  My dissertation revolves around Bayesian approaches towards constrained
statistical inference in the factor analysis (FA) model. Two interconnected
types of restricted-model selection are considered. These types have a natural
connection to selection problems in the exploratory FA (EFA) and confirmatory
FA (CFA) model and are termed Type I and Type II model selection. Type I
constrained-model selection is taken to mean the determination of the
appropriate dimensionality of a model. This type of constrained-model selection
connects with EFA in the sense of selecting the optimal dimensionality of the
latent vector. Type II model selection is taken to mean the determination of
appropriate inequality, order or shape restrictions on the parameter space. The
dissertation connects Type II constrained-model selection to CFA by focusing on
the determination of linear inequality constraints as expressions of the
direction and (relative) strength of factor loadings. The figures accompanying
this article are taken from the slides of my Division 5 Awards Symposium
Invited address at the APA 2015 Annual Convention in Toronto. These slides can
be retrieved from \url{https://github.com/CFWP/ConventionTalk}.
