Degree Granting Department
Epidemiology and Biostatistics
Charles Hendricks Brown, Ph.D.
Getachew Dagne, Ph.D.
Yiliang Zhu, Ph.D.
Paul Greenbaum, Ph.D.
Wei Wang, Ph.D.
Generalized Additive Model, EM algorithm, Monte Carlo EM, Markov Chain Monte Carlo, Metropolis-Hastings algorithm, nonlinear structural equation model
In order to personalize or tailor treatments to maximize impact among different
subgroups, there is need to model not only the main effects of intervention but also the variation
in intervention impact by baseline individual level risk characteristics. To this end a suitable
statistical model will allow researchers to answer a major research question: who benefits or is
harmed by this intervention program? Commonly in social and psychological research, the
baseline risk may be unobservable and have to be estimated from observed indicators that are
measured with errors; also it may have nonlinear relationship with the outcome. Most of the
existing nonlinear structural equation models (SEM’s) developed to address such problems
employ polynomial or fully parametric nonlinear functions to define the structural equations.
These methods are limited because they require functional forms to be specified beforehand and
even if the models include higher order polynomials there may be problems when the focus of
interest relates to the function over its whole domain.
To develop a more flexible statistical modeling technique for assessing complex
relationships between a proximal/distal outcome and 1) baseline characteristics measured with
errors, and 2) baseline-treatment interaction; such that the shapes of these relationships are data
driven and there is no need for the shapes to be determined a priori.
In the ALV model structure
the nonlinear components of the regression equations are represented as generalized additive
model (GAM), or generalized additive mixed-effects model (GAMM).
Replication study results show that the ALV model estimates of underlying relationships
in the data are sufficiently close to the true pattern. The ALV modeling technique allows
researchers to assess how an intervention affects individuals differently as a function of baseline
risk that is itself measured with error, and uncover complex relationships in the data that might
otherwise be missed. Although the ALV approach is computationally intensive, it relieves its
users from the need to decide functional forms before the model is run. It can be extended to
examine complex nonlinearity between growth factors and distal outcomes in a longitudinal
Scholar Commons Citation
Toyinbo, Peter Ayo, "Additive Latent Variable (ALV) Modeling: Assessing Variation in Intervention Impact in Randomized Field Trials" (2009). Graduate Theses and Dissertations.