Table 2.

Response Distributions From the Simple and Full Joint Mixture Models, Combined Across Both Nonspatial-Feature Dimensions

Item and response type	m simple	m full	Response combination	Joint probability density
Correlated
Correlated target	1	1	TCTO	${\mathrm{\varphi }}_{{\mu }_{\mathrm{C}},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{O}},{\kappa }_{\mathrm{O}}}$
Correlated swap	2	2	N1CN1O	${\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{4},{\kappa }_{\mathrm{O}}}$
Correlated swap		3	N2CN2O	${\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{-\frac{\pi }{4},{\kappa }_{\mathrm{O}}}$
Correlated swap		4	N3CN3O	${\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{O}}}$
Independent T*
Illusory conjunction	3	5	TCN1O	${\mathrm{\varphi }}_{{\mu }_{\mathrm{C}},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{4},{\kappa }_{\mathrm{O}}}$
Illusory conjunction	4	6	N1CTO	${\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{O}},{\kappa }_{\mathrm{O}}}$
Illusory conjunction		7	TCN2O	${\mathrm{\varphi }}_{{\mu }_{\mathrm{C}},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{-\frac{\pi }{4},{\kappa }_{\mathrm{O}}}$
Illusory conjunction		8	N2CTO	${\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{O}},{\kappa }_{\mathrm{O}}}$
Illusory conjunction		9	TCN3O	${\mathrm{\varphi }}_{{\mu }_{\mathrm{C}},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{O}}}$
Illusory conjunction		10	N3CTO	${\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{O}},{\kappa }_{\mathrm{O}}}$
Unbound guess	5	11	TCUO	${\mathrm{\varphi }}_{{\mu }_{\mathrm{C}},{\kappa }_{\mathrm{C}}}{\gamma }_{\mathrm{O}}$
Unbound guess	6	12	UCTO	${\gamma }_{\mathrm{C}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{O}},{\kappa }_{\mathrm{O}}}$
Independent N*
Illusory conjunction		13	N1CN2O	${\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{-\frac{\pi }{4},{\kappa }_{\mathrm{O}}}$
Illusory conjunction		14	N2CN1O	${\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{4},{\kappa }_{\mathrm{O}}}$
Illusory conjunction		15	N1CN3O	${\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{O}}}$
Illusory conjunction		16	N3CN1O	${\mathrm{\varphi }}_{\pi ,\kappa \mathrm{C}}{\mathrm{\varphi }}_{\frac{\pi }{4},{\kappa }_{\mathrm{O}}}$
Illusory conjunction		17	N2CN3O	${\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{O}}}$
Illusory conjunction		18	N3CN2O	${\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{-\frac{\pi }{4},{\kappa }_{\mathrm{O}}}$
Unbound guess	7	19	N1CUO	${\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\gamma }_{\mathrm{O}}$
Unbound guess	8	20	UCN1O	${\gamma }_{\mathrm{C}}{\mathrm{\varphi }}_{\frac{\pi }{4},{\kappa }_{\mathrm{O}}}$
Unbound guess		21	N2CUO	${\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\gamma }_{\mathrm{O}}$
Unbound guess		22	UCN2O	${\gamma }_{\mathrm{C}}{\mathrm{\varphi }}_{-\frac{\pi }{4},{\kappa }_{\mathrm{O}}}$
Unbound guess		23	N3CUO	${\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{C}}}{\gamma }_{\mathrm{O}}$
Unbound guess		24	UCN3O	${\gamma }_{\mathrm{C}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{O}}}$
Random guessing	9	25	UCUO	${\gamma }_{\mathrm{C}}{\gamma }_{\mathrm{O}}$

Note: The simple joint model includes only 9 parameters, as numbered by m_simple, where m indicates the index of each response combination; the full joint model includes all 25 parameters, as numbered by m_full. In the column for joint response combinations, the color response is always written first. In the rightmost column, φ is a von Mises probability density function, with concentration ${\kappa }_{\mathrm{C}}$ or ${\kappa }_{\mathrm{O}}$ (standard deviation $\sigma =\sqrt{1/\kappa }$) and means of ${\mu }_{\mathrm{C}}$, 90°, −90°, and 180° (color) or ${\mu }_{\mathrm{O}}$, 45°, −45°, and 90° (orientation) for the target (T), critical nontarget (N1), adjacent nontarget (N2), and diagonal nontarget (N3), respectively; ${\gamma }_{\mathrm{C}}$ and ${\gamma }_{\mathrm{O}}$ are uniform distributions that reflect the probability of responding at random. Rows 1 to 4 describe correlated responses: reporting both features of the target object or misreporting both features of the same nontarget (correlated swap errors). Rows 5 to 12 describe independent T* errors: reporting one target feature and one nontarget feature (illusory conjunctions) or reporting one target feature and guessing the other feature (unbound guesses). Rows 13 to 25 describe the remaining errors (e.g., misreporting features from different nontargets and guessing).