Table 1. Mixture model components describing the distribution of responses within a single feature dimension.

θ is the true feature value of the target item, and $\widehat{\theta }$ the feature value reported by the subject (range −π < θ ≤ π). φ_i is the true feature value of the ith non-target item (m in total). ϕ_σ is the von Mises distribution with mean zero and standard deviation σ. Diagrams indicate how the response probabilities contributed by each component are distributed around target (T) and non-target (N) feature values (for illustration, only two non-targets are shown). The model proposed by Zhang & Luck (2008) is described by rows 1–2 (target and uniform components). Bays et al. (2009) added a third component (row 3) to distinguish non-target from uniform responses.

k		Mixture component	Response type	Probability density (pk)
1	T		target	${\varphi }_{\sigma }\left(\widehat{\theta }-\theta \right)$
2	U		uniform	$\frac{1}{2\pi }$
3	N		non-target	$\frac{1}{m}\sum _i^m{\varphi }_{\sigma }\left(\widehat{\theta }-{\phi }_i\right)$