Overcoming duality: the fused bousfieldian function for modeling word production in verbal fluency tasks

Abstract

Word production is generally assumed to occur as a function of a broadly interconnected language system. In terms of verbal fluency tasks, word production dynamics can be assessed by analyzing respective time courses via curve fitting. Here, a new generalized fitting function is presented by merging the two dichotomous classical Bousfieldian functions into one overarching power function with an adjustable shape parameter. When applied to empirical data from verbal fluency tasks, the error of approximation was significantly reduced while also fulfilling the Bayesian information criterion, suggesting a superior overall application value. Moreover, the approach identified a previously unknown logarithmic time course, providing further evidence of an underlying lexical network structure. In view of theories on lexical access, the corresponding modeling differentiates task-immanent lexical suppression from automatic lexical coactivation. In conclusion, our approach indicates that process dynamics result from an increasing cognitive effort to suppress automatic network functions.Keywords Math modeling and model evaluation . Word production . Verbal fluency Since the landmark works of 19th-century scientists like Broca, Wernicke (1874), and Lichtheim (1885) on speech and language processing, both the linguistic and neuroscientific view on language function has undergone many refinements. Most prominently, the language system's network structure that had already been suggested implicitly by these early approaches has been further elucidated. In so doing, the functions and spatiotemporal characteristics of corresponding anatomical structures have been thoroughly described by means of complementary techniques, including clinical approaches, neuroimaging, and electrophysiological assessments (e.g. Braun et al

Computerized Analysis of Verbal Fluency: Normative Data and the Effects of Repeated Testing, Simulated Malingering, and Traumatic Brain Injury

“…We anticipated that SOIs would be higher in semantic than phonemic conditions. However, because of the fundamental semantic organization of verbal memory [88], we hypothesized that some semantic influences (i.e., SOIs above 1.0) would also be evident during phonemic testing [26]. …”

A Vector Space Model for Neural Network Functions: Inspirations From Similarities Between the Theory of Connectivity and the Logarithmic Time Course of Word Production

“…In the given context it appears of interest that a newly derived logarithmic function for modeling word production during verbal fluency (VF) tasks indicated the connectivity pattern of the underlying semantic network to follow a power-of-two distribution (Ehlen et al, 2016 ) reminiscent of the one described by Tsien ( 2015 ).…”

“…For this purpose, an exponential (Bousfield and Sedgewick, 1944 ) and an alternative hyperbolic (Bousfield et al, 1954 ) function were first introduced by Bousfield and co-workers. By unifying their descriptors and their units, we could previously show that instead of being contradictory, both two-parametric formulae are special cases of a three-parametric overarching “fused Bousfieldian function” (FBF; Ehlen et al, 2016 ) expressed by n ( t ) = c · [1 − ( 1 + α r t / c ) − 1/α ] with n : number of words produced; t : time (in seconds); c : asymptote (in words); r : reciprocal of elementary process duration (second −1 ); α: shape factor (dimensionless). Unexpectedly however, clinical data indicated that almost 80 % of the analyzed VF data sets followed a logarithmic function, i.e., n ( t ) = k · ln (1 + r t / k ) with k = c /α which emerged from the FBF due to a coupling of the parameters c and α. Evaluations of VF performance among participants with essential tremor (Ehlen et al, 2017 ) and autism spectrum disorder without intellectual impairment (Ehlen et al, 2020 ) confirmed this high rate of logarithmic time courses, which therefore appears to be a common distribution pattern.…”

“…Unexpectedly however, clinical data indicated that almost 80 % of the analyzed VF data sets followed a logarithmic function, i.e., n ( t ) = k · ln (1 + r t / k ) with k = c /α which emerged from the FBF due to a coupling of the parameters c and α. Evaluations of VF performance among participants with essential tremor (Ehlen et al, 2017 ) and autism spectrum disorder without intellectual impairment (Ehlen et al, 2020 ) confirmed this high rate of logarithmic time courses, which therefore appears to be a common distribution pattern. Seeking an underlying organization principle, the extension of a stochastic sampling-with-replacement model (Wixted and Rohrer, 1994 ), which had originally been suggested for the Bousfieldian exponential function (Bousfield and Sedgewick, 1944 ) delivered a method according to which the time course of word production inevitably indicates the probabilities of retrieving the respective words (Ehlen et al, 2016 ). This relationship is expressed by [with p n +1 : probability of word retrieval of the n + 1 item; n ′: first derivative of the time course of word production; r : reciprocal of elementary process duration (second −1 )].…”

“…The only possible type of interitem connectivity which could explain a corresponding geometric sequence is a set of items which is composed of all possible non-ordered tuples (i.e., single, double, triple, quadruple) that can be built from i elements, including the empty tuple. The number of the respective tuples is then given by N = 2 i [note: in the original formulation, the letter “ i ” was labeled “ N ”; the letter “ N ” in the present version corresponds to “number of favorable objects” in the original version which indicated the number of all tuples; relabelings were performed here to obtain a unified labeling between the formulae by Tsien ( 2015 ) and Ehlen et al ( 2016 )]. Accordingly, the modeling of the logarithmic time course proposes an interconnected semantic system consisting of all possible connections between the words retrieved per VF category.…”