Table 3.

Response Distributions From the Triple Joint Mixture Model, Combined Across Color, Orientation, and Location Dimensions

Location response and nonspatial-feature response	m triple	Response combination	Joint probability density
Target location
Correlated target	1	TCTOTL	${\mathrm{\varphi }}_{0,{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{O}},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{L}},{\kappa }_{\mathrm{L}}}$
Correlated N1	2	N1CN1OTL	${\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{4},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{L}},{\kappa }_{\mathrm{L}}}$
Correlated N2	3	N2CN2OTL	${\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{-\frac{\pi }{4},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{L}},{\kappa }_{\mathrm{L}}}$
Correlated N3	4	N3CN3OTL	${\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{L}},{\kappa }_{\mathrm{L}}}$
Other	5	UCUOTL	${\gamma }_{\mathrm{C}}{\gamma }_{\mathrm{O}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{L}},{\kappa }_{\mathrm{L}}}$
Nontarget N1 location
Correlated target	6	TCTON1L	${\mathrm{\varphi }}_{{\mu }_{\mathrm{C}},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{O}},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{L}}}$
Correlated N1	7	N1CN1ON1L	${\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{4},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{L}}}$
Correlated N2	8	N2CN2ON1L	${\mathrm{\varphi }}_{-\mathrm{\pi },{\mathrm{\kappa }}_{\mathrm{C}}}{\mathrm{\varphi }}_{-\frac{\mathrm{\pi }}{2},{\mathrm{\kappa }}_{\mathrm{O}}}{\mathrm{\varphi }}_{\mathrm{\pi },{\mathrm{\kappa }}_{\mathrm{L}}}$
Correlated N3	9	N3CN3ON1L	${\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{L}}}$
Other	10	UCUON1L	${\gamma }_{\mathrm{C}}{\gamma }_{\mathrm{O}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{L}}}$
Nontarget N2 location
Correlated target	11	TCTON2L	${\mathrm{\varphi }}_{{\mu }_{\mathrm{C}},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{O}},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{L}}}$
Correlated N1	12	N1CN1ON2L	${\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{4},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{L}}}$
Correlated N2	13	N2CN2ON2L	${\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{-\frac{\pi }{4},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{L}}}$
Correlated N3	14	N3CN3ON2L	${\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{L}}}$
Other	15	UCUON2L	${\gamma }_{\mathrm{C}}{\gamma }_{\mathrm{O}}{\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{L}}}$
Nontarget N3 location
Correlated target	16	TCTON3L	${\mathrm{\varphi }}_{{\mu }_{\mathrm{C}},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{{\mu }_{\mathrm{O}},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{L}}}$
Correlated N1	17	N1CN1ON3L	${\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{4},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{L}}}$
Correlated N2	18	N2CN2ON3L	${\mathrm{\varphi }}_{-\frac{\pi }{2},{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{-\frac{\pi }{4},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{L}}}$
Correlated N3	19	N3CN3ON3L	${\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{C}}}{\mathrm{\varphi }}_{\frac{\pi }{2},{\kappa }_{\mathrm{O}}}{\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{L}}}$
Other	20	UCUON3L	${\gamma }_{\mathrm{C}}{\gamma }_{\mathrm{O}}{\mathrm{\varphi }}_{\pi ,{\kappa }_{\mathrm{L}}}$

Note: The triple joint model includes 20 parameters, as numbered by mtriple, where m indicates the index of each response combination. In the rightmost column, φ is a von Mises probability density function, with concentration ${\kappa }_{\mathrm{C}}$, ${\kappa }_{\mathrm{O}}$, or ${\kappa }_{\mathrm{L}}$ (standard deviation $\sigma =\sqrt{1/\kappa }$) and means of 0°, 90°, −90°, and 180° (color or location) or 0°, 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.