Fig. 2: Analysis of GLM-HMM fits.

a Test log-likelihood (LL) of the GLM-HMM with and without multinomial GLM transition, as a function of the number of latent states, using pooled data from all 37 animals in our dataset. The model with GLM transition (GLM-T) outperformed the basic GLM-HMM for all models with multiple states. The four-state model (purple box) came close to saturating the test log-likelihood yet had highly interpretable states, and we therefore selected it for further analysis. Data are presented as mean test log-likelihood; error bars denote 68% bootstrap confidence intervals across cross-validation folds (5-fold cross-validation). b The fitted observation-GLM weights for the four-state model revealed two Engaged states, which we refer to as Engaged-L and Engaged-R. In these two states, the weight on stimulus contrast (Δ contrast) was large and the bias weight was negative or positive, respectively. The other two states exhibited small stimulus weight and a large left or right bias, leading us to refer to them as Biased-L and Biased-R states. These biased or disengaged states also exhibited small weights on previous choice, indicating a greater tendency to preserve. c State-specific psychometric curves for each of the four states in the fitted model, which show how the GLM weights in (b) map signed stimulus contrast into the probability of a rightward choice. d The model-based psychometric curve for an example mouse is a linear combination of the state-specific psychometric curves shown in (c), and provides a close match to the empirical choice data for an example mouse (green triangles). Source data are provided as a Source Data file. Stim. stimulus.