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 six 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. We introduce features to stand in for student-level intercepts and argue that to be maximally applicable, a learner model needs to adapt to student differences. The results of our comparisons show the general importance of modeling recent learning for all datasets, with special importance for terms that model memory in datasets involving fact learning. [This article was published in "IEEE Transactions on Learning Technologies" (EJ1324365).]