A program for fitting two-phase segmented-curve models with an unknown change point,with an application to the analysis of strategy shifts in a cognitive task

A program is described for fitting a regression model in which the relationship between the dependent and the independent variables is described by two regression equations, one for each of two mutually exclusive ranges of the independent variable. The point at which the change from one equation to the other occurs is often unknown, and thus must be estimated. In cognitive psychology, such models are relevant for studying the phenomenon of strategy shifts. The program uses a (weighted) least squares algorithm to estimate the regression parameters and the change point. The algorithm always finds the global minimum of the error sum of squares. The model is applied to data from a mental-rotation experiment. The program’s estimates of the point at which the strategy shift occurs are compared with estimates obtained from a nonlinear least squares minimization procedure in SPSSX.     

A double bootstrap method to analyze linear models with autoregressive error terms

A new method for the analysis of linear models that have autoregressive errors is proposed. The approach is not only relevant in the behavioral sciences for analyzing small-sample time-series intervention models, but it is also appropriate for a wide class of small-sample linear model problems in which there is interest in inferential statements regarding all regression parameters and autoregressive parameters in the model. The methodology includes a double application of bootstrap procedures. The 1st application is used to obtain bias-adjusted estimates of the autoregressive parameters. The 2nd application is used to estimate the standard errors of the parameter estimates. Theoretical and Monte Carlo results are presented to demonstrate asymptotic and small-sample properties of the method; examples that illustrate advantages of the new approach over established time-series methods are described.     

Using saccade tasks as a tool to analyze executive dysfunctions in schizophrenia

Executive dysfunctions can be frequently observed in schizophrenia. They are more persistent than psychotic symptoms and are assumed to contribute to a variety of clinical signs of the disease. However, the cognitive mechanisms underlying dysexecutive behaviors are not yet understood. The aim of this article is to demonstrate how saccade tasks can be used to analyze the mechanisms involved in the dysexecutive syndrome of schizophrenic patients. There are numerous reports showing that schizophrenic patients make many unwanted reflexive saccades in the antisaccade task. These errors are usually explained by an impairment of a distinct inhibitory mechanism. However, unwanted reflexive saccades may also be secondary to a more fundamental deficit in activating goal-directed behavior. Recent theoretical and empirical approaches to this issue are reviewed and discussed. An integrative view of deficits in inhibition, goal-directed behavior, and working memory in schizophrenic patients is proposed.     

Using the linear mixed model to analyze nonnormal data distributions in longitudinal designs

Using a Monte Carlo simulation and the Kenward–Roger (KR) correction for degrees of freedom, in this article we analyzed the application of the linear mixed model (LMM) to a mixed repeated measures design. The LMM was first used to select the covariance structure with three types of data distribution: normal, exponential, and log-normal. This showed that, with homogeneous between-groups covariance and when the distribution was normal, the covariance structure with the best fit was the unstructured population matrix. However, with heterogeneous between-groups covariance and when the pairing between covariance matrices and group sizes was null, the best fit was shown by the between-subjects heterogeneous unstructured population matrix, which was the case for all of the distributions analyzed. By contrast, with positive or negative pairings, the within-subjects and between-subjects heterogeneous first-order autoregressive structure produced the best fit. In the second stage of the study, the robustness of the LMM was tested. This showed that the KR method provided adequate control of Type I error rates for the time effect with normally distributed data. However, as skewness increased—as occurs, for example, in the log-normal distribution—the robustness of KR was null, especially when the assumption of sphericity was violated. As regards the influence of kurtosis, the analysis showed that the degree of robustness increased in line with the amount of kurtosis.     

Significance tests to determine the direction of effects in linear regression models

Previous studies have discussed asymmetric interpretations of the Pearson correlation coefficient and have shown that higher moments can be used to decide on the direction of dependence in the bivariate linear regression setting. The current study extends this approach by illustrating that the third moment of regression residuals may also be used to derive conclusions concerning the direction of effects. Assuming non‐normally distributed variables, it is shown that the distribution of residuals of the correctly specified regression model (e.g., Y is regressed on X) is more symmetric than the distribution of residuals of the competing model (i.e., X is regressed on Y). Based on this result, 4 one‐sample tests are discussed which can be used to decide which variable is more likely to be the response and which one is more likely to be the explanatory variable. A fifth significance test is proposed based on the differences of skewness estimates, which leads to a more direct test of a hypothesis that is compatible with direction of dependence. A Monte Carlo simulation study was performed to examine the behaviour of the procedures under various degrees of associations, sample sizes, and distributional properties of the underlying population. An empirical example is given which illustrates the application of the tests in practice.     

Using generalized additive (mixed) models to analyze single case designs

This article shows how to apply generalized additive models and generalized additive mixed models to single-case design data. These models excel at detecting the functional form between two variables (often called trend), that is, whether trend exists, and if it does, what its shape is (e.g., linear and nonlinear). In many respects, however, these models are also an ideal vehicle for analyzing single-case designs because they can consider level, trend, variability, overlap, immediacy of effect, and phase consistency that single-case design researchers examine when interpreting a functional relation. We show how these models can be implemented in a wide variety of ways to test whether treatment is effective, whether cases differ from each other, whether treatment effects vary over cases, and whether trend varies over cases. We illustrate diagnostic statistics and graphs, and we discuss overdispersion of data in detail, with examples of quasibinomial models for overdispersed data, including how to compute dispersion and quasi-AIC fit indices in generalized additive models. We show how generalized additive mixed models can be used to estimate autoregressive models and random effects and discuss the limitations of the mixed models compared to generalized additive models. We provide extensive annotated syntax for doing all these analyses in the free computer program R.     

使用验证性补偿多维IRT模型进行认知诊断评估

随着人们对测验反馈结果精细化的需求逐渐提高, 具有认知诊断功能的测量方法逐渐受到人们的关注。在认知诊断模型(CDMs)闪耀着光芒的同时, 另一类能够在连续量尺上提供精细反馈的多维IRT模型(MIRTMs)似乎受到些许冷落。为探究MIRTMs潜在的认知诊断功能, 本文以补偿模型为视角, 聚焦于分别属于MIRTMs的多维两参数logistic模型(M2PLM)和属于CDMs的线性logistic模型(LLM); 之后为使两者具有可比性, 可对补偿M2PLM引入验证性矩阵(Q矩阵)来界定题目与维度之间的关系, 进而得到验证性的补偿M2PLM (CC-M2PLM), 并通过把潜在特质按切点划分为跨界属性, 以期使CC-M2PLM展现出其本应具有的认知诊断功能; 预研究表明logistic量尺上的0点可作为相对合理的切点; 然后, 通过模拟研究对比探究CC-M2PLM和LLM的认知诊断功能, 结果表明CC-M2PLM可用于分析诊断测验数据, 且认知诊断功能与直接使用LLM的效果相当; 最后, 以两则实证数据为例来说明CC-M2PLM在实际诊断测验分析中的可行性。     

Response time analysis in cognitive tasks with increasing difficulty

In the present study, speeded tasks with differing assumed difficulties of the trials are regarded as a special class of simple cognitive tasks. Exploratory latent growth modeling with data-driven shape of a growth curve and nonlinear structured latent curve modeling with predetermined monotonically increasing functions were used to analyze individual response-time change with an increase in task difficulty and to investigate latent response-time growth variables in relation to cognitive ability. A task that required participants to state the number of dots in a set was used as an example of a simple cognitive task with increasing difficulty; the response latencies obtained in this task and the magnitude of RT-IQ correlations changed depending on the complexity of the trial.Consistent with theoretical predictions, the individual speed of baseline performance was only weakly negatively correlated with each of the three measures of cognitive ability used in the study. The rate of change in response times with increasing task difficulty, estimated as a generalized growth parameter in the exploratory latent growth model, was significantly negatively related to cognitive ability. Response times of less intelligent individuals increased more rapidly in the task with increasing difficulty than the response times of highly intelligent individuals. Within the nonlinear structured latent curve modeling, the growth of response times with an increase in task difficulty was best described by a function that approached an oblique asymptote after an initial interval of convexity. A slope of this oblique asymptote was significantly negatively related to cognitive ability; for less intelligent individuals, the asymptote of response-time change was steeper than that for more intelligent individuals. In addition, a parameter that determined the shape of response-time growth trajectories on the interval of convexity was related to one of the three measures of cognitive ability.     

Using phantom and imaginary latent variables to parameterize constraints in linear structural models

The most widely-used computer programs for structural equation models analysis are the LISREL series of Jöreskog and Sörbom. The only types of constraints which may be made directly are fixing parameters at a constant value and constraining parameters to be equal. Rindskopf (1983) showed how these simple properties could be used to represent models with more complicated constraints, namely inequality constraints on unique variances. In this paper, two new concepts are introduced which enable a much wider variety of constraints to be made. The concepts, phantom and imaginary latent variables, allow fairly general equality and inequality constraints on factor loadings and structural model coefficients.During the preparation of this article, it was discovered that another researcher, Jack McArdle, had concurrently and independently discovered some of the techniques reported here. While he has chosen not to publish his research, I wish to acknowledge his work. I would like to thank Art Woodward for telling me about sort-of simple structure.     

Using the Observer to analyze learning in virtual worlds

In this study, we describe and analyze the ways in which high school students explored a virtual solar system (VSS). VSS is a nonimmersive virtual environment that affords visual manipulations of space by altering its frame of reference. The Observer software was used to code and analyze the participants’ real-time free-exploration task. Two basic behaviors were identified across participants: establishing several home bases, and shifting between a still mode and a dynamic mode. Moreover, three overall exploration patterns emerged: thebutterfly pattern represents a superficial mode of learning; thebee pattern represents an in-depth mode of studying the various celestial objects; and theeagle pattern represents a global approach of studying the complex system. This virtual reality environment promises to provide a setting in which to further study consistent patterns and individual differences in exploration strategies.     

Using cognitive models to map relations between neuropsychological disorders and human decision-making deficits

Findings from a complex decision-making task (the Iowa gambling task) show that individuals with neuropsychological disorders are characterized by decision-making deficits that lead to maladaptive risk-taking behavior. This article describes a cognitive model that distills performance in this task into three different underlying psychological components: the relative impact of rewards and punishments on evaluations of options, the rate that the contingent payoffs are learned, and the consistency between learning and responding. Findings from 10 studies are organized by distilling the observed decision deficits into the three basic components and locating the neuropsychological disorders in this component space. The results reveal a cluster of populations characterized by making risky choices despite high attention to losses, perhaps because of difficulties in creating emotive representations. These findings demonstrate the potential contribution of cognitive models in building bridges between neuroscience and behavior.     

Obstacle crossing with lower visual field restriction: shifts in strategy

In this study, the authors investigated how restriction of the vertical viewing angle influences obstacle-crossing behavior. Twelve participants stepped over obstacles of different dimensions while wearing visual-field-restricting goggles. Using full-body motion capture, several kinematic measures were extracted and analyzed. Results indicate that both a 40° and 90° vertical viewing angle yielded increased step length and toe clearance as compared to an unrestricted view (i.e., 135°), whereas speed remained unaltered. A further decrease (to 25°) caused participants to slow down in addition to a further increase of step length and toe clearance. These results are discussed in terms of a change in priorities, from conservation of energy and time to safety.     

Learning to map: strategy discovery and strategy change in young children

A series of microgenetic experiments was conducted to examine the role of experience on 2.5- to 5-year-old children's discovery of spatial mapping strategies. With experience, 3- to 4-year-olds discovered a strategy for mapping corresponding locations that shared both featural and spatial similarities. When featural and spatial correspondences were placed in conflict, requiring children to negotiate both object-centered and location-centered mapping possibilities, 4- to 5-year-olds proved capable of discovering a novel mapping strategy, abandoning an ineffective strategy, and generalizing the acquired strategy across analogous tasks. Upon examining the mechanisms underlying developmental differences in strategy discovery and strategy change, the author observed that 3 key components contributed to the children's spatial mapping skills: encoding locations within each space, noticing a potential analogy between spaces, and detecting precise mapping correspondences.     

Interpret with caution: multicollinearity in multiple regression of cognitive data

Shibihara and Kondo in 2002 reported a reanalysis of the 1997 Kanji picture-naming data of Yamazaki, Ellis, Morrison, and Lambon-Ralph in which independent variables were highly correlated. Their addition of the variable visual familiarity altered the previously reported pattern of results, indicating that visual familiarity, but not age of acquisition, was important in predicting Kanji naming speed. The present paper argues that caution should be taken when drawing conclusions from multiple regression analyses in which the independent variables are so highly correlated, as such multicollinearity can lead to unreliable output.     

An evolutionary approach to support decision making with linear decision models

In this paper we consider decision problems that can be described as linear decision models. These models have been traditionally solved using linear programming, fuzzy linear programming, multiple-objective linear programming or ‘what-if’ analysis. Using these approaches, one encounters a number of difficulties. We propose an ‘evolutionary approach’ to overcome these difficulties. In the proposed approach the decision maker does not have to precisely specify the model (i.e. the objective functions, the RHS values, etc.) at the beginning of the solution procedure. In fact, the model evolves as the solution procedure proceeds.     

Using image analysis techniques to analyze figure-copying performance of patients with visuospatial neglect and control groups

Figure copying is often used to detect visuospatial neglect (VSN) in brain-damaged patients. We describe algorithms that enable the computation of parameters for describing figure-copying performance. The researcher can readily implement these algorithms on a computer using image analysis software, and they provide information on goodness-of-fit, relative to a standard model, as well as on dynamic aspects of subjects’ performance in completing figure copies. To demonstrate the clinical utility of these algorithms, preliminary results from a group of right-hemisphere brain-damaged patients, some of whom have VSN, are compared with those for age-matched controls.     

The prediction of intelligence in preschool children using alternative models to regression

Statistical prediction of an outcome variable using multiple independent variables is a common practice in the social and behavioral sciences. For example, neuropsychologists are sometimes called upon to provide predictions of preinjury cognitive functioning for individuals who have suffered a traumatic brain injury. Typically, these predictions are made using standard multiple linear regression models with several demographic variables (e.g., gender, ethnicity, education level) as predictors. Prior research has shown conflicting evidence regarding the ability of such models to provide accurate predictions of outcome variables such as full-scale intelligence (FSIQ) test scores. The present study had two goals: (1) to demonstrate the utility of a set of alternative prediction methods that have been applied extensively in the natural sciences and business but have not been frequently explored in the social sciences and (2) to develop models that can be used to predict premorbid cognitive functioning in preschool children. Predictions of Stanford–Binet 5 FSIQ scores for preschool-aged children is used to compare the performance of a multiple regression model with several of these alternative methods. Results demonstrate that classification and regression treesprovided more accurate predictions of FSIQ scores than does the more traditional regression approach. Implications of these results are discussed.     

Using image analysis techniques to analyze figure-copying performance of patients with visuospatial neglect and control groups.

Figure copying is often used to detect visuospatial neglect (VSN) in brain-damaged patients. We describe algorithms that enable the computation of parameters for describing figure-copying performance. The researcher can readily implement these algorithms on a computer using image analysis software, and they provide information on goodness-of-fit, relative to a standard model, as well as on dynamic aspects of subjects' performance in completing figure copies. To demonstrate the clinical utility of these algorithms, preliminary results from a group of right-hemisphere brain-damaged patients, some of whom have VSN, are compared with those for age-matched controls.     

Facilitating cognitive performance in children: A comparison of strategy modeling and strategy modeling with overt self-verbalization

Children, 3, 4, 5, 6, 8, and 10 years old, were randomly divided into three training conditions—a strategy modeling condition, a strategy modeling with overt self-verbalization condition, and a control condition. The subjects in the two modeling conditions were given training on four cognitive tasks, a signal task, a match-to-standard task, a paired-associates task, and a twenty-questions task. A 6 (age) × 2 (sex) × 3 (treatment) × 2 (trial) analysis of variance was performed on each of the dependent variables associated with each of the four tasks. The results of these analyses indicate that both modeling conditions facilitated performance on the signal and match-to-standard tasks for all six age groups. However, the two modeling procedures facilitated performance on the paired-associates and twenty-questions tasks only in the three older age groups. Since the two modeling procedures did not differ in effectiveness, it was suggested that strategy modeling without overt self-verbalization is the more practical and efficient procedure for facilitating cognitive performance in normal children.