  Adaptive learning technology solutions often use a learner model to trace
learning and make pedagogical decisions. The present research introduces a
formalized methodology for specifying learner models, Logistic Knowledge
Tracing (LKT), that consolidates many extant learner modeling methods. The
strength of LKT is the specification of a symbolic notation system for
alternative logistic regression models that is powerful enough to specify many
extant models in the literature and many new models. To demonstrate the
generality of LKT, we fit 12 models, some variants of well-known models and
some newly devised, to 6 learning technology datasets. The results indicated
that no single learner model was best in all cases, further justifying a broad
approach that considers multiple learner model features and the learning
context. The models presented here avoid student-level fixed parameters to
increase generalizability. We also introduce features to stand in for these
intercepts. We argue that to be maximally applicable, a learner model needs to
adapt to student differences, rather than needing to be pre-parameterized with
the level of each student's ability.
