ABSTRACT
Traditionally, two kinds of methods are applied in trajectory analysis: 1) hierarchical
modeling based on a multilevel structure, or 2) latent growth curve modeling (LGCM) based
on a covariance structure (Raudenbush & Bryk, 2002; Bollen & Curran, 2006). However, this
thesis used a third trajectory analysis method: group-based trajectory modeling (GBTM).
GBTM was an extension of the finite mixture modeling (FMM) method that has been widely
used in various fields of trajectory analysis in the last 25 years (Nagin & Odgers, 2010).
GBTM was able to detect unobserved subgroups based on the multinomial logit function
(Nagin, 1999). As an extended form of FMM, GBTM parameters could be estimated using
maximum likelihood estimation (MLE) procedures. Since FMMs had no closed-form solution
to the maximum likelihood, the Expectation-Maximization (EM) algorithm would often be
applied to find maximized likelihood (Schlattmann, 2009). However, GBTM used a different
optimization method called the Quasi-Newton procedure to perform the maximization.
This thesis studied both GBTM with a single outcome and trajectory modeling with
multiple outcomes. Nagin constructed two extended trajectory models that can involve multiple outcomes. Group-based dual trajectory modeling (GBDTM) deals with two outcomes
combined with comorbidity or heterotypic continuity, while group-based multi-trajectory
modeling (GBMTM) could include more than two outcomes in one model with the same
subgroup weights among the outcomes (Nagin, 2005; Nagin, Jones, Passos, & Tremblay,
2018; Nagin & Tremblay, 2001).
The methodology was applied to the Korea health panel survey (KHPS) data, which
included 3983 individuals who were 65 years old or older at the baseline. GBTM, GBDTM,
and GBMTM were three approaches performed with two binary longitudinal outcomes - depression and anxiety. GBDTM was selected as the best model with this data set because it is
more flexible than GBMTM when handling group membership, and unlike GBTM, GMDTM
addressed the interrelationship between the outcomes based on conditional probability. Four
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depression trajectories were identified across eight years of follow-up: “low-flat” (n = 3641;
87.0%), “low-to-middle” (n = 205; 8.8%), “low-to-high” (n = 33; 1.3%) and “high-curve”
(n = 104; 2.8%). Also, four anxiety trajectories were identified with: “low-flat” (n =3785;
92.5%), “low-to-middle” (n = 96; 4.7%), “high-to-low” (n =89; 2.2%) and “high-curve” (n
= 13; 0.6%) trajectory groups. Female sex, the presence of more than three chronic diseases,
and income-generating activity were significant risk factors for depression trajectory groups.
Anxiety trajectory groups had the same risk factors except for the presence of more than
three chronic diseases.
To further study the GBTM, GBDTM and GBMTM approach, the simulation study was
also performed based on two correlated repeatedly measured binary outcomes. Compared
based on these two outcomes with different correlation levels (ρ = 0.1, 0.2, 0.4, 0.6). GBDTM was always a better model than GBTM when we were interested in the association
between the two outcomes. GBMTM could be used instead of GBDTM when the correlation
coefficients between two longitudinal outcomes were high
