using stata a plug-in to estimate group-based trajectory models
DESCRIPTION
Using Stata a Plug-in to Estimate Group-Based Trajectory Models. Daniel S. Nagin Carnegie Mellon University. Installing the Plug-in. Traj can be installed by issuing the following commands within Stata. An additional command, trajplot, supports plotting the results. - PowerPoint PPT PresentationTRANSCRIPT
Using Stata a Plug-in to Estimate Group-Based Trajectory Models
Daniel S. Nagin
Carnegie Mellon University
Installing the Plug-inTraj can be installed by issuing the following commands within Stata. An additional command, trajplot, supports plotting the results.. net from http://www.andrew.cmu.edu/user/bjones/traj . net install traj, replace
Trajectories of Physical Aggression(Child Development, 1999)
00.5
11.5
22.5
33.5
44.5
6 10 11 12 13 14 15
Age
Phys
ical A
ggre
ssio
n
Low-actual Mod. desister-actual High desister-actual Chronic-actualLow-pred. Mod. desister-pred. High desister-pred. Chronic-pred
4%
28%
52%16%
Calculation & Use of Posterior Probabilities of Group Membership
Maximum Probability Group Assignment Rule
jji
jii jgroupdatap
jgroupdatapdatajgroupp
ˆ)|(ˆ
ˆ)|(ˆ)|(ˆ
Group Profiles
Variable Group
Low HighNever Desister Desister Chronic
Years of School - Mother 11.1 10.8 9.8 8.4
Years of School - Father 11.5 10.7 9.8 9.1
Low IQ (%) 21.6 26.8 44.5 46.4
Completed 8th Grade 80.3 64.6 31.8 6.5 on Time (%)
Juvenile Record (%) 0.0 2.0 6.0 13.3
# of Sexual Partners at 1.2 1.7 2.2 3.5 Age 17 (Past Year)
01
23
convi
ctio
n r
ate
1 1.5 2 2.5 3scaled age
1 69.5% 2 12.4% 3 12.2%4 5.9%
Cambridge Study of Delinquent DevelopmentTrajectories of Convictions
Logit Model for Binary Data
33
2210
33
2210
1)1(
ageageage
ageageage
e
eyp
where y=1 if yes & y=0 if no
Trajectories of Delinquent Group Membership
(Development & Psychopathology, 2003)
0.2
.4.6
.8
Pro
b o
f g
an
g m
em
bers
hip
1 1.2 1.4 1.6 1.8scaled age
1 74.3% 2 13.1% 3 12.6%
Statistically Linking Group Membership to Individual Characteristics (Chapter 6)
Use of Multinomial Logit Model to Create a Multivariate Probabilistic Linkage
ji
ji
x
x
ij eex
)(
Risk Factors for Physical Aggression Trajectory Group Membership
Broken Home at Age 5 Low IQ Low Maternal Education Mother Began Childbearing as a Teenager
Impact of Risk Factors on Group Membership Probabilities
00.10.20.30.40.50.60.7
prob
abili
ty
Low
Moderate Declining
High Declining
Chronic
Does School Grade Retention and Family Break-up Alter Trajectories of Violent Delinquency Themselves?
(Nagin, 2005; Development and Psychopathology
2003)Trajectories of Violent Delinquency
0
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17
Age
Rate
Low 1 (34.8$) Low 2(30.6%) Rising (13.4%)Declining (16.7%) Chronic (4.5%)
Probability of Trajectory Group
Membership
Z1 Z2 Z3 Z4 Z5 ………. …. Zm
Trajectory 1 Trajectory 2 Trajectory 3 Trajectory 4
The Overall Model
X1t X2t X3t……………Xlt
Model of Impact of Grade Retention and Parental Separation on Trajectory Group j
Trajectory with retention and separation impacts:
Model without retention or separation impact:
2210)ln( tj
tjjj
t AgeAge
tj
tj
tj
tjjj
t SeparationFailAgeAge 212
210
~~~)ln(
Dual Trajectory Analysis: Trajectory of Modeling of Comorbidity and Heterotypic Continuity (Nagin and Tremblay, 2001; Nagin (2005)
Panel A-Conventional Approach
Behavior X: X1 X 2 X3 ……………… XT
Comorbidity
Behavior Z: Z1 Z2 Z3 ……………… ZT
Behavior X: X1 X 2 X3
……………… XT
Heterotypic Continuity
Behavior Z: ZT ZT+1 Zt+3 ……………… ZT+K
Panel B-Dual Trajectory Approach
Behavior X: X1 X 2 X3 ……………… XT
Comorbidity
Behavior Z: Z1 Z2 Z3 ……………… ZT
Behavior X: X1 X 2 X3
……………… XT
Heterotypic Continuity
Behavior Z: ZT ZT+1 Zt+3 ……………… ZT+K
Modeling the Linkage Between Trajectories of Physical Aggression in Childhood and Trajectories of Violent Delinquency in Adolescence
Trajectories of Childhood Physical Aggression from Age 6 to 13
0
1
2
3
4
6 8 10 12
Age
Phys
ical
Agg
ress
ion Low
Desisting
High
Trajectories of Adolescent Violent Delinqunecy from Age 13 to 17
0123456789
13 14 15 16 17
AgeR
ate
Low 1
Low 2
Declining
Rising
Chronic
Transition Probabilities Linking Trajectories in Adolescent to Childhood Trajectories
Trajectory in Adolescence
Trajectoryin Childhood
Low
1&2
Rising Declining Chronic
Low .889 .092 .019 .000
Declining .707 .136 .128 .029
High .422 .215 .206 .158
The Dual-Trajectory Model Generalized to Include Predictors of Conditional Probabilities Are drug use and family break-up at age 12
predict the conditional probabilities linking childhood physical aggression trajectories with adolescent violent delinquency trajectories?
Answer: yes for drug use but no family break-up Conditional probabilities specified to follow a
“constrained” multinomial logit function (see section 8.7 of Nagin)
Probability of Transition to Chronic Trajectory Depending on Drug Use at Age 12 and Childhood Physical Aggression Trajectory
Drug Use at age 12
Low Physical Aggression
Moderate Physical Aggression
High Physical Aggression
None .00 .02 .1275th Percentile
.00 .18 .46
Multi-Trajectory Modeling
Linking Trajectories to Later Out Comes—Trajectories of Physical Aggression from 6 to 15 and Sexual Partners at 16
Adding Subject Attrition to the Model
Probability of Death by Trajectory Group
.1.2
.3.4
Drop
out p
roba
bility
0 2 4 6 8Time (weeks)
1 40.2% 2 45.7% 3 14.1%