We obtained the monocular contrast detection thresholds, dichoptic masking thresholds, and stereo thresholds by fitting logistic psychometric functions using Palamedes.
28 In all cases, the lapse rate was fixed at 1% for fitting. The thresholds for the 2AFC and four-alternative-force choice data were calculated at a proportion correct of 75.0% and 62.5%, respectively. We used parametric bootstrapping routines to obtain bootstrapped estimates of standard error and 95% confidence intervals (1000 samples).
We obtained interocular suppression weights by fitting our data with the two-stage model of contrast gain control based on that described by Meese et al.
29 For the case where targets are presented to the left eye, the response at the first stage is given by:
\begin{equation}res{p_L} = \frac{{{{\left( {{g_L} \times {C_L}} \right)}^m}}}{{1 + {g_L} \times {C_L} + {\omega _R} \times {g_R} \times {C_R}}},\end{equation}
where
CL and
CR are the contrasts of the target in the left eye and the mask in the right eye, respectively. The three fitted parameters are the gain in the left and right eyes (
gL and
gR) and the interocular masking weight from the right eye
wR. The exponent
m is set at 1.3 based on previous results.
30 The target is only presented to one eye at a time, so for targets presented in the left eye the second stage is given by
\begin{equation}\;resp = \frac{{resp_L^p}}{{1 + resp_L^q}},\end{equation}
where
p, and
q are fixed at
p = 8, and
q = 6.6 based on previous results. Therefore, accounting for left and right eye target conditions requires four fitted model parameters:
gL,
gR,
wL, and
wR. It is worth noting that the construction of
Equation 1 means that the masking weight parameters for each eye have an effect that is separate from the input gain parameters. Any imbalances found in masking weight are additional to the effects of any imbalances in input gain. Assuming a constant internal noise variance, predicting thresholds requires simply solving for some criterion value of
resp (we chose to solve for a value of
resp = 1). We fit this model in MATLAB using the fminsearch function to minimize the root mean square error between the thresholds predicted by the model and the empirical data.
To obtain the balance point of each subject, we fitted the proportion of trials in which they reported that the left side of the grating tilted up by using a logistic function. The estimated midpoint of the logistic function defines the point of subjective equality, which indicates the balance point where the two eyes were balanced in binocular combination. For this analysis, the lapse rate of 1% affected both the upper and lower asymptotes (gamma and lambda parameters) of the psychometric function. The estimated points of subjective equality were derived from 1000 parametric bootstrapped samples.