Which variability?

Brain and Language 96 (2006) 154–156 www.elsevier.com/locate/b&l Commentary Which variability? Alessio Toraldo a,*, Claudio Luzzatti b a b University of Pavia, Italy University of Milan-Bicocca, Italy Accepted 29 August 2005 Available online 20 October 2005 Abstract Drai and Grodzinsky provide a valuable analysis that offers a way of disentangling the effects of Movement and Mood in agrammatic comprehension. However, their mathematical implementation (Beta model) hides theoretically relevant information, i.e., qualitative heterogeneities of performance within the patient sample. This heterogeneity is crucial in the variability debate. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Agrammatism; Multimodality; Variability; Qualitative and quantitative heterogeneity 1. Introduction In the last 15 years Grodzinsky and his colleagues have provided an excellent example of a research program in investigating the comprehension impairment of BrocaÕs aphasic patients. In the present paper, Drai and Grodzinsky (D&G henceforth) propose theoretically driven comparisons between conditions that disentangle Movement from Complexity and Mood. They also propose a statistical implementation that is a step forward with respect to ANOVA models, since the latter are inadequate for the probability space [0, 1]. However, we think that such a statistical device may not (yet) be a step forward in the cognitive neuropsychology debate about inter-patient variability. We will discuss this latter issue. 2. Which variability? D&G address the problem of between-subjects differences in the performance of agrammatic patients. They admit that there is considerable variability within single experimental conditions, like for example in comprehension of * DOI of original article: 10.1016/j.bandl.2004.10.016. Corresponding author. E-mail address: [email protected] (A. Toraldo). 0093-934X/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.bandl.2005.08.013 passive or active sentences. Nevertheless they show that within-condition variability does not hide between-conditions differences, which they call Ôstructure.Õ For instance, in spite of the broad score variability found in agrammatic patients on both +Movement and Movement sentences, the two score distributions differ massively from each other (see D&GÕs Figs. 2D and 4D). However, to obtain a description of the score distribution within each condition, D&G used the Beta general model, which assumes an over-simplified notion of betweensubjects variability. We will show that the Beta model reduces the between-subjects variability to purely quantitative differences, whereas the current debate in cognitive neuropsychology is mainly regarding qualitative differences. 3. Qualitative and quantitative variability in cognitive neuropsychology There are two main sources of between-subjects variability: (i) patients with the same clinical diagnosis (e.g., BrocaÕs aphasia) may differ from each other qualitatively, i.e., in the subset of cognitive modules that are damaged; (ii) patients with an identical cognitive impairment, i.e.. damage to exactly the same module(s) may differ quantitatively, i.e., in the degree of damage. Unlike quantitative differences, qualitative differences contain theoretically relevant A. Toraldo, C. Luzzatti / Brain and Language 96 (2006) 154–156 155 information: they can suggest functional fractionation, and therefore, help to drive inferences about mental architecture. However, qualitative variability also constitutes an impasse, since it invalidates the ÔsyndromeÕ approach, and therefore prevents both inferences driven from group average scores and attempts to localize cognitive processes in the brain. In the following, we describe an example of qualitative variability. Brain-damaged patients may be unable to retrieve the name of objects on visual confrontation in the absence of early visual deficits. This phenomenon may be caused by impaired access either to semantic knowledge, or to output lexical representations. These two classes of patients could be told apart by means of a word-to-picture matching task, with agnosic patients still performing poorly, and anomic patients performing in the normal range. Fig. 1 shows the distribution of scores from the word-to-picture matching task of a hypothetical group of patients with poor picture naming. Note that different loci of damage generate a bimodal distribution in our example. Although multimodal profiles do not necessarily follow qualitative heterogeneity within a group, any mathematical model devised to describe score distributions has to allow multimodality, i.e., theoretically relevant information, to emerge. 4. Bimodal profiles in BrocaÕs patientsÕ comprehension performance Although very large samples would be necessary to describe the exact shape of any empirical distribution, there are already hints of multimodality in D&GÕs data. Consider D&GÕs results from comprehension of +Movement sentences with Passive Mood (English). These are shown in their Fig. 5 in terms of solid black confidence intervals for single individuals. The distribution of punctual estimates—simple percentage scores—was deduced from these Fig. 2. (A) Histogram: distribution of percentage scores from 27 BrocaÕs patients on comprehension of English passive reversible sentences (D&G, this issue); punctual estimates were deduced from their Fig. 5 (see Footnote 1 for comments). Solid line: Beta model provided by D&G for the same (n = 27) data set (M = .63, r = .2). (B) Distribution of percentage scores from 11 agrammatic patients on comprehension of Italian reversible passive sentences (Luzzatti et al., 2001). confidence intervals1 and from the underlying equations. The histogram obtained is shown in Fig. 2A. Seven out of 27 patients scored at—or very close to— ceiling, while the remaining patients were distributed, with some variability, slightly above chance level (50%). This distribution is quite similar to that emerging from Luzzatti et al.Õs (2001) study on the comprehension impairment of reversible active and passive sentences in Italian agrammatic and fluent aphasic patients. This study was not included 1 Fig. 1. Fictitious distributions of scores on a word-to-picture matching task. Horizontal axis: rate of correct responses; vertical axis: probability density. The normal range is shown as a shadowed region along the scale. Gray solid curve, patients with associative visual agnosia; dashed curve, patients with anomia; black solid curve, overall distribution (sum of the previous two). Significant changes were made to D&GÕs target article after the ‘‘final’’ version had been sent out for commentaries. In particular the authors added seven cases to the analysis reported in Fig. 5 and eliminated the table reporting the best-fit parameters for the Beta distribution. We were made aware of these changes only at the proof stage, when we discovered that the original table had been eliminated; consequently we were not able to update our reanalysis of their data. However, no important difference in distribution seems to emerge from a comparison of the original (n = 27) and the amended (n = 34) Fig. 5. 156 A. Toraldo, C. Luzzatti / Brain and Language 96 (2006) 154–156 in D&GÕs analysis because comprehension was tested in a sentence-to-picture matching paradigm with four instead of two response alternatives, i.e., with chance level = 25% instead of 50%. By applying D&GÕs classification, also Italian passive sentences are +Movement and have Passive Mood. Fig. 2B plots the performance of the 11 Italian agrammatic patients with reversible passive sentences. The performance of 3 out of 11 patients was within the normal range, that is virtually at ceiling, whereas the remaining 8 patients scored about 50%. As suggested by Luzzatti et al. (2001, p. 438), the performance of these three patients cannot be simply considered as the effect of statistical fluctuation. In fact, even after very conservative Bonferroni correction, their scores remain significantly above 50%. Several other studies reported similar results, with a sub-sample of agrammatic patients performing reliably above chance, or even at ceiling (e.g., Berndt, Mitchum, & Haendiges, 1996). Therefore, a clear-cut bimodal distribution emerges from the agrammatic comprehension performance on +Movement, passive sentences. 5. Beta mathematical models D&G propose the Beta Family for fitting empirical distributions of success scores, i.e., individual proportions of correct responses, ranging from 0 to 1. This is an improvement with respect to the use of ANOVA models that assume distributions extending ideally from 1 to +1. However, Beta distributions are almost always unimodal.2 Thus, their use would be justified only by assuming little or no qualitative variability between participants.3 In Fig. 2A the black line shows the best fit given by the Beta model for D&GÕs data (mean = .63; r = .2). The mismatch between real data distribution and best-fit curve is evident. Therefore, the Beta model hid the rather clear qualitative heterogeneity visible in the empirical distribution (bimodal profile). There is a further issue suggesting the inappropriateness of the Beta model. This model describes the distribution of the individual true scores, after having removed the withinsubject noise (measurement error). According to the best-fit curve obtained by D&G to describe +Movement data (see our Fig. 2A), the true score of about 1/3 of the patients is 2 Beta distributions can be bimodal, but only where the two modes are at the extremes, i.e., 0 and 1. These cases are irrelevant for the present purpose since score distributions with subjects either at ceiling or at floor are very unlikely to occur. The Beta distribution has another limit. It cannot fit a variety of unimodal empirical distributions that are widespread in neuropsychology. These are asymmetrical two-tailed shapes with the longer tail between the peak and the end of the scale that is closer to the peak. For example, the frequency histogram of punctual estimates in D&GÕs Fig. 4B (+Movement data) has its peak at about .55 and its longer tail towards the ceiling (1.00); the Beta model offers an unsatisfactory fit with a basically symmetrical curve and a peak at about .62 (solid curve in D&GÕs Fig. 4D). 3 This assumption is untenable in neuropsychology since considerable qualitative variability within a syndrome is very frequent. below chance (lower than 50%). However, the confidence intervals of these same scores were all above or around the chance level line (see solid black confidence intervals in D&GÕs Fig. 5). Relying on this latter (model-free) analysis, there is no reason to believe that any true score was below chance. D&G have to account for such a discrepancy. In our view, the long and heavy below-chance tail of the distribution is an artifact produced by the fitting procedure that squeezes out a unimodal curve to best approximate the bimodal data. 6. Conclusions D&G showed that structure is discernable within the comprehension performance of BrocaÕs aphasic patients, according to the +/ Movement dichotomy. They are undoubtedly right in this respect. Yet, qualitative variability was not, and cannot be, taken into account by the Beta model. The structure found in the data set arises from the majority of patients, who show an advantage of Movement over +Movement sentences (i.e., a confirmation of the Trace Deletion Hypothesis). However, some patients do not show such advantage and, in the outermost condition, there are agrammatic patients who do not show any comprehension deficits at all. This qualitative heterogeneity should have obvious consequences on the inferences driven about the cognitive structure underlying syntactic processing. D&GÕs mathematical approach is a fruitful starting point; however it needs to develop into a multimodal model. Acknowledgment We are indebted to Nicola van Rijsbergen for her kind help in revising the English. References Berndt, R. S., Mitchum, C. C., & Haendiges, A. N. (1996). Comprehension of reversible sentences in ÔagrammatismÕ: A meta-analysis. Cognition, 58, 289–308. Luzzatti, C., Toraldo, A., Guasti, M. T., Ghirardi, G., Lorenzi, L., & Guarnaschelli, C. (2001). Comprehension of reversible active and passive sentences in agrammatism. Aphasiology, 15, 419–441.