Detecting Preknowledge Cheating via Innovative Measures: A Mixture Hierarchical Model for Jointly Modeling Item Responses, Response Times, and Visual Fixation Counts

Preknowledge cheating jeopardizes the validity of inferences based on test results. Many methods have been developed to detect preknowledge cheating by jointly analyzing item responses and response times. Gaze fixations, an essential eye-tracker measure, can be utilized to help detect aberrant testing behavior with improved accuracy beyond using product and process data types in isolation. As such, this study proposes a mixture hierarchical model that integrates item responses, response times, and visual fixation counts collected from an eye-tracker (a) to detect aberrant test takers who have different levels of preknowledge and (b) to account for nuances in behavioral patterns between normally-behaved and aberrant examinees. A Bayesian approach to estimating model parameters is carried out via an MCMC algorithm. Finally, the proposed model is applied to experimental data to illustrate how the model can be used to identify test takers having preknowledge on the test items.

Nonconvergence, covariance constraints, and class enumeration in growth mixture models

Growth mixture models (GMMs) are a popular method to identify latent classes of growth trajectories. One shortcoming of GMMs is nonconvergence, which often leads researchers to apply covariance equality constraints to simplify estimation, though this may be a dubious assumption. Alternative model specifications have been proposed to reduce nonconvergence without imposing covariance equality constraints. These methods perform well when the correct number of classes is known, but research has not yet examined their use when the number of classes is unknown. Given the importance of selecting the number of classes, more information about class enumeration performance is crucial to assess the potential utility of these methods. We conducted an extensive simulation to explore class enumeration and classification accuracy of model specifications that are more robust to nonconvergence. Results show that the typical approach of applying covariance equality constraints performs quite poorly. Instead, we recommended covariance pattern GMMs because they (a) had the highest convergence rates, (b) were most likely to identify the correct number of classes, and (c) had the highest classification accuracy in many conditions, even with modest sample sizes. An analysis of empirical posttraumatic stress disorder (PTSD) data is provided to show that the typical four-class solution found in many empirical PTSD studies may be an artifact of the covariance equality constraint method that has permeated this literature. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Using Simulated Annealing to Investigate Sensitivity of SEM to External Model Misspecification

Sensitivity analyses encompass a broad set of post-analytic techniques that are characterized as measuring the potential impact of any factor that has an effect on some output variables of a model. This research focuses on the utility of the simulated annealing algorithm to automatically identify path configurations and parameter values of omitted confounders in structural equation modeling (SEM). An empirical example based on a past published study is used to illustrate how strongly related an omitted variable must be to model variables for the conclusions of an analysis to change. The algorithm is outlined in detail and the results stemming from the sensitivity analysis are discussed.

Bridging Models of Biometric and Psychometric Assessment: A Three-Way Joint Modeling Approach of Item Responses, Response Times, and Gaze Fixation Counts

Recently, joint models of item response data and response times have been proposed to better assess and understand test takers' learning processes. This article demonstrates how biometric information such as gaze fixation counts obtained from an eye-tracking machine can be integrated into the measurement model. The proposed joint modeling framework accommodates the relations among a test taker's latent ability, working speed and test engagement level via a person-side variance-covariance structure, while simultaneously permitting the modeling of item difficulty, time-intensity, and the engagement intensity through an item-side variance-covariance structure. A Bayesian estimation scheme is used to fit the proposed model to data. Posterior predictive model checking based on three discrepancy measures corresponding to various model components are introduced to assess model-data fit. Findings from a Monte Carlo simulation and results from analyzing experimental data demonstrate the utility of the model.

A Comparison of Label Switching Algorithms in the Context of Growth Mixture Models

Simulation studies involving mixture models inevitably aggregate parameter estimates and other output across numerous replications. A primary issue that arises in these methodological investigations is label switching. The current study compares several label switching corrections that are commonly used when dealing with mixture models. A growth mixture model is used in this simulation study, and the design crosses three manipulated variables-number of latent classes, latent class probabilities, and class separation, yielding a total of 18 conditions. Within each of these conditions, the accuracy of a priori identifiability constraints, a priori training of the algorithm, and four post hoc algorithms developed by Tueller et al.; Cho; Stephens; and Rodriguez and Walker are tested to determine their classification accuracy. Findings reveal that, of all a priori methods, training of the algorithm leads to the most accurate classification under all conditions. In a case where an a priori algorithm is not selected, Rodriguez and Walker's algorithm is an excellent choice if interested specifically in aggregating class output without consideration as to whether the classes are accurately ordered. Using any of the post hoc algorithms tested yields improvement over baseline accuracy and is most effective under two-class models when class separation is high. This study found that if the class constraint algorithm was used a priori, it should be combined with a post hoc algorithm for accurate classification.

Assessing Preknowledge Cheating via Innovative Measures: A Multiple-Group Analysis of Jointly Modeling Item Responses, Response Times, and Visual Fixation Counts

Many approaches have been proposed to jointly analyze item responses and response times to understand behavioral differences between normally and aberrantly behaved test-takers. Biometric information, such as data from eye trackers, can be used to better identify these deviant testing behaviors in addition to more conventional data types. Given this context, this study demonstrates the application of a new method for multiple-group analysis that concurrently models item responses, response times, and visual fixation counts collected from an eye-tracker. It is hypothesized that differences in behavioral patterns between normally behaved test-takers and those who have different levels of preknowledge about the test items will manifest in latent characteristics of the different data types. A Bayesian estimation scheme is used to fit the proposed model to experimental data and the results are discussed.

African American English and Early Literacy: A Comparison of Approaches to Quantifying Nonmainstream Dialect Use

Purpose Many studies have found a correlation between overall usage rates of nonmainstream forms and reading scores, but less is known about which dialect differences are most predictive. Here, we consider different methods of characterizing African American English use from existing assessments and examine which methods best predict literacy achievement. Method Kindergarten and first-grade students who speak African American English received two assessments of dialect use and two assessments of decoding at the beginning and end of the school year. Item-level analyses of the dialect-use assessments were used to compute measures of dialect usage: (a) an overall feature rate measure based on the Diagnostic Evaluation of Language Variation-Screening Test, (b) a subscore analysis of the Diagnostic Evaluation of Language Variation-Screening Test based on items that pattern together, (c) an alternative assessment where children repeat and translate sentences, and (d) "repertoire" measures based on a categorical distinction of whether a child used a particular feature of mainstream American English. Results Models using feature rate measures provided better data-model fit than those with repertoire measures, and baseline performance on a sentence repetition task was a positive predictor of reading score at the end of the school year. For phonological subscores, change from the beginning to end of the school year predicted reading at the end of the school year, whereas baseline scores were most predictive for grammatical subscores. Conclusions The addition of a sentence imitation task is useful for understanding a child's dialect and anticipating potential areas for support in early literacy. We observed some support for the idea that morphological dialect differences (i.e., irregular verb morphology) have a particularly close tie to later literacy, but future work will be necessary to confirm this finding. Supplemental Material https://doi.org/10.23641/asha.13425968.

Improving convergence in growth mixture models without covariance structure constraints

Growth mixture models are a popular method to uncover heterogeneity in growth trajectories. Harnessing the power of growth mixture models in applications is difficult given the prevalence of nonconvergence when fitting growth mixture models to empirical data. Growth mixture models are rooted in the random effect tradition, and nonconvergence often leads researchers to modify their intended model with constraints in the random effect covariance structure to facilitate estimation. While practical, doing so has been shown to adversely affect parameter estimates, class assignment, and class enumeration. Instead, we advocate specifying the models with a marginal approach to prevent the widespread practice of sacrificing class-specific covariance structures to appease nonconvergence. A simulation is provided to show the importance of modeling class-specific covariance structures and builds off existing literature showing that applying constraints to the covariance leads to poor performance. These results suggest that retaining class-specific covariance structures should be a top priority and that marginal models like covariance pattern growth mixture models that model the covariance structure without random effects are well-suited for such a purpose, particularly with modest sample sizes and attrition commonly found in applications. An application to PTSD data with such characteristics is provided to demonstrate (a) convergence difficulties with random effect models, (b) how covariance structure constraints improve convergence but to the detriment of performance, and (c) how covariance pattern growth mixture models may provide a path forward that improves convergence without forfeiting class-specific covariance structures.

Heterogeneity in the dynamic arousal and modulation of fear in young foster children

Guided by emotional security theory, we explored how child and context-related factors were associated with heterogeneity in young foster children's organized patterns of fear response to distress. Results from group-based trajectory modeling used to analyze observational data from a fear-eliciting task showed that children from our sample (mean age = 62 months, SD = 9) were classified into 3 specific fear regulation patterns differentiated by the emotional response parameters of onset intensity, peak intensity, and rise time. A descriptive examination of child's emotion knowledge, aggressive behaviors, and attention problems, as well as length of time in current foster home, placement transitions, and caregiver responsiveness and modeling showed class-specific differences in means. Moreover, the likelihood of class membership was significantly predicted by children's emotion knowledge, aggressive behaviors, and foster mothers' responsiveness and modeling of appropriate boundaries. Results show promising support for the implementation of individualized, child-directed interventions targeting specific patterns of response parameters of emotion regulation for young foster children. Further, parenting intervention services need to promote the emotion socialization skills of foster parents that are tailored toward each specific trajectory pattern of emotion arousal and modulation.

Joint Modeling of Compensatory Multidimensional Item Responses and Response Times

Computer-based testing (CBT) is becoming increasingly popular in assessing test-takers' latent abilities and making inferences regarding their cognitive processes. In addition to collecting item responses, an important benefit of using CBT is that response times (RTs) can also be recorded and used in subsequent analyses. To better understand the structural relations between multidimensional cognitive attributes and the working speed of test-takers, this research proposes a joint-modeling approach that integrates compensatory multidimensional latent traits and response speediness using item responses and RTs. The joint model is cast as a multilevel model in which the structural relation between working speed and accuracy are connected through their variance-covariance structures. The feasibility of this modeling approach is investigated via a Monte Carlo simulation study using a Bayesian estimation scheme. The results indicate that integrating RTs increased model parameter recovery and precision. In addition, Program of International Student Assessment (PISA) 2015 mathematics standard unit items are analyzed to further evaluate the feasibility of the approach to recover model parameters.

Latent Growth Models with Floors, Ceilings, and Random Knots

In longitudinal/developmental studies, individual growth trajectories are sometimes bounded by a floor at the beginning of the observation period and/or a ceiling toward the end of the observation period (or vice versa), resulting in inherently nonlinear growth patterns. If the trajectories between the floor and ceiling are approximately linear, such longitudinal growth patterns can be described with a linear piecewise (spline) model in which segments join at knots. In these scenarios, it may be of specific interest for researchers to examine the timing when transition occurs, and in some occasions also to examine the levels of the floors and/or ceilings if they are not known and fixed. In the current study, we propose a reparameterized piecewise latent growth curve model so that a direct estimation of the random knots (and, if needed, a direct estimation of random floors and ceilings) is possible. We derive the model reparameterization using a 4-step structured latent curve modeling approach. We provide two illustrative examples to demonstrate how the proposed reparameterized models can be fitted to longitudinal growth data using the popular SEM software Mplus and we supply the full coding for applied researchers' reference.

Negative Binomial Models for Visual Fixation Counts on Test Items

With the development of technology-enhanced learning platforms, eye-tracking biometric indicators can be recorded simultaneously with students item responses. In the current study, visual fixation, an essential eye-tracking indicator, is modeled to reflect the degree of test engagement when a test taker solves a set of test questions. Three negative binomial regression models are proposed for modeling visual fixation counts of test takers solving a set of items. These models follow a similar structure to the lognormal response time model and the two-parameter logistic item response model. The proposed modeling structures include individualized latent person parameters reflecting the level of engagement of each test taker and two item parameters indicating the visual attention intensity and discriminating power of each test item. A Markov chain Monte Carlo estimation method is implemented for parameter estimation. Real data are fitted to the three proposed models, and the results are discussed.

The effects of getting a new teacher on the consistency of personality

Objective

In the present research, we examined the effect of getting a new teacher on consistency in students’ personality measures, including trait and social cognitive constructs.

Method

To test the effect of this kind of situational transition, we analyzed two large longitudinal samples (N = 5,628; N = 2,458) with quasi‐experimental study designs. We used two consistency measures (i.e., rank‐order clations and changes in variance over time) to compare students who got a new teacher with students who kept the same teacher.

Results

Multiple‐group latent variable analyses showed no differences in the rank‐order correlations for the math‐related social cognitive constructs of interest, effort, self‐concept, self‐regulation, anxiety, and the Big Five personality traits. Significantly lower rank‐order correlations were found for some of the German‐ and English‐related social cognitive constructs (i.e., effort measures) for the group of students who got a new teacher. Regarding the changes in variance (over time), we found no systematic differences between groups in both studies.

Conclusions

We found partial support for the idea that social cognitive variables are more susceptible to environmental changes (i.e., getting a new teacher) than the Big Five personality traits are.

Using phantom variables in structural equation modeling to assess model sensitivity to external misspecification

External misspecification, the omission of key variables from a structural model, can fundamentally alter the inferences one makes without such variables present. This article presents 2 strategies for dealing with omitted variables, the first a fixed parameter approach incorporating the omitted variable into the model as a phantom variable where all associated parameter values are fixed, and the other a random parameter approach specifying prior distributions for all of the phantom variable's associated parameter values under a Bayesian framework. The logic and implementation of these methods are discussed and demonstrated on an applied example from the educational psychology literature. The argument is made that such external misspecification sensitivity analyses should become a routine part of measured and latent variable modeling where the inclusion of all salient variables might be in question. (PsycINFO Database Record

Correcting Model Fit Criteria for Small Sample Latent Growth Models With Incomplete Data

To date, small sample problems with latent growth models (LGMs) have not received the amount of attention in the literature as related mixed-effect models (MEMs). Although many models can be interchangeably framed as a LGM or a MEM, LGMs uniquely provide criteria to assess global data-model fit. However, previous studies have demonstrated poor small sample performance of these global data-model fit criteria and three post hoc small sample corrections have been proposed and shown to perform well with complete data. However, these corrections use sample size in their computation-whose value is unclear when missing data are accommodated with full information maximum likelihood, as is common with LGMs. A simulation is provided to demonstrate the inadequacy of these small sample corrections in the near ubiquitous situation in growth modeling where data are incomplete. Then, a missing data correction for the small sample correction equations is proposed and shown through a simulation study to perform well in various conditions found in practice. An applied developmental psychology example is then provided to demonstrate how disregarding missing data in small sample correction equations can greatly affect assessment of global data-model fit.

Investigating Approaches to Estimating Covariate Effects in Growth Mixture Modeling: A Simulation Study

Researchers continue to be interested in efficient, accurate methods of estimating coefficients of covariates in mixture modeling. Including covariates related to the latent class analysis not only may improve the ability of the mixture model to clearly differentiate between subjects but also makes interpretation of latent group membership more meaningful. Very few studies have been conducted that compare the performance of various approaches to estimating covariate effects in mixture modeling, and fewer yet have considered more complicated models such as growth mixture models where the latent class variable is more difficult to identify. A Monte Carlo simulation was conducted to investigate the performance of four estimation approaches: (1) the conventional three-step approach, (2) the one-step maximum likelihood (ML) approach, (3) the pseudo class (PC) approach, and (4) the three-step ML approach in terms of their ability to recover covariate effects in the logistic regression class membership model within a growth mixture modeling framework. Results showed that when class separation was large, the one-step ML approach and the three-step ML approach displayed much less biased covariate effect estimates than either the conventional three-step approach or the PC approach. When class separation was poor, estimation of the relation between the dichotomous covariate and latent class variable was severely affected when the new three-step ML approach was used.

Exploring Symptom Clusters in People With Heart Failure

Patients with heart failure (HF) experience multiple symptoms or symptom clusters. The purposes of this study were to (a) determine if distinct latent classes of HF symptoms could be identified, and (b) explore whether sociodemographic and clinical characteristics influenced symptom cluster membership. A total of 4,011 HF patients recruited from outpatient setting completed the Minnesota Living With Heart Failure Questionnaire (MLHFQ), including five physical symptoms (edema, shortness of breath, fatigue-increased need to rest, fatigue-low energy, and sleep difficulties) and three psychological symptoms (worrying, feeling depressed, and cognitive problems). Four distinct classes using latent class profile analysis were identified: low distress (Class 1), physical distress (Class 2), psychological distress (Class 3), and high distress (Class 4). Significant differences among the four latent classes were found for age, education level, and comorbidities. Symptom clusters are useful for recognition of HF symptoms, allowing for the development of strategies that target symptom groups.

The Effect of Extreme Response and Non-extreme Response Styles on Testing Measurement Invariance

Extreme and non-extreme response styles (RSs) are prevalent in survey research using Likert-type scales. Their effects on measurement invariance (MI) in the context of confirmatory factor analysis are systematically investigated here via a Monte Carlo simulation study. Using the parameter estimates obtained from analyzing a 2007 Trends in International Mathematics and Science Study data set, a population model was constructed. Original and contaminated data with one of two RSs were generated and analyzed via multi-group confirmatory factor analysis with different constraints of MI. The results indicated that the detrimental effects of response style on MI have been underestimated. More specifically, these two RSs had a substantially negative impact on both model fit and parameter recovery, suggesting that the lack of MI between groups may have been caused by the RSs, not the measured factors of focal interest. Practical implications are provided to help practitioners to detect RSs and determine whether RSs are a serious threat to MI.

A Note on Recurring Misconceptions When Fitting Nonlinear Mixed Models

Nonlinear mixed-effects (NLME) models are used when analyzing continuous repeated measures data taken on each of a number of individuals where the focus is on characteristics of complex, nonlinear individual change. Challenges with fitting NLME models and interpreting analytic results have been well documented in the statistical literature. However, parameter estimates as well as fitted functions from NLME analyses in recent articles have been misinterpreted, suggesting the need for clarification of these issues before these misconceptions become fact. These misconceptions arise from the choice of popular estimation algorithms, namely, the first-order linearization method (FO) and Gaussian-Hermite quadrature (GHQ) methods, and how these choices necessarily lead to population-average (PA) or subject-specific (SS) interpretations of model parameters, respectively. These estimation approaches also affect the fitted function for the typical individual, the lack-of-fit of individuals' predicted trajectories, and vice versa.

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.

Nonlinear latent curve models for multivariate longitudinal data

Latent curve models have become a useful approach to analyzing longitudinal data, due in part to their allowance of and emphasis on individual differences in features that describe change. Common applications of latent curve models in developmental studies rely on polynomial functions, such as linear or quadratic functions. Although useful for describing linear forms of change and some that are nonlinear, latent curve models based on polynomial functions are not suitable for describing many developmental processes that change in a nonlinear manner. This article considers nonlinear latent curve models that permit researchers to consider a variety of nonlinear functions to characterize developmental processes. An example is provided that considers simultaneous development of two behaviors.

Assessing Spurious Interaction Effects in Structural Equation Modeling: A Cautionary Note

Several studies have stressed the importance of simultaneously estimating interaction and quadratic effects in multiple regression analyses, even if theory only suggests an interaction effect should be present. Specifically, past studies suggested that failing to simultaneously include quadratic effects when testing for interaction effects could result in Type I errors, Type II errors, or misleading interactions. Research investigating this issue has been limited to multiple regression models. Contrarily, structural equation modeling is a more appropriate analysis when hypotheses include latent variables. The current study utilized Monte Carlo simulation to investigate whether quadratic effects should be included in the latent variable interaction model. Consistent with previous research, it was found that including latent variable quadratic effects in the model successfully reduced the frequency of spurious interaction effects but at a cost of low power to detect true interaction effects, inaccurate parameter estimates, inaccurate standard error estimates, and reduced convergence rates. Based on findings from the current study, we recommend that researchers hypothesizing interactions between latent variables should test for these relations using the latent variable interaction model rather than the interaction quadratic model. If researchers are concerned about spurious interactions, then they may want to consider including quadratic effects in the model, provided that they have sample sizes of at least 500 and high indicator reliability. We caution all researchers to base higher order effects models on theory.

A Note on the Specification of Error Structures in Latent Interaction Models

Latent interaction models have motivated a great deal of methodological research, mainly in the area of estimating such models. Product-indicator methods have been shown to be competitive with other methods of estimation in terms of parameter bias and standard error accuracy, and their continued popularity in empirical studies is due, in part, to their straightforward implementation and relative ease of estimation in mainstream structural equation modeling software. In recent years, the impact of different specifications of the mean structure of the structural model has been the focus of a fair amount of investigation in this area. Yet the effects of misspecification of the error structure of the observed variables implied by the model have not been investigated. In this study, the authors demonstrate algebraically the ramifications of misspecifying these error structures for the unconstrained product-indicator approach. Recommendations to practitioners based on these results are discussed.

Modeling Growth in Latent Variables Using a Piecewise Function

Latent growth curve models with piecewise functions for continuous repeated measures data have become increasingly popular and versatile tools for investigating individual behavior that exhibits distinct phases of development in observed variables. As an extension of this framework, this research study considers a piecewise function for describing segmented change of a latent construct over time where the latent construct is itself measured by multiple indicators gathered at each measurement occasion. The time of transition from one phase to another is not known a priori and thus is a parameter to be estimated. Utility of the model is highlighted in 2 ways. First, a small Monte Carlo simulation is executed to show the ability of the model to recover true (known) growth parameters, including the location of the point of transition (or knot), under different manipulated conditions. Second, an empirical example using longitudinal reading data is fitted via maximum likelihood and results discussed. Mplus (Version 6.1) code is provided in Appendix C to aid in making this class of models accessible to practitioners.

A comparison of methods for estimating quadratic effects in nonlinear structural equation models

Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent moderated structural equation method, (d) a fully Bayesian approach, and (e) marginal maximum likelihood estimation. Of the 5 estimation methods, it was found that overall the methods based on maximum likelihood estimation and the Bayesian approach performed best in terms of bias, root-mean-square error, standard error ratios, power, and Type I error control, although key differences were observed. Similarities as well as disparities among methods are highlight and general recommendations articulated. As a point of comparison, all 5 approaches were fit to a reparameterized version of the latent quadratic model to educational reading data.

A Second-Order Conditionally Linear Mixed Effects Model With Observed and Latent Variable Covariates

A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a nonlinear manner are common to all subjects. In this article we describe how a variant of the Michaelis-Menten (M-M) function can be fit within this modeling framework using Mplus 6.0. We demonstrate how observed and latent covariates can be incorporated to help explain individual differences in growth characteristics. Features of the model including an explication of key analytic decision points are illustrated using longitudinal reading data. To aid in making this class of models accessible, annotated Mplus code is provided.

Statistically characterizing intra- and inter-individual variability in children with Developmental Coordination Disorder

Previous research investigating children with Developmental Coordination Disorder (DCD) has consistently reported increased intra- and inter-individual variability during motor skill performance. Statistically characterizing this variability is not only critical for the analysis and interpretation of behavioral data, but also may facilitate our understanding of the processes underlying DCD. Thus, the primary purpose of this research was to demonstrate the utility of a flexible statistical technique, a random coefficient model (RCM), that characterizes the increased intra- and inter-individual variability in children with and without DCD. We analyzed data from a sensorimotor adaptation task during which participants executed discrete aiming movements under conditions of rotated visual feedback. To highlight the advantages of this statistical approach, we contrasted the results from the RCM with those from a traditionally employed general linear model (GLM). The RCM revealed differences between the two groups of children that the GLM did not detect; and, characterized trajectories of change for each individual. The RCM provides researchers an opportunity to probe behavioral deficits at the individual level and may provide new insights into the behavioral heterogeneity in children with DCD.

The undergraduate teaching assistant experience offers opportunities similar to the undergraduate research experience

There has been a growing concern in higher education about our failure to produce scientifically trained workers and scientifically literate citizens. Active-learning and research-oriented activities are posited as ways to give students a deeper understanding of science. We report on an undergraduate teaching assistant (UTA) experience and suggest that students who participate as a UTA obtain benefits analogous to those who participate as an undergraduate research assistant (URA). We examined the experiences of 24 undergraduates acting as UTAs in a general microbiology course. Self-reported gains by the UTAs were supported by observational data from undergraduates in the course who were mentored by the UTAs and by the graduate teaching assistants (GTAs) with whom the UTAs worked. Specifically, data from the UTAs' journals and self-reported Likert scales and rubrics indicated that our teaching assistants developed professional characteristics such as self-confidence and communication and leadership skills, while they acquired knowledge of microbiology content and laboratory skills. Data from the undergraduate Likert scale as well as the pre- and post-GTA rubrics further confirmed our UTA's data interpretations. These findings are significant because they offer empirical data to support the suggestion that the UTA experience is an effective option for developing skills and knowledge in undergraduates that are essential for careers in science. The UTA experience provides a valuable alternative to the URA experience.

Longitudinal construct validity of Brief Symptom Inventory subscales in schizophrenia

Longitudinal validity of Brief Symptom Inventory subscales was examined in a sample (N = 318) with schizophrenia-related illness measured at baseline and every 6 months for 3 years. Nonlinear factor analysis of items was used to test graded response models (GRMs) for subscales in isolation. The models varied in their within-time and between-times parameter constraints, with the homogeneous model being the least constrained, followed by the 2-parameter GRM and 1-parameter GRM. Results show that 4 subscales (Interpersonal Sensitivity, Hostility, Paranoid Ideation, Psychoticism) were consistent with the 1-parameter GRM, and 5 subscales (Somatization, Obsessive-Compulsive, Depression, Anxiety, Phobic Anxiety) were consistent with the 2-parameter GRM. There is evidence that the 9 subscales may be validly used to study change in single constructs over time.

Analysis of nonlinear patterns of change with random coefficient models

Nonlinear patterns of change arise frequently in the analysis of repeated measures from longitudinal studies in psychology. The main feature of nonlinear development is that change is more rapid in some periods than in others. There generally also are strong individual differences, so although there is a general similarity of patterns for different persons over time, individuals exhibit substantial heterogeneity in their particular response. To describe data of this kind, researchers have extended the random coefficient model to accommodate nonlinear trajectories of change. It can often produce a statistically satisfying account of subject-specific development. In this review we describe and illustrate the main ideas of the nonlinear random coefficient model with concrete examples.

Fitting Partially Nonlinear Random Coefficient Models as SEMs

The nonlinear random coefficient model has become increasingly popular as a method for describing individual differences in longitudinal research. Although promising, the nonlinear model it is not utilized as often as it might be because software options are still somewhat limited. In this article we show that a specialized version of the model can be fit to data using SEM software. The specialization is to a model in which the parameters that enter the function in a linear manner are random, whereas those that are nonlinear are common to all individuals. Although this kind of function is not as general as is the fully nonlinear model, it still is applicable to many different data sets. Two examples are presented to show how the models can be estimated using popular SEM computer programs.