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%