Latent class regression analysis for describing cognitive developmental phenomena: An application to transitive reasoning

The aim of cognitive developmental research is to explain latent cognitive processes or structures by means of manifest variables such as age, cognitive behaviour, and environmental influences. In this paper the usefulness of the latent class regression model is discussed for studying cognitive developmental phenomena. Using this model, the relationships between latent and manifest variables can be explained by means of empirical data without the need of strong a priori assumptions made by a cognitive developmental theory. In the latent class regression model a number of classes are distinguished which may be characterized by particular cognitive behaviour. Environmental influences on cognitive behaviour may vary for different (developmental) classes. An application is given of the latent class regression model to transitive reasoning data. The results showed that a Five-Class model best fitted the data and that the latent classes differ with respect to age, strategy use (cognitive behaviour) and the influence of task characteristics (environmental influences) on the strategy use. The flexibility of the model in terms of mixed measurement levels and treatment of different cognitive variables offers a broad application to several cognitive developmental phenomena.     

Measuring the ability of transitive reasoning,using product and strategy information

Cognitive theories disagree about the processes and the number of abilities involved in transitive reasoning. This led to controversies about the influence of task characteristics on individuals' performance and the development of transitive reasoning. In this study, a computer test was constructed containing 16 transitive reasoning tasks having different characteristics with respect to presentation form, task format, and task content. Both product and strategy information were analyzed to measure the performance of 6- to 13-year-old children. Three methods (MSP, DETECT, and Improved DIMTEST) were used to determine the number of abilities involved and to test the assumptions imposed on the data by item response models. Nonparametric IRT models were used to construct a scale for transitive reasoning. Multiple regression was used to determine the influence of task characteristics on the difficulty level of the tasks. It was concluded that: (1) the qualitatively distinct abilities predicted by Piaget's theory could not be distinguished by means of different dimensions in the data structure; (2) transitive reasoning could be described by one ability, and some task characteristics influenced the difficulty of a task; and (3) strategy information provided a stronger scale than product information.     

A latent class model for rating data

A latent class model for rating data is presented which is the analogue of Andrich's binomial Rasch model for Lazarsfeld's latent class analysis (LCA). The response probabilities for the rating categories follow a binomial distribution and depend on class-specific item parameters. The EM-algorithm for parameter estimation as well as goodness of fit tests for the model are described. An example using questionnaire items on interest in physics illustrates the use of the model as an alternative to the latent trait approach of analyzing test data.I would like to thank Clifford Clogg and the anonymous reviewers for their helpful comments.     

The left visual hemispace bias for the perception of chimeric faces: a further test of the difficulty of discrimination hypothesis

When people make judgments of visual-spatial forms, they generally perform better if the information is presented in their left visual hemispace (LVH), whereas for verbal material, they generally show a right visual hemispace (RVH) bias. For verbal material, the strength and direction of the effect also has been linked to task difficulty, with the bias shifting toward the RVH as task difficulty increases. Two experiments are presented that show the reverse direction of change for a nonverbal task; that is, when a nonverbal task is more difficult, the usual LVH effect shifts toward an RVH bias. Taking into account recent developments in theory and research on hemispheric differences in styles of information processing, we propose that task difficulty is related more generally to changes in processing style.     

The latent variable approach as applied to transitive reasoning

We discuss the limitations of hypothesis testing using (quasi-) experiments in the study of cognitive development and suggest latent variable modeling as a viable alternative to experimentation. Latent variable models allow testing a theory as a whole, incorporating individual differences with respect to developmental processes or abilities in the model. Experiments, in contrast, aim at testing hypotheses that refer to a specific part of a theory; also they ignore individual differences or model the individual differences using age group as a proxy for developmental stage. Drawing on a sample of 409 5–13-year olds, we demonstrate the advantages of latent variable models in the area of transitive reasoning. A comparison of three models showed that the latent variable model that represented fuzzy trace theory had a better fit than the models representing Piaget's theory or linear ordering theory.     

新世纪20年国内心理统计方法研究回顾

新世纪头20年, 国内心理学11本专业期刊一共发表了213篇统计方法研究论文。研究范围主要包括以下10类(按论文篇数排序)：结构方程模型、测验信度、中介效应、效应量与检验力、纵向研究、调节效应、探索性因子分析、潜在类别模型、共同方法偏差和多层线性模型。对各类做了简单的回顾与梳理。结果发现, 国内心理统计方法研究的广度和深度都不断增加, 研究热点在相互融合中共同发展; 但综述类论文比例较大, 原创性研究论文比例有待提高, 研究力量也有待加强。     

The role of cues to differential absolute size in children's transitive inferences

To investigate the role that "nonlogical" cues might play in transitive inference, 6- and 7-year-olds were given a three-term transitive task in which perceptual cues to differential absolute size were either present or absent. Relationships between the taught premises and the relational information that was physically present were manipulated using four basic conditions: "congruent," "inverse," "pretended," or "persuaded." Both age groups showed identical overall premise memory, but the younger group tended to reason more on the basis of the perceptual information rather than on the successfully encoded premise information. Contrasts between the various conditions showed that categorical effects can be circumvented in three-term problems with appropriate controls, that there may be qualitative as well as quantitative differences in transitive inference with age, and that transitive inference is not based solely on memory. The findings also indicate that, although 7-year-olds are competent in "logic-based" transitive inference, they experience great difficulty on tasks involving pretend information.     

Optimization-Based Model Fitting for Latent Class and Latent Profile Analyses

Statisticians typically estimate the parameters of latent class and latent profile models using the Expectation-Maximization algorithm. This paper proposes an alternative two-stage approach to model fitting. The first stage uses the modified k-means and hierarchical clustering algorithms to identify the latent classes that best satisfy the conditional independence assumption underlying the latent variable model. The second stage then uses mixture modeling treating the class membership as known. The proposed approach is theoretically justifiable, directly checks the conditional independence assumption, and converges much faster than the full likelihood approach when analyzing high-dimensional data. This paper also develops a new classification rule based on latent variable models. The proposed classification procedure reduces the dimensionality of measured data and explicitly recognizes the heterogeneous nature of the complex disease, which makes it perfect for analyzing high-throughput genomic data. Simulation studies and real data analysis demonstrate the advantages of the proposed method.     

Modeling Incomplete Longitudinal Substance Use Data Using Latent Variable Growth Curve Methodology

Longitudinal data sets typically suffer from attrition and other forms of missing data. When this common problem occurs, several researchers have demonstrated that correct maximum likelihood estimation with missing data can be obtained under mild assumptions concerning the missing data mechanism. With reasonable substantive theory, a mixture of cross-sectional and longitudinal methods developed within multiple-group structural equation modeling can provide a strong basis for inference about developmental change. Using an approach to the analysis of missing data, the present study investigated developmental trends in adolescent (N = 759) alcohol, marijuana, and cigarette use across a 5-year period using multiple-group latent growth modeling. An associative model revealed that common developmental trends existed for all three substances. Age and gender were included in the model as predictors of initial status and developmental change. Findings discuss the utility of latent variable structural equation modeling techniques and missing data approaches in the study of developmental change.     

传递性推理的ERP研究

以抽象的内容作为实验材料,测定15名大学生在完成三种不同类型的传递性推理任务和基线任务(记忆判断任务)时的事件相关电位(ERP),探讨传递性推理过程的脑内时程动态变化。研究发现,三种推理任务所诱发的波形基本一致,而推理任务与基线任务之间的ERP波形存在明显的差异。这说明对于传递性推理,被试可能是根据视觉的空间表征对信息进行加工的,结果进一步支持了心理模型理论。     

A transitive-chain theory of syllogistic reasoning

A new theory of syllogistic reasoning, called the transitive-chain theory, is presented. The transitive-chain theory proposes that information about set relations is represented in memory by pairs of informational components. The theory further proposes that information about set relations is integrated by applying a small set of rules to transitive chains of these set relations. The rules that are applied to these chains are specified in detail. The theory is cast in terms of information-processing models for variants of the syllogistic reasoning task, and then mathematical models that quantify each of these information-processing models are presented. In a series of five experiments, the transitive-chain theory provides a good account of the response-choice data for syllogisms with various types of content, quantifiers, and logical relations (categorical and conditional). The results of these experiments offer tentative answers to four issues in the theory of syllogistic reasoning: (a) representation of premise information; (b) combination of premise information; (c) sources of difficulty in syllogistic reasoning; and (d) generality of the processes used in syllogistic reasoning.     

Stability and change in longitudinal water-level task performance.

Three longitudinal samples of children (N = 481), 8 to 16 years old, were assessed 3 times at yearly intervals on 8 water-level items. The within-child change in task performance over age is viewed as a stochastic process of the child changing or remaining in 1 of 3 latent (strategy) states: (a) bottom-parallel responders, (b) random responders, or (c) accurate responders. A random-effects binomial mixture distribution is used to model performance at each age. Change over age is gauged by a stochastic transition model. Although there was improvement in task performance over age, the more general finding is that strategy stability, not change, is most typical.     

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.     

Testing the Rasch model by means of the mixture fit index

Rudas, Clogg, and Lindsay (RCL) proposed a new index of fit for contingency table analysis. Using the overparametrized two‐component mixture, where the first component with weight 1?w represents the model to be tested and the second component with weight w is unstructured, the mixture index of fit was defined to be the smallest w compatible with the saturated two‐component mixture. This index of fit, which is insensitive to sample size, is applied to the problem of assessing the fit of the Rasch model. In this application, use is made of the equivalence of the semi‐parametric version of the Rasch model to specifically restricted latent class models. Therefore, the Rasch model can be represented by the structured component of the RCL mixture, with this component itself consisting of two or more subcomponents corresponding to the classes, and the unstructured component capturing the discrepancies between the data and the model. An empirical example demonstrates the application of this approach. Based on four‐item data, the one‐ and two‐class unrestricted latent class models and the one‐ to three‐class models restricted according to the Rasch model are considered, with respect to both their chi‐squared statistics and their mixture fit indices.     

小学儿童一维空间方位传递性推理能力的发展

研究了小学儿童一维空间方位传递性推理能力的发展水平及认知策略 ,同时 ,对心理模型理论进行了检验。被试为城市中等小学 7岁、9岁、11岁儿童各 2 4名 ,男女各半。 4种实验任务分别为三前提单模型、三前提双模型、四前提单模型和四前提双模型。采用个别实验 ,儿童在前提呈现的情况下进行推理。主要研究结果 :(1)从小学 7岁到 11岁 ,儿童的一维空间方位传递性推理能力明显提高 ,7岁儿童初步形成了一维空间方位推理能力 ,9岁和 11岁基本具有了这种能力 ;(2 )随着年龄增长 ,使用模型建构策略解决问题的儿童人次越来越多 ,绝大部分 11岁儿童都能使用这一策略进行推理。但即使儿童使用了模型建构策略 ,他们的推理成绩也没有反映出模型数量所造成的任务难度差异 ,即不符合心理模型理论关于模型数量的主要预期。     

Growth modeling with nonignorable dropout: alternative analyses of the STAR*D antidepressant trial

This article uses a general latent variable framework to study a series of models for nonignorable missingness due to dropout. Nonignorable missing data modeling acknowledges that missingness may depend not only on covariates and observed outcomes at previous time points as with the standard missing at random assumption, but also on latent variables such as values that would have been observed (missing outcomes), developmental trends (growth factors), and qualitatively different types of development (latent trajectory classes). These alternative predictors of missing data can be explored in a general latent variable framework with the Mplus program. A flexible new model uses an extended pattern-mixture approach where missingness is a function of latent dropout classes in combination with growth mixture modeling. A new selection model not only allows an influence of the outcomes on missingness but allows this influence to vary across classes. Model selection is discussed. The missing data models are applied to longitudinal data from the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study, the largest antidepressant clinical trial in the United States to date. Despite the importance of this trial, STAR*D growth model analyses using nonignorable missing data techniques have not been explored until now. The STAR*D data are shown to feature distinct trajectory classes, including a low class corresponding to substantial improvement in depression, a minority class with a U-shaped curve corresponding to transient improvement, and a high class corresponding to no improvement. The analyses provide a new way to assess drug efficiency in the presence of dropout.     

Modeling population heterogeneity in appearance- and performance-enhancing drug (APED) use: applications of mixture modeling in 400 regular APED users

Appearance- and performance-enhancing drugs (APEDs) constitute a wide range of substances, including anabolic-androgenic steroids, nonsteroidal anabolics, and licit and illicit ergo/thermogenics. A great deal of heterogeneity exists in APED use patterns among weight-lifting men, and, consequently, little is known about how these patterns are related to side effect profiles or risk potential. In the current study, a sample of 400 adult men who were regular APED users completed an interactive Web-based instrument detailing information about APED use, side effects, and related indicators of risk. To explore the heterogeneity of APED use patterns, the authors subjected data on use patterns to (a) latent class analysis (LCA), (b) latent trait analysis (LTA), and (c) factor mixture analysis to determine the best model of APED use. Results indicated that a 4-class factor mixture model provided a better fit than LCA and LTA models. The authors also found that severity and latent class were uniquely associated with negative outcomes. Each of the 4 classes was associated with unique side effects, motivations, and participant use patterns. Implications for identifying pathological forms of APED use are discussed.     

A general diagnostic model applied to language testing data

Probabilistic models with one or more latent variables are designed to report on a corresponding number of skills or cognitive attributes. Multidimensional skill profiles offer additional information beyond what a single test score can provide, if the reported skills can be identified and distinguished reliably. Many recent approaches to skill profile models are limited to dichotomous data and have made use of computationally intensive estimation methods such as Markov chain Monte Carlo, since standard maximum likelihood (ML) estimation techniques were deemed infeasible. This paper presents a general diagnostic model (GDM) that can be estimated with standard ML techniques and applies to polytomous response variables as well as to skills with two or more proficiency levels. The paper uses one member of a larger class of diagnostic models, a compensatory diagnostic model for dichotomous and partial credit data. Many well‐known models, such as univariate and multivariate versions of the Rasch model and the two‐parameter logistic item response theory model, the generalized partial credit model, as well as a variety of skill profile models, are special cases of this GDM. In addition to an introduction to this model, the paper presents a parameter recovery study using simulated data and an application to real data from the field test for TOEFL^® Internet‐based testing.     

Using Multilevel Mixtures to Evaluate Intervention Effects in Group Randomized Trials

There is evidence to suggest that the effects of behavioral interventions may be limited to specific types of individuals, but methods for evaluating such outcomes have not been fully developed. This study proposes the use of finite mixture models to evaluate whether interventions, and, specifically, group randomized trials, impact participants with certain characteristics or levels of problem behaviors. This study uses latent classes defined by clustering of individuals based on the targeted behaviors and illustrates the model by testing whether a preventive intervention aimed at reducing problem behaviors affects experimental users of illicit substances differently than problematic substance users or those individuals engaged in more serious problem behaviors. An illustrative example is used to demonstrate the identification of latent classes, specification of random effects in a multilevel mixture model, independent validation of latent classes, and the estimation of power for the proposed models to detect intervention effects. This study proposes specific steps for the estimation of multilevel mixture models and their power and suggests that this model can be applied more broadly to understand the effectiveness of interventions.     

A Finite Mixture of Nonlinear Random Coefficient Models for Continuous Repeated Measures Data

Nonlinear random coefficient models (NRCMs) for continuous longitudinal data are often used for examining individual behaviors that display nonlinear patterns of development (or growth) over time in measured variables. As an extension of this model, this study considers the finite mixture of NRCMs that combine features of NRCMs with the idea of finite mixture (or latent class) models. The efficacy of this model is that it allows the integration of intrinsically nonlinear functions where the data come from a mixture of two or more unobserved subpopulations, thus allowing the simultaneous investigation of intra-individual (within-person) variability, inter-individual (between-person) variability, and subpopulation heterogeneity. Effectiveness of this model to work under real data analytic conditions was examined by executing a Monte Carlo simulation study. The simulation study was carried out using an R routine specifically developed for the purpose of this study. The R routine used maximum likelihood with the expectation–maximization algorithm. The design of the study mimicked the output obtained from running a two-class mixture model on task completion data.