Is schizotypy taxonic? Response to

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Personality and Individual Differences 44 (2008) 1663–1672

Is schizotypy taxonic? Response to Beauchaine,Lenzenweger, and Waller

David Rawlings a,*, Ben Williams b, Nick Haslam a, Gordon Claridge c

a Department of Psychology, University of Melbourne, VIC 3052, Australiab Department of Psychology, Swinburne University of Technology, Hawthorn VIC 3122, Australia

c Department of Experimental Psychology, South Parks Road, Oxford Ox1 3UD, UK

Received 10 December 2007; received in revised form 14 January 2008; accepted 29 January 2008Available online 10 March 2008

Abstract

Beauchaine, Lenzenweger, and Waller (2008) criticize our taxometric study of schizotypy (Rawlings,Williams, Haslam, & Claridge, in press) on a variety of methodological and philosophical grounds. Weargue that their critique selectively applies more stringent standards to our work than to studies supportingtheir view that schizotypy is taxonic (i.e., categorical). Many of their criticisms apply at least equally toexisting studies that offer support for a schizotypy taxon, and these studies are vulnerable to biases favour-ing taxonic conclusions that were controlled for in our study. Contrary to their criticisms, we did not claimto have disconfirmed previous taxonic findings about schizotypy, and our findings positively supportdimensional models of schizotypy rather than merely being null results. Similarly, our findings are not arte-facts of the sampling or measurement decisions that they question. Even well-replicated taxometric findingsare not immune to empirical challenge, and evaluation of such challenges must be even-handed.� 2008 Elsevier Ltd. All rights reserved.

Keywords: Schizotypy; Psychosis proneness; Taxometric analysis; Taxon; Dimensionality

0191-8869/$ - see front matter � 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.paid.2008.01.021

* Corresponding author. Tel.: +61 3 83446358; fax: +61 3 93476618.E-mail address: [email protected] (D. Rawlings).

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1664 D. Rawlings et al. / Personality and Individual Differences 44 (2008) 1663–1672

1. Introduction

We welcome the opportunity to respond to Beauchaine, Lenzenweger, and Waller’s (2008)thorough critique of our taxometric study of schizotypy (Rawlings, Williams, Haslam, & Cla-ridge, in press), which affords an unusual opportunity to discuss openly a number of unsupportedassertions that often remain shrouded by the anonymity of peer review. We respond to their maincriticisms below.

2. Criticism 1: Rawlings et al. claim to disconfirm the taxonic status of schizotypy with a single study

Beauchaine et al.’s tutorial on hard vs. soft science declares that psychological theories arerarely disconfirmed by a single experimental result, and instead rely for their support on consis-tently replicated findings. Taxonic findings on the structure of schizotypy are extensively repli-cated – indeed, they represent a ‘‘consensus” – so a single study that does not replicate ataxonic finding cannot refute that consensus.

We agree that a single study does not refute all previous taxometric work on schizotypy. Weexplicitly acknowledged this in our original paper, which presents its findings cautiously and withabundant qualification. Contrary to Beauchaine et al.’s claim that we do not recognize the pos-sibility that some aspects of schizotypy may be taxonic and others dimensional, we state thisexplicitly and acknowledge that the latent structure of schizotypy may be taxonic in some popu-lations and in some conceptualizations of schizotypy. In short, our interpretation of our findingsis measured, tentative, and conciliatory, and not presented as a disconfirmation.

Even so, Beauchaine et al.’s claims that there is a ‘‘consensus” on the taxonic structure of schizo-typy and that this structure is consistently replicated are both exaggerations. If there is a consensusit is a consensus of a few American taxometricians. Dimensional views of schizotypy are wide-spread, and the insularity of Beauchaine et al.’s perspective is reflected in a fundamentally inaccu-rate claim – to which we return later – about Claridge’s view of schizotypy. In addition, althoughBeauchaine et al. cite several taxometric studies that support a taxonic latent structure for schizo-typy, they fail to mention several studies that do not. As our original paper noted, three studiesprior to our own have supported a dimensional structure for at least one component of schizotypyor have yielded evidence that was inconclusive. Subsequently, two papers (Fossati, Raine, Borroni,& Maffei, 2007; Linscott, 2007) have appeared that also support a dimensional view of schizotypyfor one of its components or in one sample. Whereas a preponderance of taxometric evidence fa-vours a taxonic view, a sizeable minority of studies reaches different conclusions.

Even if there is a preponderance of evidence, doubts arise if that evidence has systematic lim-itations or biases. Findings may replicate for reasons other than being correct. With respect toschizotypy, much prior taxometric research on which the ‘‘consensus” rests is weaker than Beau-chaine et al. suggest, for reasons we described in the original paper. Samples were sometimes smal-ler than the minimum required for taxometric analysis and drawn from restricted populations(usually American undergraduates). Studies often relied on a single taxometric procedure, imple-mented in rather primitive ways, and yielded plots of a rising, unpeaked form, that is now knownto be consistent with positively skewed dimensional data but that was previously taken as unam-biguous evidence of a taxon.

D. Rawlings et al. / Personality and Individual Differences 44 (2008) 1663–1672 1665

Given that measures of schizotypy are consistently positively skewed this possible source of in-valid taxonic inferences casts doubt on some taxonic findings. The three early studies by Len-zenweger (Korfine & Lenzenweger, 1995; Lenzenweger, 1999; Lenzenweger & Korfine, 1992)are cases in point. They all employ the Chapman scales, Cornell University undergraduatesand a single taxometric procedure (MAXCOV). The (smoothed) MAXCOV plots from two stud-ies rise monotonically with no peak, and only one of the four (unsmoothed) plots in the thirdstudy shows a peak. These studies have been taken to support a taxon, but on current knowledgethey are all ambiguous.

Recent taxometric research that takes skew seriously has cast significant doubt on previous tax-onic findings for personality pathologies (Guay, Ruscio, Hare, & Knight, 2007; Rothschild, Cle-land, Haslam, & Zimmerman, 2003). Taxonic findings for schizotypy deserve special scrutinybecause they run counter to the strong evidence that most variability in personality is dimensional.On methodological and substantive grounds we therefore asked whether taxometric studies ofschizotypy might have produced taxonic conclusions for spurious reasons. Our findings are con-sistent with that proposal. We nowhere argued that this constituted a refutation of past work, butdid suggest that our findings should be considered seriously. Beauchaine et al. disagree.

3. Criticism 2: Rawlings et al.’s sample is problematic: it may have under-sampled some pathologiesand over-sampled others, its admixed nature may have biased its findings, and it may have containedgender differences that were not explored in the data analysis

The argument that our sample, because it contained Oxford undergraduates, may have under-represented schizotypes for reasons of social class and personal achievement is dubious. In fact,we achieved a relatively broad demographic by including many community members alongsidestudents. If anything, Beauchaine et al.’s critique is less applicable to our study than to the manyprevious studies conducted among undergraduates at elite American universities.

How our inclusion of participants solicited for a study of out-of-the-body experiences may havedistorted our findings is equally unclear. The possible over-sampling of members of a dissociativetaxon is irrelevant because dissociative tendencies were not examined. Likewise, the possible over-sampling of people with a diffuse variety of other psychopathologies should not mask the detectionof a schizotypy taxon because the variables that we analysed were chosen as indicators of schizo-typy. Using admixed samples may indeed be problematic for taxometric analysis, but primarily be-cause it can yield spurious taxonic findings, which plainly did not occur in our study. We also notethat some previous studies that constitute the taxonic ‘‘consensus” have employed admixed sam-ples (i.e., Erlenmeyer-Kimling, Golden, & Cornblatt, 1989; Tyrka, Cannon, et al., 1995; Tyrka, Ha-slam, & Cannon, 1995) in ways that could have biased their findings towards taxonic conclusions.

How any small sex differences in the Chapman scales might yield an artefact capable of conceal-ing a schizotypy taxon is unclear. Although Beauchaine et al. argue that controlling for sex differ-ences is essential in taxometric work on schizotypy, only two of the 12 taxometric studiessummarized in our original paper’s Table 1 report doing so (i.e., Erlenmeyer-Kimling et al.,1989; Lenzenweger, 1999). Gender was not reported as controlled in two of Lenzenweger’s taxomet-ric studies of schizotypy (Korfine & Lenzenweger, 1995; Lenzenweger & Korfine, 1992). If doing sois essential, then most previous taxometric research (and the taxonic ‘‘consensus”) must be dis-


carded. Moreover, controlling for gender differences in schizotypy prior to taxometric analysis restson the debatable assumption that such differences are invalid when it comes to assessing taxonicity.

4. Criticism 3: Rawlings et al. do not use adequately precise assessments of schizotypy

We accept the importance of adequately precise measurement in taxometric research. Beaucha-ine et al. argue that our rating scale measures may not meet this requirement, yet we employedmeasures identical or nearly identical to those that have been used in the great majority of taxo-metric studies of schizotypy. Of the 12 published studies listed in our paper’s Table 1, 11 employedratings data, and 9 used self-ratings of the same sort as ours. If our study can be questioned on thebasis of insufficient measurement precision then so must the great majority of previous taxometricstudies of schizotypy, and the taxonic ‘‘consensus” that rests on them.

Beauchaine et al. claim that our supposedly inadequate measurement precision is problematicbecause we compare our work to studies with superior precision, citing in this connection Erlen-meyer-Kimling et al. (1989) and Lenzenweger, McLachlan, and Rubin (2007). We did not compareour work with the latter paper because it was not published at the time of our writing. Its measure-ment precision is indeed strong, but it is not without weaknesses: the sample size is small (311), asingle taxometric procedure is employed, no data simulations are used, it is wrongly claimed thatdimensionality implies a flat taxometric plot, and the assessed base rate of schizotypy in the com-munity sample is an implausible 27%, many times higher than rates reported in previous research.

We would happily compare our work with Erlenmeyer-Kimling et al. (1989). First, that paperrebuts Beauchaine et al.’s assumption that ratings data are invariably less precise than their alter-natives, taking, for example, verbal and performance IQ as indicators of schizotypy. Furthermore,while the study was important in its time, it is weak on multiple grounds: samples were smallerthan recommended for taxometric analysis (<200) and more problematically admixed than ourown, and data analyses employed a taxometric procedure that is no longer used.

Beauchaine et al.’s criticism of ratings data is made on the grounds that such data are especiallyprone to biases, which can alter the apparent latent structure of data sets. However, the study onwhich this claim is made (Beauchaine & Waters, 2003) demonstrated that rater expectations canproduce taxonic results when data are in fact dimensional, which casts doubt not on our dimen-sional findings but on the taxonic findings of previous ratings-based studies of schizotypy. There isas yet no evidence that rater biases can generate dimensional findings from taxonic data sets.

Beauchaine et al.’s suggestion that our study attempts a ‘‘refutation of a consistently replicatedfinding by an experiment of lower measurement precision” is mistaken on several counts. Ourstudy is not a refutation, the taxonicity of schizotypy is not consistently replicated, and our studyhas the same level of measurement precision as most previous taxometric studies.

5. Criticism 4: Rawlings et al. should not have omitted items with very low rates of endorsement, andtheir use of MAXEIG is not the improvement that they say it is

We accept that our omission of low-frequency items could have biased our findings against thedetection of a taxon. This omission was done to reduce the sometimes strong indicator skew that


results when such items are retained. We have re-analysed our data after incorporating the omit-ted items into our indicators. Our dimensional conclusions remain unchanged: for three of ourfour schizotypy scales the MAXEIG and MAMBAC plots lack taxonic peaks and resemble thedimensional simulations better than the taxonic ones; this is supported by the fit index (CCFIfor MAXEIG and MAMBAC as follows: MgI: .38 & .51, SoA: .45 & .23, PhA: .41 & .26). Addi-tion of low-frequency items renders the Perceptual Aberration (PAb) indicators more skewed, andas a result the dimensional and taxonic simulations yield indistinguishable rising, unpeaked plots.The analysis therefore does not permit a conclusion about the latent structure of PAb, but doesshow that dimensional data can generate the sorts of taxometric plots commonly used to infer ataxon in previous research.

We did not claim that our use of MAXEIG in itself constituted an improvement in ourwork. Our argument was that many previous studies had relied exclusively on a single taxomet-ric procedure (MAXCOV), and that the taxometric goal of consistency testing requires thatmultiple procedures are employed. For this reason we used MAMBAC and MAXEIG inour study. Nevertheless, we do believe that MAXEIG is a valuable refinement of MAXCOV.Beauchaine et al. observe that with three indicators MAXEIG is mathematically identical toMAXCOV ‘‘in the absence of nuisance covariance”, but all of our analyses used four indicatorsand nuisance covariance was not absent in our data set. Moreover, MAXEIG has graphingconventions (overlapping windows vs. non-overlapping slabs) that improve the clarity of taxo-metric plots. For these reasons, we believe MAXEIG was a better choice than MAXCOV inour study.

6. Criticism 5: Rawlings et al.’s simulation procedure is questionable

Beauchaine et al. criticize the simulation method we employed on several grounds. They arguethat controlling for skew was not even necessary in our data set because our levels of indicatorskew were moderate or less. One problem with this claim is that even with these levels of skewthe dimensional simulation plots show the same monotonically rising shape (see Figs. 1 and 2in our original paper) that has been taken as evidence of a taxon in previous studies. Even mod-erately skewed indicators can bias taxometric inferences towards a taxon where none exists, unlessan interpretational safeguard such as the analysis of simulated comparison data is employed. An-other problem with the claim is that the simulation procedure does not only address skew but alsoother characteristics of the data that Beauchaine et al. argued were critical to obtaining informa-tive taxometric results (e.g., indicator validity, measurement precision, taxon base rate). In otherwords, the simulation procedure is designed to provide an aid to interpretation that takes into ac-count much more than indicator skew.

The Erlenmeyer-Kimling et al. (1989), Tyrka, Cannon, et al. (1995), and Tyrka, Haslam, et al.(1995) findings do indeed show that not all taxonic findings can be attributed to skewed indicatorsof a low base rate taxon. We never claimed that they could. However, we reiterate that theseexceptions have some noteworthy weaknesses: inadequate or marginal sample sizes, admixed sam-ples (for Tyrka et al., children of zero, one and two parents with schizophrenia), and use of a sin-gle taxometric procedure. All other taxometric studies are susceptible to the skewed indicatorcritique, and these two are hardly infallible.


Beauchaine et al. argue that the validity of Ruscio’s simulation method has been scrutinized inonly one published Monte Carlo study, and that until it is evaluated by other labs it remains undera cloud. This criticism strikes us as disingenuous. Many empirical papers using the method havesurvived peer review over a period of several years, but critics have continued to argue that untilit is validated by published Monte Carlo research it is questionable. This validation has now ap-peared in not one but two Monte Carlo studies, both of which are much more substantial thanany previous study of a taxometric procedure (Ruscio, 2007; Ruscio, Ruscio, & Meron, 2007). To-gether they examine more than 35,000 simulated data sets covering a broad parameter space toshow that Ruscio’s method robustly discriminates taxonic and dimensional data sets, and thatthe comparison curve fit index (CCFI) used in our study outperforms other commonly used con-sistency tests. For example, the base rate consistency test and Bayesian probabilities test, bothwidely used to support taxonic conclusions about schizotypy, performed relatively poorly, the for-mer especially when indicators are skewed. Beauchaine et al. cite criticisms of the simulation meth-od raised by Beach, Amir, and Bau (2005) but fail to mention that Ruscio and Marcus (2007)rebutted the unsupported allegations, demonstrating that the method correctly identified the tax-onic structure of the data sets that Beach et al. created to pose a challenge for the technique.

Now that Monte Carlo validation of Ruscio’s simulation method has been published, Beaucha-ine et al. have raised the bar so that replication by independent researchers is demanded. Theynote that incorporating simulations has become routine practice in taxometric studies, and we be-lieve this is due to the sound rationale for the approach and the lack of a viable alternative. AsMeehl was fond of saying, no statistic is self-interpreting, and one must have some comparativebasis for interpreting taxometric results as more indicative of taxonic or dimensional structure.Rather than raising the evidentiary standards each time the simulation method achieves the pre-viously stated target, we challenge its critics to cite empirical evidence supporting an alternativeapproach to interpreting taxometric results that achieves comparable or superior validity in trialsthat span the breadth of data conditions that Ruscio and his colleagues have examined.

7. Criticism 6: Rawlings et al. have tested a taxonic hypothesis and failed to find support for it. Inclaiming support for a dimensional view of schizotypy they are therefore invalidly attempting to‘‘prove the null’’. Their null finding may simply represent low power

Beauchaine et al. argue that taxometrics is essentially a method for detecting taxa. Their pre-ferred inferential framework involves a taxonic conjecture and a test that either supports thathypothesis or affords no conclusion at all. What they characterize as a negative (null) result doesnot allow dimensionality to be inferred. They claim that this is what we did in our study. Opinionsdiffer on the appropriate inferential framework for taxometric analysis, and ours does not involvea null hypothesis testing approach. We do not accept that only taxonic predictions can be made,and that taxometric analyses can therefore only yield taxonic or inconclusive – but never dimen-sional – findings. This asymmetrical approach is biased because positive support can only be ob-tained for one of two structural positions (i.e., taxonic), an unsatisfactory constraint in a domainwhere dimensional structure is common.

We prefer a framework in which taxometric analysis tests between two competing structuralhypotheses, taxonic and dimensional (Ruscio, 2007). It yields findings on the relative support


for these structural alternatives, so there is no such thing as a null result when findings lean in oneof the two directions. Inconclusive findings occur when results are equally consistent with bothlatent structures (or with neither). This framework is desirable because it is not biased in favourof one structural alternative and it can yield positive support for categorical or dimensional mod-els, and it takes advantage of Ruscio’s simulation method, which allows taxometric results to becompared to explicitly presented taxonic and dimensional alternatives. Without the use of simu-lated comparison data, we agree that the interpretation of nontaxonic results can be problematic.In our case, these results did not simply fail to support a taxonic model of schizotypy, they moreclosely supported a dimensional model.

On the subject of the power of our study, we note two things. First, we reported the validities ofour indicators (i.e., how powerfully they discriminate the latent variable), and they were uniformlystrong, demonstrating adequate power. Second, the simulation method we employed allows a di-rect test of its power: if the taxonic and dimensional simulations yield clearly discrepant taxomet-ric plots, then the analysis is powerful enough to discriminate between the two latent structures.Thus, our study establishes its power more directly than any previous taxometric study of schizo-typy: we showed that data sharing the characteristics of our own, submitted to taxometric anal-yses implemented in our way, were capable of yielding taxonic results.

8. Dimensional views of schizotypy

We return finally to the short shrift Beauchaine et al. give to dimensional models of schizotypy.Such models they dismiss with a single reference to Claridge, whose dimensional view, they state,‘‘derives from Eysenck’s ‘‘psychoticism” construct, which is largely an amalgam of aggression andimpulsivity”. In referring to Claridge’s use of Eysenck’s ideas Beauchaine et al. have conflated twocompletely separate points: (a) the general philosophy behind Eysenck’s explanation of individualdifferences; and (b) Eysenck’s specific theorizing about the nature of psychotic traits, as embodiedin the Psychoticism scale. On the former, Claridge has stayed loyal to the dimensional theory pio-neered by his former mentor: that there are descriptive dimensions of personality which reflectnatural central nervous system variations and which, as predispositions to psychopathology,make people vulnerable to varieties of mental illness. Eysenckian views of this kind are well-estab-lished in personality and abnormal psychology, even among North American writers (e.g., Clon-inger, 2000; Zuckerman, 1994).

While applying this general philosophy to the explanation of psychotic traits, Claridge hasdeparted firmly from Eysenck’s emphasis on the antisocial and the aggressive as the centrallydefining criteria, articulating this criticism in a series of papers stretching back more thantwo decades (Claridge, 1981; Claridge, 1986; Claridge, 1997a). As an alternative to Eysenck’sapproach, Claridge and his colleagues have sought their descriptors and explanations in themainstream clinical and research domains of psychosis. At the descriptive level, this effort in-cluded a comprehensive factor-analytic search for the underlying components of schizotypy, firstby Bentall, Claridge, and Slade (1989) and then in an enlarged sample by Claridge et al. (1996).It was the latter data set that we drew upon for our taxometric analysis here and from which thefour-scale O-LIFE questionnaire had already been developed (Mason, Claridge, & Jackson,1995).


In parallel with that work, Claridge and his colleagues have investigated schizotypy from manypoints of view. They have concluded that psychotic traits constitute an essentially healthy dimen-sion of personality, which in adaptive form contributes to such psychological variations as crea-tivity, non-threatening hallucinations, and rewarding spiritual and mystical beliefs andexperiences. Furthermore, healthy schizotypes behave in the predictable direction on severalexperimental paradigms that are firmly grounded in mainstream schizophrenia research and oftenregarded as putative ‘‘markers’’ for psychotic illness; e.g. latent inhibition, negative priming, andbrain lateralisation (Claridge, 1997b; Claridge, 2006; Mason & Claridge, 2006).

By neglecting this work, Beauchaine et al. fail to appreciate the subtlety of the dimensional con-struct in explanations of personality and psychological disorders. (For a textbook level explana-tion of the topic see Claridge & Davis, 2003.) Fig. 1 illustrates this by portraying two differentmeanings of ‘‘dimensionality’’. One is labeled ‘‘quasi-dimensional’’ and describes continuity solelywithin the illness domain: it could equally well be called the forme fruste interpretation, referringas it does to the well-recognised variation in symptom expression to be found in all illnesses,including schizophrenia.

What is labeled the ‘fully dimensional’ model denotes variations in underlying traits that pre-dispose to psychosis but which in and of themselves are neutral with respect to psychopathology.The two versions of dimensionality are not mutually exclusive. Continuity can occur at differentlevels: in the association between underlying vulnerability to illness (adaptive traits) and in illnessitself (maladaptive symptoms). Fig. 1 merely recognizes a state of affairs that exists in all psycho-logical illness, as well as in physical diseases of the systemic type, e.g. hypertension. From thisscheme it is easy to see how both categorical and dimensional solutions to statistically analyseddata are feasible, depending on how the sample is chosen.

A version of Fig. 1 was first presented in 1993 at an international conference on schizotypalpersonality (Raine, Lencz, & Mednick, 1995). It was offered as a topic for discussion about the

Fig. 1. Diagram illustrating two dimensional models of schizotypy.


possible nature of the structure of schizotypy. In the event no real discussion ensued and in theinterim no meeting point has ever been sought by adherents of the taxonic model, who never makemention of any alternative to their view, except to rubbish it - or, as here, simply get it wrong.

Fifteen years later we invite them to leave their bunker and consider the possibility that theremight be life outside the taxon. There are some exciting questions to be addressed out here!

9. Conclusion

Beauchaine et al.’s criticisms of our study are exaggerated and unbalanced. Our work has sev-eral strengths relative to previous studies – examination of multiple schizotypy components, sta-tistical control for data characteristics such as indicator skew, automated use of fit statistics ofdemonstrated validity, use of multiple taxometric procedures – and its proposed limitations(e.g., restricted demographics, use of ‘‘imprecise” ratings data) apply at least equally to most pre-vious work that has yielded taxonic conclusions. That work has attracted none of the criticismthat Beauchaine et al. direct at ours, despite having the same and additional flaws, suggestingto us that double standards are at work.

Whatever the truth about the latent structure of schizotypy, we are concerned about the generalthrust of Beauchaine et al.’s criticism. They begin their response with a comment on correct sci-entific practice and we end with one. They appear to be arguing that if a psychological finding iswell-replicated it should be protected from challenge unless that challenge reaches a standard ofscientific conclusiveness (as judged by people who disagree with those conclusions) that clearlyexceeds the work that it disputes. In our view, the scientific attitude dictates that no finding is im-mune from empirical challenge, and that even the most widely accepted findings should always –perhaps especially – be subject to active questioning. We suspect that the latent structure ofschizotypy probably is taxonic in some respects, but the existing evidence for that claim maybe weaker than many believe and has been somewhat reduced by our findings. Beauchaineet al.’s view is, it seems, that the latent structure of schizotypy has been conclusively establishedand that our findings do not alter their certainty.

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Is schizotypy taxonic? Response to