
0 1 2 3i i i i iY b b X b Lag b X Lag
26
Multiple Regression LAM model
crmda.KU.edu
• Data are from the Early Head Start (EHS) Research and Evaluation study (N = 1,823)
• Data were collected at Time 1 when the focal children were approximately 14 months of age and again at Time 2 when the children were approximately 24 months of age
• The average lag between Time 1 and Time 2 observations was 10.3 months with values ranging from 3.0 to 17.3 months
• Measures:– The Home Observation for the Measurement of the Environment
(HOME) assessed the quality of stimulation in the home at Time 1.
– The Mental Development Index (MDI) from the Bayley Scales of Infant Development measured developmental status of children at Time 2.
27
An Empirical Example
crmda.KU.edu
28
Lag (Mean Centered)
Eff
ect o
f H
OM
ET
1 on
MD
I T2
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 70
0.5
1
1.5
2
2.5
3
2 0 1 T1 2 3 1TMDI b b HOME b Lag b HOME Lag
HOME predicting MDI
crmda.KU.edu
29
• Lag is embraced –LAM models allow us to model, not ignore,
interactions of lag and hypothesized effects
• Selecting/Sampling Lag is critical–Sampling only a single lag may limit generalizability
• Theory Building–LAM models may yield a better understanding of
relationships and richer theory regarding those relationships
Implications of LAM Models
crmda.KU.edu
30
Randomly Distributed AssessmentX1X2X3X4X5
Xn
Y1
Yn
T1 Tbegin Tend
•••
Tmid
X6X7X8X9
Y1 Y1Y1 Y1Y2Y2 Y2Y2 Y2
Y3Y3 Y3Y3 Y3Y4Y4 Y4Y4 Y4Y5Y5 Y5Y5 Y5Y6Y6 Y6Y6 Y6
Y7Y7 Y7Y7 Y7Y8Y8 Y8Y8 Y8
Y9 Y9Y9Y9 Y9
Yn Yn Yn Yn
crmda.KU.edu
Early Communication Indicators
MO6 MO9 MO12 MO15 MO18 MO21 MO24 MO27 MO30 MO33 MO360.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
GesturesVocalizationsSingle Word UtterancesMultiple Word Utterances
T-Scores
• Individual-likelihood Based Estimation– Allows individually varying values of time
yit = αi + βiλit + εit
– Ages in months ((days/365)*12) were calculated and centered around locations of latent intercepts
Gestures
Ψ31 = -.003 (ns)
6 9 12 15 18 21 24
S1_GES I_GES15 S2_GES
-.031.69.07Ψ21 = .05
Ψ22 = .86 Ψ33 = .01Ψ11 = .01
Ψ32 = -.06
IFSPIFSP
Vocalizations
Ψ31 = -.006
6 9 12 15 18 21 24 27 30 33 36
S1_VOC I_VOC18 S2_VOC
-.133.70.18Ψ21 = .20
Ψ22 = 2.59 Ψ33 = .01Ψ11 = .02
Ψ32 = -.13
IFSPIFSPIFSP
Single Word Utterances
Ψ21 = .10
12 15 18 21 24 27 30 33 36
S_WRD I_WRD36
Ψ22 = 2.47Ψ11 = .004
IFSPIFSP
3.81.16
Multiple Word Utterances
Ψ21 = .43
18 21 24 27 30 33 36
S_MUL I_MUL36
Ψ22 = 7.79
4.30 .24Ψ11 = .02
IFSPIFSP
38crmda.KU.edu
Todd D. LittleUniversity of Kansas
Director, Quantitative Training ProgramDirector, Center for Research Methods and Data Analysis
Director, Undergraduate Social and Behavioral Sciences Methodology MinorMember, Developmental Psychology Training Program
crmda.KU.eduColloquium presented 04-06-2013 @
Purdue University
Thank You!
39www.Quant.KU.edu
Update
Dr. Todd Little is currently at
Texas Tech UniversityDirector, Institute for Measurement, Methodology, Analysis and Policy (IMMAP)
Director, “Stats Camp”
Professor, Educational Psychology and Leadership
Email: [email protected]
IMMAP (immap.educ.ttu.edu)
Stats Camp (Statscamp.org)