Linear mixed-effect models (LMMs) are being increasingly widely used in psychology to analyse multi-level research designs. This feature allows LMMs to address some of the problems identified by Speelman and McGann ( 2013 ) about the use of mean data, because they do not average across individual responses. However, recent guidelines for using LMM to analyse skewed reaction time (RT) data collected in many cognitive psychological studies recommend the application of non-linear transformations to satisfy assumptions of (...) normality. Uncritical adoption of this recommendation has important theoretical implications which can yield misleading conclusions. For example, Balota et al. ( 2013 ) showed that analyses of raw RT produced additive effects of word frequency and stimulus quality on word identification, which conflicted with the interactive effects observed in analyses of transformed RT. Generalized linear mixed-effect models (GLMM) provide a solution to this problem by satisfying normality assumptions without the need for transformation. This allows differences between individuals to be properly assessed, using the metric most appropriate to the researcher's theoretical context. We outline the major theoretical decisions involved in specifying a GLMM, and illustrate them by reanalysing Balota et al.'s datasets. We then consider the broader benefits of using GLMM to investigate individual differences. (shrink)

Item context effects refer to the impact of features of a test on an examinee’s item responses. These effects cannot be explained by the abilities measured by the test. Investigations typically focus on only a single type of item context effects, such as item position effects, or mode effects, thereby ignoring the fact that different item context effects might operate simultaneously. In this study, two different types of context effects were modeled simultaneously drawing on data from an item calibration study (...) of a multidimensional computerized test (N = 1,632) assessing student competencies in mathematics, science, and reading. We present a generalized linear mixed model (GLMM) parameterization of the multidimensional Rasch model including item position effects (distinguishing between within-block position effects and block position effects), domain order effects, and the interactions between them. Results show that both types of context effects played a role, and that the moderating effect of domain orders was very strong. The findings have direct consequences for planning and applying mixed domain assessment designs. (shrink)

Generalized linear mixed models estimate fixed and random effects and are especially useful when the dependent variable is binary, ordinal, count or quantitative but not normally distributed. They are also useful when the dependent variable involves repeated measures, since GLMMs can model autocorrelation. This study aimed to determine how and how often GLMMs are used in psychology and to summarize how the information about them is presented in published articles. Our focus in this respect was mainly (...) on frequentist models. In order to review studies applying GLMMs in psychology we searched the Web of Science for articles published over the period 2014–2018. A total of 316 empirical articles were selected for trend study from 2014 to 2018. We then conducted a systematic review of 118 GLMM analyses from 80 empirical articles indexed in Journal Citation Reports during 2018 in order to evaluate report quality. Results showed that the use of GLMMs increased over time and that 86.4% of articles were published in first- or second-quartile journals. Although GLMMs have, in recent years, been increasingly used in psychology, most of the important information about them was not stated in the majority of articles. Report quality needs to be improved in line with current recommendations for the use of GLMMs. (shrink)

A non-repeated item design refers to an experimental design in which items used in one level of experimental conditions are not repeatedly used at other levels. Recent literature has suggested the use of generalized linear mixed-effects models for experimental data analysis, but the existing specification of GLMMs does not account for all possible dependencies among the outcomes in NRI designs. Therefore, the current study proposed a GLMM with a level-specific item random effect for NRI designs. The (...) hypothesis testing performance of the newly proposed model was evaluated via a simulation study to detect the experimental condition effect. The model with a level-specific item random effect performed better than the existing model in terms of power when the variance of the item effect was heterogeneous. Based on these results, we suggest that experimental researchers using NRI designs consider setting a level-specific item random effect in the model. (shrink)

The effects of psycholinguistic variables on reading development are critical to the evaluation of theories about the reading system. Although we know that the development of reading depends on both individual differences (endogenous) and item-level effects (exogenous), developmental research has focused mostly on average-level performance, ignoring individual differences. We investigated how the development of word recognition in Chinese children in both Chinese and English is affected by (a) item-level, exogenous effects (word frequency, radical consistency, and curricular grade level); (b) subject-level, (...) endogenous individual differences (orthographic awareness and phonological awareness); and (c) their interactive effect. We tested native Chinese (Putonghua)-speaking children (n = 763) in grades 1 to 6 with both Chinese character and English word identification (lexical) decision tasks. Our findings show that (a) there were effects of both word frequency and age of acquisition in both Chinese and English, but these item-level effects generally weakened with increasing age; (b) individual differences in phonological and orthographic awareness each contributed to successful performance; and (c) in Chinese, item-level effects were weaker for more proficient readers. We contend that our findings can be explained by theoretical models that incorporate cumulative learning as the basis for development of item-level effects in the reading system. (shrink)

We apply molecular code theory to a rule-based model of the human inner kinetochore and study how complex formation in general can give rise to molecular codes. We analyze 105 reaction networks generated from the rule-based inner kinetochore model in two variants: with and without dissociation of complexes. Interestingly, we found codes only when some but not all complexes are allowed to dissociate. We show that this is due to the fact that in the kinetochore model proteins can only bind (...) at kinetochores by attaching to already attached proteins and cannot form complexes in free solution. Using a generalized linear mixed model we study which centromere protein can take which role in a molecular code . By this, associations between CENPs and code roles are found. We observed that CenpA is a major risk factor while CenpQ is a major protection factor . Finally we show, using an abstract model of copolymer formation, that molecular codes can also be realized solely by the formation of stable complexes, which do not dissociate. For example, with particular dimers as context a molecular code mapping from two different monomers to two particular trimers can be realized just by non-selective complex formation. We conclude that the formation of protein complexes can be utilized by the cell to implement molecular codes. Living cells thus facilitate a subsystem allowing for an enormous flexibility in the realization of mappings, which can be used for specific regulatory processes, e.g. via the context of a mapping. (shrink)

Linear mixed-effects models (LMMs) are increasingly being used for data analysis in cognitive neuroscience and experimental psychology, where within-participant designs are common. The current article provides an introductory review of the use of LMMs for within-participant data analysis and describes a free, simple, graphical user interface (LMMgui). LMMgui uses the package lme4 (Bates et al., 2014a, b ) in the statistical environment R (R Core Team).

This study adopted a mixed-method study design to investigate the acquisitional features of English existential constructions at the syntax-pragmatics interface by Chinese learners, and explore the factors for non-native performance from the perspective of the Interface Hypothesis. A questionnaire was administered online to 300 Chinese learners of English and 20 English natives at a university in China, which included a picture description test and a context-matching test. Follow-up interviews were conducted with 30 Chinese learners. The experimental data were conducted (...) using comparing means and generalized linear mixed model. Results showed that Chinese learners overproduced existential constructions and reached a native-like level until the advanced stage. Moreover, Chinese learners displayed different preference patterns for existential constructions from English natives, and basically reached a native-like level by the intermediate stage. The qualitative data provided possible explanations for non-native performance. The analysis revealed that non-native performance in production attributed to L1 negative transfer and input frequency, while that in comprehension resulted from underspecification of form-function mapping, input frequency and contexts. Based on the findings, some implications on syntax-pragmatics teaching and L2 interface studies are provided. (shrink)

Animal vocalizations convey important information about the emitter, including sex, age, biological quality, and emotional state. Early on, Darwin proposed that sex differences in auditory signals and vocalizations were driven by sexual selection mechanisms. In humans, studies on the association between male voice attributes and physical formidability have thus far reported mixed results. Hence, with a view to furthering our understanding of the role of human voice in advertising physical formidability, we sought to identify acoustic attributes of male voices (...) associated with physical formidability proxies. Mean fundamental frequency, formant dispersion, formant position, and vocal tract length data from a sample of 101 male voices was analyzed for potential associations with height, weight, and maximal handgrip strength. F0 correlated negatively with HGS; Pf showed negative correlations with HGS, height and weight, whereas VTL positively correlated with HGS, height and weight. All zero-order correlations remained significant after controlling for false discovery rate with the Benjamini–Hochberg method. After controlling for height and weight—and controlling for FDR—the correlation between F0 and HGS remained significant. In addition, to evaluate the ability of human male voices to advertise physical formidability to potential mates, 151 heterosexual female participants rated the voices of the 10 strongest and the 10 weakest males from the original sample for perceived physical strength, and given that physical strength is a desirable attribute in male partners, perceived attractiveness. Generalized linear mixed model analyses—which allow for generalization of inferences to other samples of both raters and targets—failed to support a significant association of perceived strength or attractiveness from voices alone and actual physical strength. These results add to the growing body of work on the role of human voices in conveying relevant biological information. (shrink)

This paper presents the findings of an ultrasound study of ten New Zealand English and ten Tongan -speaking trombone players, to determine whether there is an influence of native language speech production on trombone performance. Trombone players’ midsagittal tongue positions were recorded while reading wordlists and during sustained note productions. After normalizing to account for differences in vocal tract shape and ultrasound transducer orientation, we used generalized additive mixed models (GAMMs) to estimate average tongue shapes used by (...) the players from the two language groups when producing notes at different pitches and intensities, and during the production of the monophthongs in their native languages. The average midsagittal tongue contours predicted by our models show a statistically robust difference at the back of the tongue distinguishing the two groups, although tongue shape during playing does not directly map onto vowel tongue shapes as prescribed by the pedagogical literature. While the New Zealand English-speaking participants employed a playing tongue position approximating the neutral vowel schwa and vowel used in the word ‘lot’, the Tongan participants used a tongue shape loosely patterning with the back vowels /o/ and /u/. We argue that these findings represent evidence for native language influence on brass instrument performance; however, this influence seems to be secondary to more basic constraints of brass playing related to airflow requirements and acoustical considerations, with the vocal tract configurations observed across both groups satisfying these conditions in different ways. Our findings furthermore provide evidence for the functional independence of various sections of the tongue and indicate that speech production, itself an acquired motor skill, can influence another skilled behavior via motor memory of vocal tract gestures forming the basis of local optimization processes to arrive at a suitable tongue position for sustained note production. (shrink)

BackgroundThe preferable position of Deep Brain Stimulation electrodes is proposed to be located in the dorsolateral subthalamic nucleus to improve general motor performance. The optimal DBS electrode localization for the post-operative improvement of balance and gait is unknown.MethodsIn this single-center, retrospective analyses, 66 Parkinson’s disease patients were assessed pre- and post-operatively by using MDS-UPDRS, freezing of gait score, Giladi’s gait and falls questionnaire and Berg balance scale. The clinical outcome was related to the DBS electrode coordinates in x, y, z (...) plane as revealed by image-based reconstruction. Binomial generalized linear mixed models with fixed-effect variables electrode asymmetry, parkinsonian subtype, medication, age class and clinical DBS induced changes were analyzed.ResultsSubthalamic nucleus-deep brain stimulation improved all motor, balance and FoG scores in MED OFF condition, however there were heterogeneous results in MED ON condition. DBS electrode reconstructed coordinates impacted the responsiveness of axial symptoms. FoG and balance responders showed slightly more medially located STN electrode coordinates and less medio-lateral asymmetry of the electrode reconstructed coordinates across hemispheres compared to non-responders.ConclusionDeep brain stimulation electrode reconstructed coordinates, particularly electrode asymmetry on the medio-lateral axis affected the post-operative responsiveness of balance and FoG symptoms in PD patients. (shrink)

In this research, we shed new light on the empirical link between corporate social performance (CSP) and corporate financial performance (CFP) via the application of empirical models and methods new to the CSP–CFP literature. Applying advanced financial models to a uniquely constructed panel dataset, we demonstrate that a significant overall CSP–CFP relationship exists and that this relationship is, in part, conditioned on firms’ industry-specific context. To accommodate the estimation of time-invariant industry and industry-interaction effects, we estimate linear (...) mixed models in our test of the CSP–CFP relationship. Our results show both a significant overall CSP effect as well as significant industry effects between CSP and CFP. In conflict with expectations, the unweighted average effect of CSP on CFP is negative. Our industry analysis, however, shows that in over 17% of the industries in our sample, the effect of CSP on CFP for socially responsible firms is positive. We also examine the multidimensional nature of the CSP construct in an industry context by exploring the CSP dimension–industry nexus and identify dimensions of social performance that are associated with either better or worse financial performance. Our results confirm the existence of disparate CSP dimension–industry effects on CFP, thus our results provide important and actionable information to decision makers considering whether and how to commit corporate resources to social performance. (shrink)

Most theories and hypotheses in psychology are verbal in nature, yet their evaluation overwhelmingly relies on inferential statistical procedures. The validity of the move from qualitative to quantitative analysis depends on the verbal and statistical expressions of a hypothesis being closely aligned – that is, that the two must refer to roughly the same set of hypothetical observations. Here, I argue that many applications of statistical inference in psychology fail to meet this basic condition. Focusing on the most widely used (...) class of model in psychology – the linear mixed model – I explore the consequences of failing to statistically operationalize verbal hypotheses in a way that respects researchers' actual generalization intentions. I demonstrate that although the “random effect” formalism is used pervasively in psychology to model intersubject variability, few researchers accord the same treatment to other variables they clearly intend to generalize over (e.g., stimuli, tasks, or research sites). The under-specification of random effects imposes far stronger constraints on the generalizability of results than most researchers appreciate. Ignoring these constraints can dramatically inflate false-positive rates, and often leads researchers to draw sweeping verbal generalizations that lack a meaningful connection to the statistical quantities they are putatively based on. I argue that failure to take the alignment between verbal and statistical expressions seriously lies at the heart of many of psychology's ongoing problems (e.g., the replication crisis), and conclude with a discussion of several potential avenues for improvement. (shrink)

BackgroundSexual minority (SM) older adults experience mental health disparities. Psychiatric disorders and neuropsychiatric symptoms (NPS) are risk factors for cognitive decline. Although older people in same-sex (SSR) compared to mixed-sex relationships (MSR) perform more poorly on cognitive screening tests, prior studies found no differences in rates of dementia diagnosis or neuropsychological profiles. We sought to explore the role of NPS on neurocognitive outcomes for SM populations. We compared cognitive performance and structural brain parameters of older adults in SSR and (...) MSR.MethodsData were originally collected at Alzheimer's Disease Research Centers (ADRCs). Inclusion criteria were: age of 55+ years, a study partner identified as a spouse/partner, and availability of T1-MRI brain volumes/thickness. Participants were labeled as either SSR or MSR based on their/their co-participant's reported sex. We identified 1,073 participants (1,037 MSR−555 cognitively unimpaired [CU]; 36 SSR−23 CU) with structural MRI data, Mini-Mental State Exam (MMSE), and Neuropsychiatric Inventory Questionnaire (NPI-Q) scores. A subset of the overall sample completed comprehensive neuropsychological assessment (n = 939; 908 MSR−494 CU; 31 SSR−22 CU). Covariates included in statistical models were age, sex, education, total intracranial volume, and apolipoprotein E genotype.ResultsMultivariate general linear models showed significant diagnosis-by-relationship interaction effects on the left parahippocampal gyrus volume. After stratification by relationship group, only cognitively impaired (CI) MSR had significantly smaller left parahippocampal volumes than MSR-CU. The SSR group showed better episodic memory performance. Severity of neuropsychiatric symptoms was negatively associated with volume/thickness of bilateral fronto-temporal areas and with MMSE scores, predominantly in the MSR group.ConclusionIn our study, MSR participants presented with a more compromised cognitive profile than SSR participants. MSR-CI participants showed significantly smaller left medio-temporal volumes, a neural signature of AD. Neuropsychiatric symptoms predicted smaller fronto-temporal volumes in the MSR more consistently than in the SSR group. These findings may be due to unexplored protective factors against cognitive decline in SM elders. Indeed, social support has been proposed as a protective factor warranting future investigation. (shrink)

Several theories link consciousness to complex cortical dynamics, as suggested by comparison of brain signal diversity between conscious states and states where consciousness is lost or reduced. In particular, Lempel-Ziv complexity, amplitude coalition entropy and synchrony coalition entropy distinguish wakefulness and REM sleep from deep sleep and anesthesia, and are elevated in psychedelic states, reported to increase the range and vividness of conscious contents. Some studies have even found correlations between complexity measures and facets of self-reported experience. As suggested by (...) integrated information theory and the entropic brain hypothesis, measures of differentiation and signal diversity may therefore be measurable correlates of consciousness and phenomenological richness. Inspired by these ideas, we tested three hypotheses about EEG signal diversity related to sleep and dreaming. First, diversity should decrease with successively deeper stages of non-REM sleep. Second, signal diversity within the same sleep stage should be higher for periods of dreaming vs. non-dreaming. Third, specific aspects of dream contents should correlate with signal diversity in corresponding cortical regions. We employed a repeated awakening paradigm in sleep deprived healthy volunteers, with immediate dream report and rating of dream content along a thought-perceptual axis, from exclusively thought-like to exclusively perceptual. Generalized linear mixed models were used to assess how signal diversity varied with sleep stage, dreaming and thought-perceptual rating. Signal diversity decreased with sleep depth, but was not significantly different between dreaming and non-dreaming, even though there was a significant positive correlation between Lempel-Ziv complexity of EEG recorded over the posterior cortex and thought-perceptual ratings of dream contents. (shrink)

In “patchwork” families, full siblings, maternal and paternal half-siblings, and non-related children are raised together, and sometimes, genetically related children are separated. As their number is steadily growing, the investigation of the factors that influence within-family relations is becoming more important. Our aim was to explore whether people differentiate between half- and full-siblings in their social relations as implied by the theory of inclusive fitness, and to test whether co-residence or genetic relatedness improves sibling relations to a larger extent. We (...) administered the Sibling Relationship Questionnaire to 196 individuals who were in contact with full-, half-, or step-siblings in their childhood. We built Generalized Linear Mixed Models models to test for the effects of relatedness and co-residence on sibling relations. In general, a higher degree of relatedness was associated with better sibling relations, but only among those who did not live together during childhood. Co-resident siblings’ overall pattern of relation quality was not influenced by the actual level of genetic relatedness. In contrast to this, full siblings reported having experienced more conflicts during childhood than half-siblings, possibly resulting from enhanced competition for the same parental resources. The results suggest that inclusive fitness drives siblings’ relations even in recent industrial societies. However, among individuals who live together, the effect of relatedness might be obscured by fitness interdependence and the subjective feeling of kinship. (shrink)

About one-third of Australians use the services of complementary and alternative medicine (CAM); but debate about the role of CAM in public healthcare is vociferous. Despite this, the mechanisms driving CAM healthcare choices are not well understood, especially in rural Australia. From 2016 to 2018, 2,679 persons from the Goulburn Valley, northern Victoria, were surveyed, 28% (755) of whom reporting visiting CAM practitioners. A Generalized Linear Mixed Model was used to assess associations between various socio-demographic variables and (...) the use of CAM services. The strongest significant inverse (p < 0.05) association with CAM use overall was being unemployed, with markedly lower odds of using CAM than those employed full-time (OR 0.22 [0.12, 0.41]). The next strongest inverse relationship was being retired (OR 0.44 [0.30, 0.65]). The strongest positive associations were with English spoken at home (OR 2.38 [1.34, 4.24]), private health insurance (hospital cover) (1.57 [1.28, 1.91]), being Australian born (OR 1.61 [1.14, 2.28]), and female sex (1.25 [1.02, 1.52])). Females had significantly higher odds of using osteopathy than males (OR 1.98 [1.33, 2.96]) but there were no significant sex differences for chiropractic or massage. This is the first such study conducted solely for a rural Australian population. The drivers of CAM use differed from previous nation-wide studies and they varied across modalities. The factors identified here as being associated with CAM use could be used by CAM practitioners in developing person-centred services. Similarly, the findings are relevant to primary-care services in understanding what sectors of society might eschew conventional health care for CAM in rural regions, where health services are often limited. (shrink)

This study investigates the role of locality (a task/material-related variable), demographic factors (age, education, and sex), cognitive capacities (verbal working memory [WM], verbal short-term memory [STM], speed of processing [SOP], and inhibition), and morphosyntactic category (time reference and grammatical aspect) in verb-related morphosyntactic production (VRMP). A sentence completion task tapping production of time reference and grammatical aspect in local and nonlocal configurations, and cognitive tasks measuring verbal WM capacity, verbal STM capacity, motor SOP, perceptual SOP, and inhibition were administered to (...) 200 neurotypical Greek-speaking participants, aged between 19 and 80 years. We fitted generalized linear mixed-effects models and performed path analyses. Significant main effects of locality, age, education, verbal WM capacity, motor SOP, and morphosyntactic category emerged. Production of time reference and aspect did not interact with any of the significant factors (i.e., age, education, verbal WM capacity, motor SOP, and locality), and locality did not interact with any memory system. Path analyses revealed that the relationships between age and VRMP, and between education and VRMP were partly mediated by verbal WM; and the relationship between verbal WM and VRMP was partly mediated by perceptual SOP. Results suggest that subject-, task/material- and morphosyntactic category-specific factors determine accuracy performance on VRMP; and the effects of age, education, and verbal WM on VRMP are partly indirect. The fact that there was a significant main effect of verbal WM but not of verbal STM on accuracy performance in the VRMP task suggests that it is predominantly the processing component (and not the storage component) of verbal WM that supports VRMP. Lastly, we interpret the results as suggesting that VRMP is also supported by a procedural memory system whose efficiency might be reflected in years of formal education. (shrink)

The pandemic outbreak in March 2020 and its associated sanitary regulations and restrictions triggered an abrupt and significant change for society in general and for families’ organization in particular. In Chile, the Santiago Metropolitan District was under a strict lockdown that involved the closure of the entire educational system. From a systemic-family stress perspective, the impact of these changes might have consequences not only for each individual family member, but for the parental dynamic and, consequently, for children’s well-being. This paper (...) presents the results of a follow-up study showing changes in self-reported parental depression and the perceived home organization of mothers and fathers assessed at three different moments: before the pandemic, at the initial outbreak, and after 1 month of strict lockdown. Relevant moderators were explored using linear mixed models to understand the within-subject changes in mothers’ and fathers’ self-reports across the different assessment times. Financial strain, personality traits of self-criticism and dependency, previous parent–child quality interaction, recent major stressful events, and number of children are highlighted as relevant factors that moderate changes in home chaos and parental mental health perception. Significant risks and protective factors are described for fathers and mothers. The use of pre-pandemic measures as baseline levels enabled the identification of personal and family characteristics that were related to better outcomes. The results help increase our understanding of the sanitary regulations’ impacts on the family system and identify vulnerability indicators that should be considered. (shrink)

This article examines mixed ℋ -infinity and passivity synchronization of Markovian jumping neutral-type complex dynamical network models with randomly occurring coupling delays and actuator faults. The randomly occurring coupling delays are considered to design the complex dynamical networks in practice. These delays complied with certain Bernoulli distributed white noise sequences. The relevant data including limits of actuator faults, bounds of the nonlinear terms, and external disturbances are available for designing the controller structure. Novel Lyapunov–Krasovskii functional is constructed to (...) verify the stability of the error model and performance level. Jensen’s inequality and a new integral inequality are applied to derive the outcomes. Sufficient conditions for the synchronization error system are given in terms of linear matrix inequalities, which can be analyzed easily by utilizing general numerical programming. Numerical illustrations are given to exhibit the usefulness of the obtained results. (shrink)

A large body of psycholinguistic research demonstrates that both language processing and language acquisition are sensitive to the distributions of linguistic constructions in usage. Here we investigate how statistical distributions at different linguistic levels – morphological and lexical (Experiments 1 and 2), and phrasal (Experiment 2) – contribute to the ease with which morphosyntax is processed and produced by second language learners. We analyze Chinese ESL learners’ knowledge of four English inflectional morphemes:-ed,-ing, and third-person-son verbs, and plural-son nouns. In Elicited (...) Imitation Tasks, participants listened to length- and difficulty-matched sentences each containing one target morpheme and typed the whole sentence as accurately as they could after a short delay. Experiment 1 investigated lexical and morphemic levels, testing the hypotheses that a morpheme is expected to be more easily processed when it is (1) highlyavailable(i.e., occurring in frequent word-forms), and (2) highlyreliable(i.e., occurring in lemma words that are consistently conjugated in the form containing this morpheme). Thirty sentences were made for each morpheme, divided into three Availability-Reliability Distribution (ARD) groups on the basis of corpus analysis in the Corpus of Contemporary American English (COCA;Davies, 2008-): 10 target words high in availability, 10 high in reliability, and 10 low in both reliability and availability. Responses were scored on whether the target morpheme was accurately reproduced given the provision of the correct lemma. A generalized linear mixed-effects logit model (GLMM) revealed fixed effects of morpheme type, availability, and reliability on the accuracy of morpheme provision. There were no effects of lemma frequency. Experiment 2 successfully replicated these results and extended the investigation to explore phrasal formulaicity by manipulating the frequency of the four-word strings in which the morpheme was embedded. GLMMs replicated the effects of word-form availability and reliability and additionally revealed independentphrase-superiority effectswhere morphemes were better reproduced in contexts of higher string-frequency. Taken together, these findings demonstrate that morpheme acquisition reflects the distributional properties of learners’ experience and the mappings therein between lexis, morphology, phraseology, and semantics. These conclusions support an emergentist view of the statistical symbolic learning of morphology where language acquisition involves the satisfaction of competing constraints across multiple grain-sizes of units. (shrink)

We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discounting functions to characterize impatience. There are several unexpected benefits of this extension, apart from the ability to directly estimate structural parameters of theoretical interest.

This paper argues that the dominance of linear models has led many sociologists to construe the social world in terms of a "general linear reality." This reality assumes (1) that the social world consists of fixed entities with variable attributes, (2) that cause cannot flow from "small" to "large" attributes/events, (3) that causal attributes have only one causal pattern at once, (4) that the sequence of events does not influence their outcome, (5) that the "careers" of entities (...) are largely independent, and (6) that causal attributes are generally independent of each other. The paper discusses examples of these assumptions in empirical work, consider standard and new methods addressing them, and briefly explores alternative models for reality that employ demographic, sequential, and network perspectives. (shrink)

RationaleThere are growing concerns over the occurrence of adverse physiologic events occurring in pilots during operation of United States Air Force and Navy high-performance aircraft. We hypothesize that a heightened inspiratory work of breathing experienced by jet pilots by virtue of the on-board life support system may constitute a “distraction stimulus” consequent to an increased sensation of respiratory muscle effort. As such, the purpose of this study was to determine whether increasing inspiratory muscle effort adversely impacts on attentional performance.MethodsTwelve, healthy (...) participants were recruited for this study. Participants completed six repetitions of a modified Masked Conjunctive Continuous Performance Task protocol while breathing against four different inspiratory threshold loads to assess median reaction times. A computer-controlled threshold loading device was used to set the inspiratory threshold loads. Repeated measures analysis of variances were performed to examine: the efficacy of the threshold loading device to impose significantly higher loading at each loading condition; the effects of loading condition on respiratory muscle effort sensation; and the influence of hypercapnia on MCCPT scores during inspiratory threshold loading. Generalized additive mixed effects models were used to examine the potential non-linear effects of respiratory muscular effort sensation, device loading, and hypercapnia, on MCCPT scores during inspiratory threshold loading.ResultsInspiratory threshold loading significantly augmented inspiratory effort sensation and the inspiratory pressure-time product. Our analyses also revealed that median hit RT was positively associated with inspiratory effort sensation during inspiratory loading trials.ConclusionThe findings of this work suggest that it was not increasing inspiratory muscle effort per se, but rather participant’s subjective perception of inspiratory “load” that impacts negatively on attentional performance; i.e., as the degree of inspiratory effort sensation increased, sotoo did median hit RT. As such, it is reasonable to suggest that minimizing inspiratory effort sensation during high-performance flight operations may prove useful in reducing pilot RTs during complex behavioral tasks. (shrink)

IntroductionCerebral visual impairment results from damage to cerebral visual processing structures. It is the most common cause of pediatric visual impairment in developed countries and rising in prevalence in developing nations. There is currently limited understanding on how neurologic, developmental, and ophthalmic factors predict outcome for pediatric CVI.MethodA retrospective manual chart review of pediatric CVI patients seen at the tertiary pediatric hospital neurology and neuro-ophthalmology service between 2010 and 2019 was conducted. Patients were stratified into severity groups, and followed over (...) time to identify outcome predictors. Collected baseline characteristics included perinatal, genetic, developmental, and neurologic history, along with neuroimaging and fundoscopic findings on examination. Longitudinal data collected included age, seizure control, and type of therapy received. Linear mixed-effect models were used for longitudinal CVI grade outcome analysis.ResultsA total of 249 individuals spanning 779 patient visits were identified. Mean age at diagnosis was 18.8 ± 16.8 months. About 64.3% were born at term age. Perinatal history revealed hypoxic ischemic encephalopathy in 16.5%, intraventricular hemorrhage in 11.6%, and seizures in 21.7%. At presentation, 60.3% had a diagnosis of cerebral palsy and 84.7% had developmental delay. Among all subjects, 78.6% had epilepsy; 33.8% had an epileptic encephalopathy, with spasms/hypsarrhythmia being most common. Abnormal neuroimaging was present in 93.8%. Genetic anomalies were present in 26.9%. Baseline visual examination revealed no blink-to-light in 24.5%; only BTL in 34.5%, fixation/tracking in 26.5%, and optokinetic drum follow in 14.4%. Longitudinal data analysis showed that perinatal history of HIE, a positive epilepsy history, using multiple epilepsy medications, cerebral palsy, and abnormal fundoscopic findings were all negatively associated with CVI grade change over time. After controlling for significant confounders, receiving any type of therapy [early childhood intervention, physical and occupational therapy, refractive error correction or glasses] was significantly associated with longitudinal improvement in CVI grade compared to patients who did not receive any therapy, with glasses yielding the largest benefit.ConclusionThis study offers extensive insights into neurologic, developmental and ophthalmologic features in patients with moderate to severe CVI. In concordance with previous findings, aspects of perinatal history and epilepsy/seizure control may help inform severity and prognosis in the general neurology or ophthalmology clinic. Conversely, these aspects, as well as genetic and specific epilepsy traits may alert vision health care providers in the clinic to pursue visual evaluation in at-risk individuals. Longitudinal follow-up of CVI patients showed that interventional therapies demonstrated vision function improvement greater than no therapy and maturational development. (shrink)

Parental mental disorders increase the risk for insecure attachment in children. However, the quality of caregiver–infant interaction plays a key role in the development of infant attachment. Dyadic interaction is frequently investigated via global scales which are too rough to uncover micro-temporal mechanisms. Prior research found that the latency to reparation of uncoordinated dyadic states is associated with infant behavioral and neuroendocrine regulation. We investigated the hypothesis that this interactive mechanism is critical in predicting secure vs. insecure attachment quality in (...) infancy. We also assessed the predictive quality of infant attachment regarding neuroendocrine reactivity later in childhood. A subsample of N = 58 dyads from a larger study were analyzed. At 3–8 months postpartum, maternal anxiety disorders were diagnosed via a structured clinical interview as well as dyadic interaction during the Face-to-Face-Still-Face was observed and coded on a micro-temporal scale. Infant attachment quality was assessed with the strange situation paradigm at 12–24 months of age. In an overlapping subsample of N = 39, we assessed child cortisol reactivity at 5 to 6 years of age. Generalized linear modeling revealed that longer latencies to interactive reparation during the reunion episode of the FFSF as well as maternal diagnosis at 3–8 months of age predict insecure attachment in children aged 12–24 months. Cox regressions demonstrated that dyads with infants who developed insecure attachment at 12–24 months of age were 48% less likely to achieve an interactive reparation at 3–8 months of age. Mixed models revealed that compared to securely attached children, children who had developed an insecure attachment at 12–24 months of age had an increased cortisol reactivity at 5 to 6 years of age during free play. The results confirm the hypothesis that the development of attachment is affected by experienced micro-temporal interactive patterns besides diagnostic categories. They also showed that infants of mothers with postpartum anxiety disorders have a more than fivefold increased risk of developing an insecure attachment than the infants of the control group. Moreover, results imply that these patterns may influence neurohormonal regulation even in preschool aged children. (shrink)

Residual confounding is a common source of bias in observational studies. In this article, we build upon a series of sensitivity analyses methods for residual confounding developed by Brumback et al. and Chiba whose sensitivity parameters are constructed to quantify deviation from conditional exchangeability, given measured confounders. These sensitivity parameters are combined with the observed data to produce a “bias-corrected” estimate of the causal effect of interest. We provide important generalizations of these sensitivity analyses, by allowing for arbitrary exposures and (...) a wide range of different causal effect measures, through the specification of the target causal effect as a parameter in a generalized linear model with the arbitrary link function. We show how our generalized sensitivity analysis can be easily implemented with standard software, and how its sensitivity parameters can be calibrated against measured confounders. We demonstrate our sensitivity analysis with an application to publicly available data from a cohort study of behavior patterns and coronary heart disease. (shrink)

BackgroundThe literature shows the negative psychological impact of the coronavirus disease 2019 outbreak on frontline healthcare workers. However, few are known about the mental health of physicians and nurses working in general hospitals during the outbreak, caring for patients with COVID-19 or not.ObjectivesThis survey assessed differences in mental health in physicians and nurses working in COVID-19 or non-COVID-19 medical care units.DesignA cross-sectional mixed-mode survey was used to assess burnout, insomnia, depression, anxiety, and stress.SettingA total of 1,244 physicians and nurses (...) from five general hospitals in Belgium, working in COVID-19 care units, non-COVID-19 care units, or both were informed of the study.ParticipantsSix hundred forty-seven healthcare workers participated in the survey.MeasurementsValidated instruments were used to assess the outcomes: the PFI, the ISI, and the DASS-21.ResultsResults showed high prevalence of burnout, insomnia, depression, and anxiety among participants. After adjusting for confounders, multivariate analysis of variance showed no differences between CCU, NCCU, and CCU + NCCU workers. Univariate general linear models showed higher level of burnout, insomnia, and anxiety among nurses in comparison to physicians. Being a nurse, young, isolated, with an increased workload were risk factors for worse mental health outcomes.LimitationsThe mental health of the tested sample, before the outbreak, is unknown. Moreover, this cross-sectional design provides no information on the evolution of the mental health outcomes over time.ConclusionDirectly caring for patients with COVID-19 is not associated with worse mental health outcomes among healthcare workers in general hospitals. High prevalence of burnout, insomnia, depression, and anxiety among physicians and nurses requires special attention, and specific interventions need to be implemented.Protocol RegistrationClinicalTrials.gov, identifier NCT04344145. (shrink)

In the past 2 decades latent variable modeling has become a standard tool in the social sciences. In the same time period, traditional linear structural equation models have been extended to include non-linear interaction and quadratic effects (e.g., Klein and Moosbrugger, 2000 ), and multilevel modeling (Rabe-Hesketh et al., 2004 ). We present a general non-linear multilevel structural equation mixture model (GNM-SEMM) that combines recent semiparametric non-linear structural equation models (Kelava and Nagengast, 2012 ; (...) Kelava et al., 2014 ) with multilevel structural equation mixture models (Muthén and Asparouhov, 2009 ) for clustered and non-normally distributed data. The proposed approach allows for semiparametric relationships at the within and at the between levels. We present examples from the educational science to illustrate different submodels from the general framework. (shrink)

BackgroundFew studies have examined factors associated with willingness of people living with HIV to participate in HIV treatment clinical trials in Sub-Saharan Africa. We assessed the factors associated with participation of PLHIV in HIV treatment clinical trials research at a large urban clinical and research facility in Uganda.MethodsA mixed methods study was conducted at the Infectious Diseases Institute, adult HIV clinic between July 2016 and January 2017. Data were collected using structured questionnaires, focused group discussions with respondents categorised as (...) either participated or never participated in clinical trials and key informant interviews with IDI staff. A generalized linear model with a logit link function was used for multivariate analyses while the qualitative data were summarized using a thematic approach.ResultsWe enrolled a total of 202 and analysed 151 participants, 77 of whom were male with mean age of 41 years. The majority 127 expressed willingness to participate in treatment clinical trials if given an opportunity. At bivariate analysis, willingness to participate was significantly associated with respondents’ perception of a satisfactory compensation package, special status accorded and belief that their health status would improve while on the clinical trial. At multivariate analysis, a satisfactory compensation package and special status accorded in clinical trials remained significant. The qualitative data analysis confirmed these findings as participants valued the privilege of jumping the clinic waiting queues and spending less time in clinic, the wide range of free tests offered to trial participants, unrestricted access to senior physicians and regular communication from study team. Additionally, free meals offered during clinic visits meant that participants were not in a hurry to go back home. Barriers to participation included the perception that new drugs were being tested on them, fear of side effects like treatment failure and the uncertainty about privacy of their data.ConclusionWe found overwhelming willingness to participate in HIV treatment clinical trials. This was largely extrinsically influenced by the perceived material and health-related benefits. Investigators should pay attention to participants’ concerns for benefits which may override the need to understand study procedures and risks. (shrink)

BackgroundIn the early phase of the COVID-19 pandemic, many restrictions hit people in ways never seen before. Mental wellbeing was affected and burden was high, especially for high-risk groups such as parents. However, to our knowledge no research has yet examined whether being a parent was not only a risk for psychological burden but also a way to cope with the COVID-19 pandemic.MethodsAn online survey was used to collect data from 1,121 participants from April to June 2020. In addition to (...) demographic variables, risk factors and protective factors were collected. The dataset was divided into three groups: parents whose children lived at home, parents whose children did not live at home, and people who were not parents.ResultsA linear mixed effect model showed that parents had no higher burden than non-parents, and even less when children did not live at home. Expected risk factors were generally less important, and there were no differences between parents and non-parents. In contrast, parents had advantages in protective factors.ConclusionIn the early phase of the COVID-19 pandemic, it was shown that parents were not necessarily at risk due to additional burden, but also had prospects of coping better with the situation than people without children. (shrink)

Let G V, E be a simple undirected complete graph with vertex and edge sets V and E, respectively. In this paper, we consider the degree-constrained k -minimum spanning tree problem which consists of finding a minimum cost subtree of G formed with at least k vertices of V where the degree of each vertex is less than or equal to an integer value d ≤ k − 2. In particular, in this paper, we consider degree values of d ∈ (...) 2,3. Notice that DC k MST generalizes both the classical degree-constrained and k -minimum spanning tree problems simultaneously. In particular, when d = 2, it reduces to a k -Hamiltonian path problem. Application domains where DC k MST can be adapted or directly utilized include backbone network structures in telecommunications, facility location, and transportation networks, to name a few. It is easy to see from the literature that the DC k MST problem has not been studied in depth so far. Thus, our main contributions in this paper can be highlighted as follows. We propose three mixed-integer linear programming models for the DC k MST problem and derive for each one an equivalent counterpart by using the handshaking lemma. Then, we further propose ant colony optimization and variable neighborhood search algorithms. Each proposed ACO and VNS method is also compared with another variant of it which is obtained while embedding a Q-learning strategy. We also propose a pure Q-learning algorithm that is competitive with the ACO ones. Finally, we conduct substantial numerical experiments using benchmark input graph instances from TSPLIB and randomly generated ones with uniform and Euclidean distance costs with up to 400 nodes. Our numerical results indicate that the proposed models and algorithms allow obtaining optimal and near-optimal solutions, respectively. Moreover, we report better solutions than CPLEX for the large-size instances. Ultimately, the empirical evidence shows that the proposed Q-learning strategies can bring considerable improvements. (shrink)

Variants of classical linear logics are presented based on the modal version of new structural rule !?mingle instead of the known rules !weakening and ?weakening. The cut-elimination theorems, the completeness theorems and a characteristic property named the mix separation principle are proved for these logics.

BackgroundSarcomas are a diverse group of neoplasms that vary greatly in clinical presentation and responsiveness to treatment. Given the differences in the sites of involvement, rarity, and treatment modality, a multidisciplinary approach is required. Previous literature suggests patients with sarcoma suffer from poorer quality of life especially physical and functional wellbeing. Adolescent and young adult patients are an underrepresented population in cancer research and have differing factors influencing QoL.MethodsRetrospective analysis of Young Adult patients enrolled in the Sarcoma Tissue Repository at (...) University of Iowa. QoL was assessed using the self-report FACT-G questionnaire at enrollment and 12 months post-diagnosis; overall scores and the 4 wellbeing subscales were calculated. Linear mixed effects models were used to measure the association between the rate of change in FACT-G subscale scores and baseline clinical, comorbidity, and treatment characteristics.Results49 patients were identified. 57.1% of patients had a malignancy involving an extremity. Mean FACT-G scores of overall wellbeing improved from baseline to 12 months. Social and emotional wellbeing did not differ significantly between baseline and 12 months. Physical wellbeing and functional wellbeing scores improved from baseline to 12 months. No difference was seen for FACT-G overall scores for age, sex, laterality, marital status, performance status, having children, clinical stage, limb surgery, chemotherapy, or tumor size. A difference was demonstrated in physical wellbeing scores for patients with baseline limitation compared to those with no baseline limitation. A difference was demonstrated in social wellbeing based on anatomical site.ConclusionYoung adults with sarcoma treated at a tertiary center had improvements in overall reported QoL at 12 months from diagnosis. Overall baseline QoL scores on FACT-G were lower than the general adult population for YA patients with sarcoma but at 12 months became in line with general population norms. The improvements seen merit further investigation to evaluate how these change over the continuum of care. Quality of life changes may be useful outcomes of interest in sarcoma trials. (shrink)

We present an algorithm to infer causal relations between a set of measured variables on the basis of experiments on these variables. The algorithm assumes that the causal relations are linear, but is otherwise completely general: It provides consistent estimates when the true causal structure contains feedback loops and latent variables, while the experiments can involve surgical or `soft' interventions on one or multiple variables at a time. The algorithm is `online' in the sense that it combines the results (...) from any set of available experiments, can incorporate background knowledge and resolves conflicts that arise from combining results from different experiments. In addition we provide a necessary and sufficient condition that determines when the algorithm can uniquely return the true graph, and can be used to select the next best experiment until this condition is satisfied. We demonstrate the method by applying it to simulated data and the flow cytometry data of Sachs et al. (shrink)

This article compares two science advisory organizations: the Intergovernmental Panel for Climate Change (IPCC) and the International Council for the Exploration of the Seas (ICES), with a special focus on how their respective policy systems absorb the knowledge delivered for use in decision processes. The science-policy processes of these two organizations differ in important respects; ICES delivers highly specified knowledge to a specified uptake mechanism, while the IPCC produces unspecified knowledge for an unspecified uptake mechanism. Since both environmental governance areas (...) are criticized for lack of needed action, a comparison is of interest asking how this might relate to the organization of science advice. As theoretical resources for this explorative comparison we utilize two approaches from the field of science and technology studies: the co-production approach, which focuses on the entanglements of scientific and political processes, and the systems-theory-oriented multiple-worlds model, which assumes a clear difference in institutional logics between the scientific and the political field. Since the IPCC has been critically analysed by several studies utilizing resources from the two approaches, we contribute with new insights by bringing in ICES, which is a much less studied organization exposing a different science-policy structure. One important finding is that the two theoretical approaches focus on different aspects, exposing ‘links’ and ‘integration’, both of which we argue are important for analysing and assessing science advisory organizations. Moreover, these aspects can be advantageously integrated into a single theoretical framework. (shrink)

We provide a general criterion for Fraenkel–Mostowski models of $${\textsf{ZFA}}$$ (i.e. Zermelo–Fraenkel set theory weakened to permit the existence of atoms) which implies “every linearly ordered set can be well ordered” ( $${\textsf{LW}}$$ ), and look at six models for $${\textsf{ZFA}}$$ which satisfy this criterion (and thus $${\textsf{LW}}$$ is true in these models) and “every Dedekind finite set is finite” ( $${\textsf{DF}}={\textsf{F}}$$ ) is true, and also consider various forms of choice for well-ordered families of well orderable (...) sets in these models. In Model 1, the axiom of multiple choice for countably infinite families of countably infinite sets ( $${\textsf{MC}}_{\aleph _{0}}^{\aleph _{0}}$$ ) is false. It was the open question of whether or not such a model exists (from Howard and Tachtsis “On metrizability and compactness of certain products without the Axiom of Choice”) that provided the motivation for this paper. In Model 2, which is constructed by first choosing an uncountable regular cardinal in the ground model, a strong form of Dependent choice is true, while the axiom of choice for well-ordered families of finite sets ( $${\textsf{AC}}^{{\textsf{WO}}}_{{\textsf{fin}}}$$ ) is false. Also in this model the axiom of multiple choice for well-ordered families of well orderable sets fails. Model 3 is similar to Model 2 except for the status of $${\textsf{AC}}^{{\textsf{WO}}}_{{\textsf{fin}}}$$ which is unknown. Models 4 and 5 are variations of Model 3. In Model 4 $${\textsf{AC}}_{\textrm{fin}}^{{\textsf{WO}}}$$ is true. The construction of Model 5 begins by choosing a regular successor cardinal in the ground model. Model 6 is the only one in which $$2{\mathfrak {m}} = {\mathfrak {m}}$$ for every infinite cardinal number $${\mathfrak {m}}$$. We show that the union of a well-ordered family of well orderable sets is well orderable in Model 6 and that the axiom of multiple countable choice is false. (shrink)

We study an extension of Stackelberg’s model in which many firms can produce at many different times. Demand is affine, while cost is linear. In this setting, we investigate whether Stackelberg’s results in a two-firm game are robust when the number of firms increases. We show that firms may not need to anticipate further entries, leaders might earn less than in the simultaneous game, and, whatever its cost and its time of entry, the firm’s entry always improves welfare.

We present an algorithm to infer causal relations between a set of measured variables on the basis of experiments on these variables. The algorithm assumes that the causal relations are linear, but is otherwise completely general: It provides consistent estimates when the true causal structure contains feedback loops and latent variables, while the experiments can involve surgical or ‘soft’ interventions on one or multiple variables at a time. The algorithm is ‘online’ in the sense that it combines the results (...) from any set of available experiments, can incorporate background knowledge and resolves con- flicts that arise from combining results from different experiments. In addition we provide a necessary and sufficient condition that (i) determines when the algorithm can uniquely return the true graph, and (ii) can be used to select the next best experiment until this condition is satisfied. We demonstrate the method by applying it to simulated data and the flow cytometry data of Sachs et al (2005). (shrink)

In this article, we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model with given observational data. We build on an algorithm proposed by Wang and Drton, and we show that one can augment the hidden variable structure of the recovered model by learning multidirected edges rather than only directed and bidirected ones. Multidirected edges appear when more than two of the observed variables have a hidden common cause. We (...) detect the presence of such hidden causes by looking at higher order cumulants and exploiting the multi-trek rule. Our method recovers the correct structure when the underlying graph is a bow-free acyclic mixed graph with potential multidirected edges. (shrink)

The paper establishes the general structure of the inconsistent models of arithmetic of [7]. It is shown that such models are constituted by a sequence of nuclei. The nuclei fall into three segments: the first contains improper nuclei: the second contains proper nuclei with linear chromosomes: the third contains proper nuclei with cyclical chromosomes. The nuclei have periods which are inherited up the ordering. It is also shown that the improper nuclei can have the order type of (...) any ordinal, of the rationals, or of any other order type that can be embedded in the rationals in a certain way. (shrink)

Order picking, which is collecting a set of products from different locations in a warehouse, has repeatedly been described as one of the most laborious and time-consuming internal logistic processes. Each order is issued to pick some products located at given locations in the warehouse. In this paper, we consider an order picking problem, in which a number of orders with different delivery due dates are going to be retrieved by a limited number of order pickers in multiperiods such that (...) the total tardiness is minimized. The aim is to determine a retrieval plan in terms of order batching and order picker multitrip routing as decision variables. Besides, products are arrived and replenished at the predetermined locations at different periods. Therefore, products sitting in those locations should be delivered soon to provide empty rooms for replenishment. A mixed integer linear programming formulation is proposed for this new problem. The model is optimally solved for small-size problems. For larger instances, grouping metaheuristic algorithms are proposed based on particle swarm optimization and the league championship algorithm that use group-based operators to generate reasonable batches of orders. Improvement heuristics are designed as well. The performance of the MILP formulation and metaheuristic algorithms is analyzed for different problem instances whose designs are based on real data gathered from an auto parts warehouse. Results indicate that our algorithms can stably solve large instances of the problem in a reasonable time. (shrink)

We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are d-separated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is point-wise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by recorded (...) variables; and (c) dependencies are linear. We compare the procedure with standard approaches over a variety of simulated structures and sample sizes, and illustrate its practical value with brief studies of social science data sets. Finally, we consider generalizations for non-linear systems. Keywords: latent variable models, causality, graphical models.. (shrink)

The main aim of this study was to analyze the patterns of changes in Approximate Number Sense precision from grade 1 to grade 9 in a sample of Russian schoolchildren. To fulfill this aim, the data from a longitudinal study of two cohorts of children were used. The first cohort was assessed at grades 1–5, and the second cohort was assessed at grades 5–9. ANS precision was assessed by accuracy and reaction time in a non-symbolic comparison test. The patterns of (...) change were estimated via mixed-effect growth models. The results revealed that in the first cohort, the average accuracy increased from grade 1 to grade 5 following a non-linear pattern and that the rate of growth slowed after grade 3. The non-linear pattern of changes in the second cohort indicated that accuracy started to increase from grade 7 to grade 9, while there were no changes from grade 5 to grade 7. However, the RT in the non-symbolic comparison test decreased evenly from grade 1 to grade 7, and the rate of processing non-symbolic information tended to stabilize from grade 7 to grade 9. Moreover, the changes in the rate of processing non-symbolic information were not explained by the changes in general processing speed. The results also demonstrated that accuracy and RT were positively correlated across all grades. These results indicate that accuracy and the rate of non-symbolic processing reflect two different processes, namely, the maturation and development of a non-symbolic representation system. (shrink)