Can you believe your eyes? Positive schizotypy is associated with increased susceptibility to the Müller-Lyer illusion

Background and hypothesis: Visual illusions provide a unique opportunity to understand cognitive and perceptual alterations in schizophrenia-spectrum conditions. Schizophrenia patients often exhibit increased susceptibility to the Müller-Lyer illusion. Here, we investigate susceptibility to the Müller-Lyer visual illusion in the general population with different levels of schizotypy. Study design: We assessed a population-based convenience sample ( N = 263) on an online platform. In addition to basic demographics, participants completed the Müller-Lyer illusion, the Cardiff Anomalous Perceptions Scale (CAPS) to measure perceptual anomalies, and the Multidimensional Schizotypy Scale – Brief (MSS-B) for schizotypic traits. To evaluate what predicts susceptibility to the illusion, we fitted a large set of multilevel logistic regression models and performed model averaging over the coefficients. Study results: We found support for increased illusion susceptibility among individuals with high positive schizotypy. However, we did not find a comparable effect for anomalous perceptions alone, or for negative or disorganized schizotypy. Conclusions: The increased Müller-Lyer effect in positive schizotypy might be specific to delusion-like beliefs and magical ideation. Further research is needed to clarify how a hierarchical Bayesian formulation of brain function (e.g. imbalances between bottom-up perceptual processing and substantial reliance on prior expectations) can account for the Müller-Lyer effect in schizophrenia-spectrum conditions.


Introduction
Schizophrenia is a severe psychiatric disorder with significant variance and heterogeneity in symptom profile, social functioning, treatment response, and clinical outcome (Guloksuz and van Os, 2018).Schizophrenia is associated with various cognitive and perceptual deficits, however, the background of these dysfunctions and their symptomspecific connections are not fully understood (Butler et al., 2008).Growing evidence supports the validity of schizotypy, a multidimensional construct that can explain the heterogeneity in the etiological and developmental trajectory of schizophrenia risk (Kwapil and Barrantes-Vidal, 2015).Multidimensional schizotypic traits refer to a set of temporally stable features in the general population that parallel the positive, negative and disorganized domains of signs and symptoms of schizophrenia (Bentall et al., 1989;Kwapil et al., 2018;Liddle, 1987;Wuthrich and Bates, 2006), although the exact nature of these dimensions is not settled (Oezgen and Grant, 2018;Polner et al., 2021).The indicators of the three dimensions can range from mild alterations to severe deficits.A dimensional account of schizotypy and schizophrenia posits that multidimensional schizotypic traits (e.g.unusual experiences and weird beliefs, in case of the positive dimension) and symptoms of schizophrenia-spectrum disorders (e.g.full-blown hallucinations and psychotic delusions) lie on the same continuum (Claridge, 1994).This account is supported by experiences resembling the symptoms of schizophrenia in milder, subclinical forms in the general population (van Os et al., 2009) and by vast empirical evidence showing that schizotypy overlaps with symptoms of schizophrenia in terms of etiology and neurocognitive alterations as well (reviewed in Ettinger et al., 2014Ettinger et al., , 2015;;Nelson et al., 2013;Siddi et al., 2017;Steffens et al., 2018).Thus, schizotypy is a useful construct for testing neurocognitive models of schizophrenia symptoms in a dimensional framework (Markon et al., 2011;Michelini et al., 2021).
Schizotypy has been linked to early visual perceptual deficits that are similar to those reported in schizophrenia (Ettinger et al., 2015).To understand these visual perceptual deficits in schizophrenia and schizotypy, a stream of recent research has focused on visual illusions (for reviews see King et al., 2017 andNotredame et al., 2014).Visual illusions demonstrate a systematic mismatch between the raw sensory input and the constructed perceptual experience (Gregory, 1997b;Silverstein and Keane, 2011) and can be categorized into higher-and lower-level illusions based on whether they reflect early vs. late steps in visual processing (the Herrmann-grid and the Müller-Lyer illusion being respective examples).Higher-level visual illusions trigger complex cognitive and perceptual mechanisms and demand top-down control and prior knowledge, whereas lower-level illusions rely on the functions of the early visual pathway up to the V1 (Gregory, 1997a;King et al., 2017).An influential hypothesis in the literature states that individuals with schizophrenia-spectrum disorders exhibit reduced susceptibility to higher-level visual illusions relative to controls due to weakened topdown control and deficits of higher-level perceptual organization (Butler et al., 2008;Notredame et al., 2014;Silverstein and Keane, 2011).Most studies using higher-level visual illusions, such as the Ebbinghaus illusion (Tibber et al., 2013;Uhlhaas et al., 2006;Yang et al., 2013) or the Hollow-mask illusion (Dima et al., 2009;Keane et al., 2013), suggest decreased susceptibility in schizophrenia.In line with continuum models, reduced susceptibility to the Ebbinghaus illusion has also been associated with schizotypy (Bressan and Kramer, 2013).
However, the Müller-Lyer illusion (Fig. 1) is an exception, as it is a high-level visual illusion that seems to contradict these results.The Müller-Lyer illusion is a frequently studied high-level illusion (same class as the Ebbinghaus illusion) (Gregory, 1997b;Segall et al., 1966), yet none of the studies has shown decreased susceptibility to the Müller-Lyer illusion in schizophrenia-spectrum conditions (King et al., 2017).The essence of the Müller-Lyer effect is that the lines with the fins of the arrow protruding outward are perceived longer, while the lines with the arrow fins pointing inward are perceived shorter.The illusion effect might be explained by the influence of learned visuo-spatial regularities in perception; in other words, it is driven by prior expectations.Intriguingly, some studies have found no difference between healthy control groups and patients with schizophrenia (Grzeczkowski et al., 2018;Tam et al., 1998), and others have even shown increased susceptibility in schizophrenia (Kantrowitz et al., 2009;Letourneau, 1974;Parnas et al., 2001;Weckowicz and Witney, 1960).These counterintuitive results raise the question whether the relationship between schizophrenia-spectrum disorders and high-level visual illusions is uniform, and urge scientists to further investigate the susceptibility to the Müller-Lyer illusion.There are separate lines of evidence in the literature leading to competing predictions regarding the association of the Müller-Lyer illusion effect with psychosis-spectrum phenotypes (decreased or increased susceptibility to high-level illusions).For instance, researchers using a Bayesian predictive coding framework claim that hallucinations are associated with excess reliance on prior expectations (Corlett et al., 2019;Powers et al., 2017;Sterzer et al., 2018), which might provide an explanation for the increased susceptibility to the Müller-Lyer illusion.Whereas widely reported visual perceptual deficits implicate a tendency of decreased susceptibility to high-level illusions (Butler et al., 2008;King et al., 2017;Notredame et al., 2014).
Here, building on the continuum model of psychosis-proneness (Claridge, 1994;Ettinger et al., 2014Ettinger et al., , 2015;;Nelson et al., 2013;Siddi et al., 2017;Steffens et al., 2018), we studied susceptibility to the Müller-Lyer illusion in a population-based convenience sample showing varying levels of schizotypic traits.Our aim is to establish that the increased susceptibility to the Müller-Lyer illusion in schizophrenia (King et al., 2017) can be extended to schizotypic traits.By doing so, we move beyond the simplifying dichotomy of case/control designs, which means increased reliability and validity (Markon et al., 2011) and reduced confounding by non-specific disease factors such as medications (Schneider et al., 2002).To further improve the accuracy and validity of our research, we designed an illusion task that increased engagement with different variants of the illusion.
Furthermore, we argue that the increased susceptibility to the Müller-Lyer illusion might be specifically linked to the positive dimension of the schizophrenia-spectrum.Even the different higher-level illusions have been suggested to be caused by unique mechanisms (Cretenoud et al., 2020).In the case of the Müller-Lyer illusion, this mechanism might be relying on expectations and inner models of the world (Howe and Purves, 2005;Notredame et al., 2014;Segall et al., 1966).Based on the theory that the positive dimension is associated with a greater top-down influence of previous knowledge during perceptual inference (Corlett et al., 2019;Sterzer et al., 2018), we hypothesized that increased susceptibility to the Müller-Lyer illusion will be specifically related to the positive dimension.The positive dimension however can be further divided into distinct categories of perceptual (hallucination-like) and belief-specific (delusion-like) traits (Bell et al., 2006;Oezgen and Grant, 2018).Previous research suggested that anomalous perceptions and anomalous beliefs rely on different hierarchical levels of prior knowledge (perceptual vs. abstract cognitive), and alterations in visual perception could be sub-dimension specific (Davies et al., 2018).Given our focus on a visual perceptual paradigm, we hypothesized that the performance on the Müller-Lyer illusion would mainly relate to anomalous perceptions.

Participants
Data were collected online via a dedicated Facebook-page 'Unusual Experiences Research' (Szokatlan Élmények Kutatás).We posted an ad with a call to take part in a study of perception and vivid mental experiences.The audience was set to those living in Hungary, aged between 18 and 59, and matching the following interests: 'Science, Community issues, Self-knowledge (psychology), Psychology, Self care, Engineering, Innovation, Photography or Love Nature'.Advantage detailed targeting was turned on.Maximum advertising budget was set to 10,000 HUF.The ad reached 10,684 accounts (71 % women) and generated 878 clicks on the link leading to the survey platform.A total of 390 participants from the general population completed our survey.After applying various exclusion criteria to ensure data quality (please see below and in the Data quality control section in Supplementary Material B.), we performed analyses in a sample of 263 subjects.(See descriptive statistics in Table 1.)Based on meta-analyses, we expected an effect size for an association between schizotypy scores and cognitive/perceptual task performance to be around 0.2 (Siddi et al., 2017;Steffens et al., 2018), in which case a sample size of 259 (with 0.05 significance level) allows for 0.9 statistical power.In order to avoid confounding by aging-related schizotypy-like alterations such as anhedonia, amotivation and subtle cognitive impairments, a few participants older than 60 (N = 13) were excluded from the analysis.Before completing the survey, all participants provided informed consent.The research was approved by the Hungarian United Ethical Review Committee for Research in Psychology.

Questionnaires
All materials were presented on an online survey platform, formr (Arslan et al., 2020) that could be opened from any browser.In order to optimize measurement, before performing the Müller-Lyer illusion task, participants were asked to find a calm place with good light conditions, wear glasses or contact lenses, if needed, and set the maximum brightness on their device.
Participants first completed a demographic questionnaire with the possibility of reporting previous clinical diagnoses.Then, they were also asked to fill out two schizotypy questionnaires, the Cardiff Anomalous Perceptions Scale (CAPS, Bell et al., 2006) and the Multidimensional Schizotypy Scale -Brief (MSS-B, Gross et al., 2018).We used the CAPS, a 32-item self-report scale to measure a specific aspect of schizotypy, proneness to anomalous perceptual experiences.The CAPS items are written in neutral language lacking any kind of evaluative tone (e.g.expressions such as weird, strange, or magical), which makes it possible to measure purely the presence of anomalous perceptual experiences.Additionally, the CAPS measures not only unusual visual and auditory experiences but covers the olfactory and gustatory modalities and phenomena related to temporal-lobe disturbances as well.The CAPS was adapted into Hungarian (Kovács, 2021) with high methodological rigor using the translation, back-translation methodology (Beaton et al., 2000;Brislin, 1970).The back-translation was reviewed by Dr. Vaughan Bell, who originally constructed the CAPS.
Multidimensional schizotypic traits were measured with the MSS-B, a self-report questionnaire containing 38 yes/no items that are grouped into subscales measuring positive (13 items), negative (13 items) and disorganized schizotypy (12 items).

Müller-Lyer illusion
After completing the above questionnaires, participants responded to 15 variants of the Müller-Lyer illusion (see Supplementary Material A. for the instructions).In order to control for bias and prior expectations, to increase engagement, and to improve the validity of the illusion effect, the angle of the arrow fins was manipulated (15 • , 30 • , 45 • -the standard illusion, 60 • , 75 • ), as well as the length of the shafts (80 %, 100 %, and 120 % ratio conditions).The angle of the fins was measured between the inward turning fins and the horizontal illusory line (outward turning fin angles were the complementary).The length of the fins was 30 % of the fixed shaft length.In all conditions, the shaft with the outwards turning fins was presented above the shaft with the inward turning fins and all stimuli were presented horizontally.In two shaftlength (ratio) conditions, a real length difference was generated between the two target lines in order to filter out random/noncompliant/low-effort respondents (ratio-80 %) and control for bias (ratio-120 %).In the ratio-100 % condition (standard illusion), the two shafts were identical in length; in the ratio-120 % condition, 1 the lower line with the inward turning fin was 120 % the length of the upper line; while in the ratio-80 % (control condition 2 ), the lower-line was 80 % the length of the upper one.Stimuli were generated with Matlab.The illusions were presented in a fixed pseudorandomized order to each participant, due to technical constraints.The illusions were present as long as the participant gave a response and decided to move on to the next trial.Participants were asked on each trial to decide on a 5-point Likert scale whether there is a length difference between the two shafts or the target lines are identical ('Is one line longer than the other?' 1 = 'The top one!'; 2 = 'Maybe the top one'; 3 = 'They are the same size'; 4 = 'Maybe the bottom one'; 5 = 'The bottom one!').A binary susceptibility variable was calculated from ordinal responses.In the ratio-100 % condition, seeing the upper line longer was considered to indicate susceptibility to the illusion, while in the ratio-120 % condition, perceiving the upper line longer or the two lines identical in length was considered an illusion effect.For data quality control, please see the Supplementary Material B.
Parameters of the illusions (ratio and angle) were included in the statistical analysis as nuisance regressors to adjust our models for their confounding effect.
For statistical inference, logistic mixed effect models were fitted and we performed model averaging to overcome the uncertainty in coefficient estimates of a single best fitting model (Harrison et al., 2018).In each model, the dependent variable was a binary variable indicating the presence of the illusion effect on a given trial.To account for the nested property of our data, random effects were included in our models.A random intercept for participants represented between-subject variance in susceptibility, while a random slope for ratio conditions was used to capture variability across subjects in the influence of ratio manipulation on the illusion effect (models including a random slope for the effect of angle did not converge).
We constructed a set of models predicting inter-individual variability in illusion susceptibility.Stimulus features such as ratio and angle were entered into every model to remove variation in illusion susceptibility that is unrelated to differences between individuals and allow a more precise estimation of the association with schizotypic traits.Each model included an additional predictor from a set of schizotypy-related variables (positive, negative, disorganized and total score on the MSS-B and the CAPS total score) and another optional control variable (no control, device, age [scaled], or sex).Age and sex were taken into consideration as they are associated both with schizotypy (Kwapil et al., 2020;Mason and Claridge, 2006) and with illusions (age: Cretenoud et al., 2020; sex: 1 Since the lower line was always equipped with the inwards turning fins, the ratio-120 % condition acted against the illusion effect and made it more difficult to -accurately -perceive the lower line shorter.Therefore, we hypothesized that this condition will lead to perceiving the two lines falsely identical in length and the illusion effect will be enhanced. 2We argued that in the ratio-80 % condition participants who have intact vision and conscientiously follow the instructions should always give a correct response; thus; erroneous performance in this condition is indicative of fundamental problems with vision and/or lack of compliance.Shaqiri et al., 2018).Note that our research question is about schizotypic traits and does not concern age-or sex-related differences; we included these in the control variable set to account for potential confounding.
We used this set of predictor variables to build 20 models with diverse fixed effect structures (find the exact models in the Supplementary Material C.) so that each schizotypy-related and control variable appeared in the models with similar frequency, which was important for obtaining reliable results with model averaging (see below).We calculated VIF (variance inflation factor) scores for each model to evaluate potential multicollinearity issues.
In order to account for the uncertainty of estimates obtained from single models, we performed an information theoretical model averaging over the coefficients.It has been shown (Lukacs et al., 2010), that "classical" model selection methods (e.g.stepwise selection) are prone to severe bias, especially for weakly correlated variables, whereas model averaging guards against spurious results.In other words, model averaging can qualitatively combine insights obtained with several models in an established framework.Thereby it can even out the overestimation and underestimation of individual models, and avoids the pitfalls of basing inference on a single best model.Specifically, model averaging performs inference using multiple models: one assigns a weight to each model based on its goodness-of-fit (we used the corrected Akaike Information Criterion [AICc]) and then computes a weighted average for each coefficient.In order to improve specificity at the cost of sensitivity, we performed model averaging with the more conservative full average approach that pretends as if all predictors were included in all models, but the variance and coefficients are set to zero for those predictors that are not explicitly entered into a given model (Burnham and Anderson, 2004).Finally, we used partially standardized coefficients, which is recommended when averaging models with different sets of predictors (Cade, 2015).

Distribution and covariation of schizotypal traits
Descriptive analysis shows that the distribution of all MSS-B subscales was positively skewed, which is in line with earlier reports on the distribution of schizotypal traits in the general population (Barrantes-Vidal et al., 2010).Compared to the U.S.-based MSS-B validation sample of Gross et al. (2018), our sample has a higher mean of positive (our sample: 2.56 [2.47] vs. Gross et al.: 1.93 [2.34]) and negative schizotypy (our sample: 2.93 [2.59] vs. Gross et al.: 1.86 [2.47]) and a smaller mean of disorganized schizotypy (our sample: 1.01 [1.86] vs. Gross et al.: 1.73 [2.85]).Thus, highly schizotypal individuals might have been overrepresented in our sample, compared to other studies in the literature.This might be due to selection bias induced by recruiting individuals using ads posted on Facebook.Furthermore, we observed a positive correlation (See Table 1.) between positive schizotypy (MSS-B) and proneness to anomalous perceptions (CAPS), confirming that the two scales measure overlapping yet separable constructs.

Distribution of responses to the Müller-Lyer illusion variants
Descriptive statistics of the illusion effect confirm that the ratio-80 % condition was a good control condition (Fig. 2.).For later analysis, responses to the ratio-80 % stimuli were excluded, since the illusion effect cannot be interpreted in this design and this condition was included only as a control.
Due to the extreme distribution observed in response to the stimulus configuration that was presented on the first trial (ratio-120 %, degree-75 • ), data in response to this stimulus was excluded from further analysis.In order to keep the factorial structure (2 × 4, df = 7) of our design, the ratio-100 %, degree-75 • condition was excluded too.

Associations of schizotypy with susceptibility to the Müller-Lyer illusion
We considered several variables that could explain differences in susceptibility to the illusion.By constructing models with only a subset of these variables as predictors, we not only improved model convergence rate, but more importantly we could avoid multicollinearity issues (max VIFs <1.05, details in Supplementary Material C.).Then, by averaging over all the models, we could account for the uncertainty of estimates obtained from single models, and even out the overestimation and underestimation.Model averaging does not function as a test that is dependent on arbitrary cutoff values (e.g.p-value greater than significance level).Instead, it provides quantitative evidence (Burnham and Anderson, 2002)  are conditional on the null hypothesis being true), information-theoretic methods deal with post-data probability statements (e.g.Akaike weights are model probabilities conditional on the data) (Burnham and Anderson, 2004).Nevertheless, for the sake of completeness, we report individual model statistics in the Supplementary Material D. Furthermore, we show coefficients from multilevel models showing the bivariate associations between each predictor and the outcome in Fig. 3C.
Coefficients estimated with model averaging and sums of model weights related to the variables are shown in Fig. 3A and B, respectively.As Akaike weights are defined as the probability that a particular model is the best of the model set given the data, higher sum values reflect that the variable was entered in the more likely models (based on Kullback-Leibler information).In the averaged model, positive schizotypy was positively associated with increased susceptibility to the Müller-Lyer illusion (Fig. 3D), whereas other dimensions of schizotypy or the total schizotypy score were not.Perceptual anomalies were also somewhat associated with enhanced susceptibility to the Müller-Lyer illusion, yet, (compared to positive schizotypy) smaller sum of model weights suggest weaker explanatory strength (also note that in Supplementary Material D. bootstrapped 95%CI interval of the coefficient contains 0 and the bootstrapped distribution is concentrated in a lower range).Therefore, our hypothesis was partially confirmed.With regards to experimental variables, participants were more susceptible to the Müller-Lyer illusion in the ratio120% condition, as compared to the ratio-100 % condition (coded as the reference level, Fig. 3E).Furthermore, there was a nonlinear effect of angle: participants showed a decreased susceptibility from 15 • to 45 • degree conditions (in line with earlier findings of Pressey and Martin, 1990); however, in the degree-60 • conditions, participants showed a slightly increased susceptibility (Fig. 3F).Finally, women were more susceptible than men (Fig. 3G).Note that there were large overlaps between the confidence intervals and the bootstrapped distributions of the coefficients of positive schizotypy, sex, and ratio (Fig. 3C, Supplementary Material C & D).Thus, the findings do not imply that any of these factors is a more informative predictor of illusion susceptibility than the other.

Discussion
Our aim was to test altered perception in the schizophrenia-spectrum by investigating the association between schizotypic traits and a wellestablished visual perceptual paradigm, the Müller-Lyer illusion.Our results confirm the hypothesis of increased susceptibility to the Müller-Fig.2. Distribution of responses among the illusion conditions.The 15 Müller-Lyer conditions (3 ratio × 5 degree) designed for the research and the distribution of the responses representing susceptibility.Susceptibility in the ratio-100 % was calculated as response < 3, and in the ratio-120 % condition response ≤ 3.
Lyer illusion in participants with high positive schizotypy, consistent with previous findings in schizophrenia (King et al., 2017).Our results, however, did not support that anomalous perceptions would specifically account for the increased illusion magnitude.This implies that an aspect of positive schizotypy other than anomalous perceptions is related to the illusion magnitude.Comparing the item content of the instruments we used to assess anomalous perceptions and positive schizotypy (CAPS and the MSS-B, respectively) reveals that the positive schizotypy subscale is mostly comprised of items referring to odd beliefs, while only a few items tap anomalous perceptions (Kwapil et al., 2018).Therefore, it is likely that belief-related aspects of positive schizotypy could be key factors accounting for the susceptibility to the Müller-Lyer illusion.Fig. 3.The association between susceptibility to the Muller-Lyer illusion and multidimensional schizotypic traits.Panels A-B represent the results of the key statistical analyses, performed with model averaging, a quantitative summary of multiple models.We present panels C-G only for illustration purposes; please note that in contrast to the key analyses, these do not take into account the nested structure of the data, task parameters, and potential confounders.A. Predictors of susceptibility to the Müller-Lyer illusion according to logistic mixed effects modeling.Partially standardized coefficient estimates are based on model averaging, using the full average approach (see details in Statistical Analysis).Bootstrapped distributions of the coefficient estimates and confidence intervals are presented in the Supplementary Materials D. B. Sum of model weights per variable.During model averaging, each model receives a weight, based on its goodness-of-fit as indicated by the corrected Akaike Information Criterion [AICc].Variables with higher weights can be considered more important in that they occur more often in models providing a better description of the data.Note that since ratio and angle were a priori included in every model to adjust for experimental parameters, sum of model weights is not informative for these predictors.C. We report coefficients from multilevel models showing the bivariate associations between each predictor and the outcome.To facilitate comparability between these effects, the only random effect we added was a random intercept per participant.Each color indicates a separate model.The error bars show 95 % confidence intervals.Note that in contrast to (A), fully standardized coefficients are shown.Following Gelman (2008), the continuous predictors were divided by 2 standard deviations, which yields coefficients that are directly comparable to the raw coefficient estimates for binary predictors.D-G.In these figures on the Y axis, we show the binary illusion susceptibility variable plotted against positive schizotypy score from the MSS-B questionnaire (D), ratio of the two lines (E), angle of the shafts (F) and participants' sex (G), respectively.Each faded dot indicates a single response (jittered width = 0.1, height = 0.075), while in the middle with a darker shade we plotted mean susceptibility scores and standard errors.CAPS: total score on the Cardiff Anomalous Perceptions Scale; MSS-B: Multidimensional Schizotypy Scale -Brief total score and score of subscales (positive, negative and disorganized schizotypy).
Previous research has suggested that visual perception is affected differently by hallucination-proneness and delusion-proneness, the two subdimensions of positive schizotypy (Davies et al., 2018).Furthermore, hallucinations and delusions are hypothesized to be caused by alterations at different levels of the information processing hierarchy, which could also explain why we did not find a strong association between anomalous perceptions and the illusion magnitude.
More generally, our results are in line with the notion of the psychosis-spectrum and support the growing body of evidence on perceptual alterations in schizotypy from a fresh perspective (Ettinger et al., 2015).Previous studies have shown that the overall level of schizotypy is associated with deficits of the magnocellular and parvocellular pathways resulting in altered depth perception (Barbato et al., 2012), as well as deficits of higher-level visual systems resulting in impaired context processing (Uhlhaas et al., 2004).EEG studies assessing visual evoked potentials (P1) have also supported the hypothesis of deficits of the early visual system in schizotypy (Bedwell et al., 2013;Koychev et al., 2010), which seemed to be specific to magical ideation and ideas of reference in the study of Bedwell and colleagues.Furthermore, impaired perception of illusions indicative of reduced visual adaptation has been documented in association with positive schizotypy (Thakkar et al., 2019).Although impairments of visual adaptation (Thakkar et al., 2019) and deficits of the visual evoked potential P1 (Bedwell et al., 2013) have been found to be particularly correlated with magical ideation and positive schizotypy in two studies, other studies did not yield information on whether visual perceptual deficits are specific to the positive dimension or its specific features.
Our study aimed to resolve the previous controversy around the Müller-Lyer illusion in schizophrenia (King et al., 2017;Notredame et al., 2014).First, methodological differences and variance in the taxed cognitive processes could be underlying the controversial results regarding the susceptibility to various illusions (Grzeczkowski et al., 2018).Therefore, we used a diverse experimental design, which helped us better understand the properties of the illusion.We constructed 15 illusion conditions where the length of the shafts was manipulated (ratio-80 %, ratio-100 %, and ratio-120 %) as well as the angle of the fins (15 • , 30 • , 45 • as the standard illusion, 60 • , and 75 • ).We hypothesized that manipulating the properties of the illusion would have a substantial effect on susceptibility.To our knowledge, no other research used a joint manipulation of shaft lengths and degree of fins.Manipulating the ratios also helped us filter out those who did not understand the task or had non-related visual deficits (with a ratio-80 %).Furthermore, we could also control for bias among subjects familiar with the Müller-Lyer illusion and expected the two lines to be equal in length.Responses in the first trial (ratio-120 % and degree-75 • , see Fig. 2.) were highly tilted towards response 3 ("The two lines are identical in length"), suggesting that many participants expected the lines to be identical (to ensure data quality, we excluded responses from the first trial).We included ratio and angle as nuisance regressors in our models to estimate the association between schizotypic traits and illusion susceptibility with greater precision.However, identifying the exact association between the illusion parameters and the illusion effect is not the goal of our study.We encourage future research to address this question.
To offer a second resolution to the controversies in the literature around the Müller-Lyer illusion, we argue that the specific nature of this illusion offers a strong explanation that fits well with state-of-the-art theories of psychosis coming from the field of computational psychiatry.A firm theoretical account of the Müller-Lyer illusion claims that it occurs due to prior expectations (e.g."carpentered world hypothesis", Bruno and Franz, 2009;McCauley and Henrich, 2006;Segall et al., 1966) and top-down control (de Brouwer et al., 2015;Howe and Purves, 2005;Weidner and Fink, 2007).These fit well with the Bayesian predictive coding framework of psychosis, which claims that the positive symptoms of schizophrenia and positive schizotypy are associated with a tilt to overweighting priors during perception (Powers et al., 2017;Sterzer et al., 2018;Teufel et al., 2015).Such a shift towards priors could enhance the Müller-Lyer effect; however, further research is needed to better understand how such a hierarchical Bayesian formulation of brain function can account for the Müller-Lyer illusion.
Many authors emphasize the importance of dimensionality in schizophrenia and related personality traits in the general population (Guloksuz and van Os, 2018).To our knowledge, no other research studied the susceptibility to Müller-Lyer illusion from the perspective of schizotypy and psychosis-spectrum traits, even though non-specific effects of enduring psychiatric disorders and medications are critical confounding variables.This research focused on positive schizotypic traits and proneness to anomalous perceptions, a subset of positive schizotypy.The finding that non-clinical individuals with high positive schizotypal traits, similarly to patients with schizophrenia, also exhibit increased illusion susceptibility to the Müller-Lyer illusion, lends further support for the psychosis-spectrum concept.
The present study is not without limitations either.First, it remains to be clarified whether altered susceptibility to the Müller-Lyer illusion is specific to belief-related subcomponents of positive schizotypy.Although most items of the MSS-B tap various unusual beliefs, there are other instruments that explicitly differentiate between belief-and perception-related aspects of positive schizotypy, such as the Schizotypal Personality Questionnaire (Raine, 1991) and its variants (Cohen et al., 2010).Second, due to the online data collection method, we have no exact information on the psychiatric diagnosis in a subgroup of our participants.However, it was apparent that individuals who reported the presence of a psychiatric diagnosis did not separate from the rest of the participants in illusion susceptibility, which is consistent with the psychosis spectrum hypothesis.Third, it was out of the scope of our research to study sex differences in susceptibility to the Müller-Lyer illusion.Our sampling procedure was not designed to investigate sex differences: the sample was not representative and we cannot rule out sampling bias (i.e.those women who volunteered to take part differed from the men who volunteered to take part).In our sample, females had increased illusion susceptibility, but the overlapping confidence intervals and bootstrapped distributions of the coefficients did not suggest that this effect was larger than the effect of positive schizotypy.And importantly, the models that contributed the most to the model averaging (i.e.models with the 3 lowest AICc) were all adjusted for potential confounding by sex.
In conclusion, we demonstrated increased susceptibility to the Müller-Lyer illusion in individuals with high positive schizotypy.Future studies are warranted to delineate the relationships between illusion susceptibility and subcomponents of positive schizotypy.Also, it is essential to understand the effect of impaired interactions between bottom-up and top-down mechanisms in schizophrenia-spectrum disorders using mechanistic modeling (e.g., Bayesian predictive coding and brain connectivity modeling), leading to various imbalances in illusion susceptibility.

Declaration of competing interest
The Authors have declared that there are no conflicts of interest in relation to the subject of this study.

Fig. 1 .
Fig. 1.The standard Müller-Lyer illusion where the two shafts are equal in length.

Table 1
Gross et al., 2018tics of the sample.For a comparison with schizotypy levels reported byGross et al., 2018, see 3.1 section in the text.Correlations: Pearson correlation (df = 261) with 95 % confidence intervals are reported, Holm-Bonferroni adjusted p-value < 0.05 is indicated with asterisk (*).CAPS: Cardiff Anomalous Perceptions Scale total score; MSS-B: Multidimensional Schizotypy Scale with positive, negative and disorganized schizotypy subscales; PC: desktop computer; SD: standard deviation.
that can be interpreted carefully.Instead of statistical inference based on pre-data probability statements (e.g.p-values, which