Trajectory. 1. Physics. The path of any body moving under the action of given forces . . . especially the curve described by a projectile in its flight through the air. [O.E.D.]. Multimedia Physics Studios. Cluster Analysis of Cases.
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1. Physics. The path of any body moving under the action of given forces . . . especially the curve described by a projectile in its flight through the air. [O.E.D.]
Multimedia Physics Studios
Runs as a SAS PROC
Produces trajectorycharts automatically
Model published in Psychological Methods(1999, 2001)
Many studies injuvenile justice
Two-group logistic model from CM WWW site.
Distress of child i at time t
Distress(i,t) = βi0 + βi1t+ βi2t2 . . .
β0 the intercept, the score at time zero
β1 the linear slope, indicating a constant increase or decrease over time
β2 is the quadratic slope indicating a curve of acceleration or deceleration
Individuals with missing observations can be included
Proc TRAJ goes up to degree 5
Each child has an observed trajectory
Each trajectory has an approximate model description
Each child is described by several numbers
Cases can be sorted into clusters by the several numbers
Nagin developed the statistical theory
Jones wrote PROC TRAJ software (free download)
Membership in a delinquent group at a given time (No, Yes)
Well-done example of trajectory analysis with PROC TRAJ
N = 287 women surviving cancer
Scott Holupka & Debra Rog
VU Washington DC
Inattentive ADHD Symptoms in a High Risk Group N = 267 school children
Recurrent Abdominal Pain (RAP) in children with no medical diagnosis
The average child with ADHD gets somewhat better over 3 years
Bickman, Wolraich, Lambert & Simmons in prep
One size fits none
“Children with RAP improve briefly then stay the same at a moderate level for 4-5 years.”
Is that what this chart really says? (Note Std Dev)
Let’s try PROC TRAJ.
Group Size Prob.
1 (21.2%) .
2 (67.1%) 0.0004
3 ( 1.7%) 0.0022Gp 3 tiny
4 (10.0%) 0.0874Gp 1-Gp 4 nonsig
Four clusters not acceptable because there are not 4 distinct clusters. In addition, cluster 3 is too small.
Knowing when to stop . . .
Group Parameter Estimate Prob > |T|
1 Intercept 15.44068 0.0000
Linear -0.68666 0.0002
Quadratic 0.01047 0.0002
2 Intercept 42.87414 0.0000
Linear -2.42765 0.0000
Quadratic 0.03429 0.0000
3 Intercept 33.74592 0.0000
Linear 0.65764 0.1630
Quadratic -0.00597 0.4160
Long term risk
Short term risk
** p < .01
*** p < .001 one-way ANOVA
Comparison of Characteristics by CSI Symptom Trajectory Group
OK, Officer, we’re fishing for a hypothesis. We’ll test it with fresh data.
Like cluster analysis or exploratory factor analysis, TRAJ needs cross validation