The value-learning models of the reinforcement-learning and computational-psychiatry literature, written as 'frmtmb' families so that each of their parameters is an ordinary distributional parameter with its own linear predictor. A learning rate then takes a condition effect, a smooth term or a correlated per-subject random effect the way a mean does, and it comes back with a standard error, which is what a separate model per group does not give. Eight families share one recursion that walks trials once and updates every subject at each step: the two-armed delta learner and its dual-rate and counterfactual variants, a Kalman filter over the restless four-armed bandit of Daw and others (2006) with an optional exploration bonus, the two-stage model-based and model-free hybrid of Daw and others (2011), prospect-theory and outcome-representation learners for the Iowa gambling task, and a joint model of choices and response times in which the learned value difference drives the drift rate of a Wiener diffusion. Families are named as 'hBayesDM' names them where a name exists. Each one is checked by an identity against an independent 'Stan' program of the same model at the same estimates, and by parameter recovery at a realistic scale.