Page 38 - Contributed Paper Session (CPS) - Volume 3

CPS1941 Jang S.
do not evolve in time. Thus, Nagin introduced several generalizations of his
model in his book (Nagin 2005). Among others, he introduced a model
allowing to add covariates to the trajectories. Let , … , be covariates
1

potentially influencing . We are then looking for trajectories

= ∑ + + … + + (3)

1 1

=0

where is normally distributed with zero mean and a constant standard

deviation . The covariates may depend or not upon time . But even this

generalized model still has two major drawbacks. First, the influence of the
covariates in this model is unfortunately limited to the intercept of the
trajectory. This implies that for different values of the covariates, the
corresponding trajectories will always remain parallel by design, which does
not necessarily correspond to reality.
Secondly, in Nagin’s model, the standard deviation of the disturbance is
the same for all the groups. That too is quite restrictive. One can easily imagine
situations in which in some of the groups all individual are quite close to the
mean trajectory of their group, whereas in other groups there is a much larger
dispersion.

3. Our model
To address and overcome these two drawbacks, we propose the following
generalization of Nagin’s model. Let … and , … , be covariates
1

1

potentially influencing . Here the variables are covariates not depending
on time like gender or cohort membership in a multicohort longitudinal study
and the variable is a covariate depending on time like being employed or
unemployed. They can of course also designate timedependent covariates not
depending on the subjects of the data set which still influence the group
trajectories, like GDP of a country in case of an analysis of salary trajectories.
The trajectories in group will then be written as

+ ) + + ,
(4)
= ∑ ( + ∑

=0 =1

where the disturbance is normally distributed with mean zero and a

standard deviation constant inside group but different from one group to

another. Since, for each group, this model is just a classical fixed effects model
for panel data regression (see Woolridge 2002), it is well defined and we can
get consistent estimates for the model parameters.

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