The approaches described above allowed us to estimate biases induced by the adaptor (task 1) and previous decision (task 2) by splitting the data according to these variables. However, previous research (e.g.,
Bosch et al., 2020) has shown that this method of splitting data can partition meaningful variance and introduce or mask influences of other variables. For example, splitting by previous response can obscure a potential effect of the previous stimulus, which contributes to the serial choice patterns in the data of task 2. In order to estimate separate influences of different current-trial variables and previous-trial variables on the current decision, we constructed a generalized linear mixed model (GLMM) for task 2.
The GLMM contained a binomial link function to predict the current decision (counterclockwise or clockwise) based on the previous decision and other trial characteristics, as well as interactions between these factors. The factors in this regression model can be conceptually split into current-trial factors, history factors, and the group factor. The current-trial factors consist of the stimulus information (i.e., evidence direction) and button mapping on the current trial. The history factors consist of the stimulus information (i.e., evidence direction) and response characteristics (i.e., decision, button pressed, response time) of the previous trial. The group factor identifies the observer's group. An overview of the GLMM with group factor can be found in
Table 2 and is described below.
As we were interested in serial choice effects, we were interested in the influence of the previous decision on the current decision. Accordingly, we added the effect of previous decision (pDecision; clockwise or counterclockwise) as a factor to the model. In order to compare the effect of the previous decision with that of the stimulus information on the previous trial, we also added the identity (clockwise or counterclockwise from vertical) of the previous stimulus (pStimIdent). Next, to examine whether the influence of the previous decision or previous stimulus identity was modulated by the previous response time (pRt), we added interaction factors (pDecision × pRt and pStimIdent × pRt). Crucially, in order to investigate any group difference between these effects, we added further interaction effects between all aforementioned factors and the group factor.
All factors described thus far reflect history effects; however, observers’ decisions were primarily based on the stimulus information present in the current trial. Therefore, we included the orientation of the stimulus on the current trial to the model (cStimIdent) and allowed for the influence of the current stimulus to be modulated by group (cStimIdent × group). To account for the possibility of a difference in general response bias between groups, we also added group as a single factor to the model (the group-independent general response bias was reflected by the intercept of the model).
Additionally, we added factors to account for effects of button- and/or motor preferences. First, to account for a preference for responding with one button over the other and consequently for an effect of the button mapping on the perceptual decision, we added the button mapping as a factor to the model (cButtonMapping). Second, we added a factor to account for a possible motor repetition or alternation effect (pButtonXcButtonMapping). As with all other factors, we accounted for possible group differences in these effects by adding their interactions with group (cButtonMapping × group and pButtonXcButtonMapping × group).
Finally, we included the main effect of the previous response time (pRt) and its interaction with group (pRt × group). As these variables on their own provide no directional information, whether it be about the previous response or the stimulus information on the previous or current trial, they were unlikely to predict the decision on the current trial and were thus not expected to be significant factors in the model. We nevertheless added them to prevent an unexpected modulation by these variables showing up in any of the interaction effects and hence being misinterpreted as such.
Considering our groups were not matched based on IQ (see
Table 1), we also constructed a variation of the model described below that included total IQ as an additional factor. This allowed us to check whether any potential group differences could instead be explained away by the difference in total IQ. The factor (
TIQ) was implemented in a similar way to
group in the sense that we included
TIQ and its interactions with
pDecision,
pStimIdent,
pDecision × pRt,
pStimIdent × pRt,
cStimIdent,
cButtonMapping, and
pButtonXcButtonMapping.
To investigate how variability in the strength of sensory atypicalities may affect perceptual decision-making, we constructed a second GLMM within the ASD group (
n = 30; one subject was excluded due to missing AASP score). The factors included in this second GLMM were similar to those described above. The main difference was that the categorical
group factor was replaced by a continuous
AASP factor, which reflected the subjects’ AASP sum scores, both as a main factor and in all interactions that included
group. See
Table 3 for a full overview of the GLMM with AASP.
Before constructing the models, variables were (re-)coded as follows. Categorical predictors (pDecision, pStimIdent, cStimIdent, pButton, cButtonMapping, pButtonXcButtonMapping, and group) were coded using effect coding (−1/1). For pDecision, pStimIdent, and cStimIdent, −1 coded for the counterclockwise direction and 1 for the clockwise direction. For pButton, −1 coded for the down button and 1 coded for the up button. For cButtonMapping, −1 coded for a configuration where the up button indicated the counterclockwise direction and the bottom button indicated the clockwise direction, whereas 1 coded for the reverse configuration. For pButtonXcButtonMapping, a value of 1 indicated that pressing the same button as on the previous trial resulted in a clockwise response on the current trial, whereas −1 indicated that a repeated button press resulted in a counterclockwise response. Finally, for group, the ASD group was coded as 1 and the TD group as −1. Non-categorical predictors were (re-)coded in the following ways. Response times (pRt) were transformed to robust z-scores by removing the subject-wise median and scaling the result by the subject-wise median absolute deviation (constant = 1.48). AASP scores were z-scored.
We used the R-package lme4 (
Bates, Mächler, Bolker, & Walker, 2015) to fit a generalized linear model from the binomial family. We fitted both models with “subjects” as the only random grouping factor. For each fixed effect, we included its corresponding random slope coefficient but without random correlations, as the model did not converge.
For significance testing we report the Wald
z-test, which is valid only in the asymptotic regime assuming a multivariate normal sampling distribution of parameters and a proportional sampling distribution of the log likelihood to χ
2. Therefore, we must be very conservative in our interpretation of the reported
p values if the effects are not obvious from effect sizes alone. An overview of the model outputs can be found in
Tables 2 and
3.