Consequences of Ignoring Guessing Effects on Measurement Invariance Analysis

Pseudo-guessing parameters are present in item response theory applications for many educational assessments. When sample size is not sufficiently large, the guessing parameters may be ignored from the analysis. This study examines the impact of ignoring pseudo-guessing parameters on measurement invariance analysis, specifically, on item difficulty, item discrimination, and mean and variance of ability distribution. Results show that when non-zero guessing parameters are ignored from the measurement invariance analysis, item discrimination estimates tend to decrease particularly for more difficult items, and item difficulty estimates decrease unless the items are highly discriminating and difficult. As the guessing parameter increases, the size of the decrease in item discrimination and difficulty tends to increase, and the estimated mean and variance of ability distribution tend to be inaccurate. When two groups have heterogeneous ability distributions, ignoring the guessing parameter affects the reference group and the focal group differently. Implications of result findings are discussed.     

The Multigroup Multilevel Categorical Latent Growth Curve Models

Longitudinal data describe developmental patterns and enable predictions of individual changes beyond sampled time points. Major methodological issues in longitudinal data include modeling random effects, subject effects, growth curve parameters, and autoregressive residuals. This study embedded the longitudinal model within a multigroup multilevel framework and allowed for autoregressive residuals. The parameter in the new model can be estimated using the computer program WinBUGS, which adopts Markov Chain Monte Carlo algorithms. Two simulation studies were conducted. An empirical example was raised and established based on models generated by the results of empirical data, which have been fitted and compared.     

Bayesian Inference for Growth Mixture Models with Latent Class Dependent Missing Data

Growth mixture models (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class probabilities depend on some observed explanatory variables and data missingness depends on both the explanatory variables and a latent class variable. A full Bayesian method is then proposed to estimate the model. Through the data augmentation method, conditional posterior distributions for all model parameters and missing data are obtained. A Gibbs sampling procedure is then used to generate Markov chains of model parameters for statistical inference. The application of the model and the method is first demonstrated through the analysis of mathematical ability growth data from the National Longitudinal Survey of Youth 1997 (Bureau of Labor Statistics, U.S. Department of Labor, 1997). A simulation study considering 3 main factors (the sample size, the class probability, and the missing data mechanism) is then conducted and the results show that the proposed Bayesian estimation approach performs very well under the studied conditions. Finally, some implications of this study, including the misspecified missingness mechanism, the sample size, the sensitivity of the model, the number of latent classes, the model comparison, and the future directions of the approach, are discussed.     

Nonlinear and Quasi-Simplex Patterns in Latent Growth Models

In the SEM literature, simplex and latent growth models have always been considered competing approaches for the analysis of longitudinal data, even if they are strongly connected and both of specific importance. General dynamic models, which simultaneously estimate autoregressive structures and latent curves, have been recently proposed in the literature. We discuss the properties of Autoregressive Latent Trajectories (ALT) with the aim of deriving their relationship with nonlinear growth models. We show how the quasi-simplex part of the ALT admits an equivalent nonlinear growth representation. A simulation study is performed to examine how the relationship holds in the presence of polynomial and bounded growths over time, whereas an empirical application on student achievement highlights the usefulness of the equivalence. The evaluation of the formative process in the European University system has been assuming an ever increasing importance since the beginning of the Bologna process. In this context, the analysis of student performances and capabilities using different approaches plays a fundamental role.     

The Latent and Manifest Consequences of Work

Jahoda's (1979) distinction between manifest and latent consequences of work was tested on samples of employed and unemployed persons to determine if such a dichotomy can help explain the psychosocial effects of unemployment. Confirmatory factor analysis on data from 393 individuals from two large American cities failed to support the two consequences of work proposed by Jahoda. Instead, these data indicate that an intrinsic versus extrinsic model of work rewards can more accurately account for the patterns among ratings. The model of best fit was equally accurate for the employed and unemployed samples, suggesting that these groups have similar reactions to and reasons for working (or wanting to work). These results indicate that more than financial loss is suffered when jobs are lost involuntarily, and that we can fully understand the debilitating effects of unemployment only when we recognize the full scope of reasons why people work.     

Latent Growth Models of Individual Change: The Case of Newcomer Adjustment

One commonality to various theoretical frameworks concerning employee work adjustment is change in employee-organization linkages over time, yet few empirical tests of employee work adjustment theories have adequately operationalized change. We develop and test a model of longitudinal change on one particular form of employee adjustment, employee attachment, operationalized in terms of O'Reilly and Chatman's (1986) triparite structure of commitment, using second-order factor (SOF) latent growth modeling (LGM). Results were generally supportive of the theoretical model and illustrate several advantages to using SOF LGM to measure longitudinal change. Copyright 2000 Academic Press.     

The Thorny Relation Between Measurement Quality and Fit Index Cutoffs in Latent Variable Models

Latent variable modeling is a popular and flexible statistical framework. Concomitant with fitting latent variable models is assessment of how well the theoretical model fits the observed data. Although firm cutoffs for these fit indexes are often cited, recent statistical proofs and simulations have shown that these fit indexes are highly susceptible to measurement quality. For instance, a root mean square error of approximation (RMSEA) value of 0.06 (conventionally thought to indicate good fit) can actually indicate poor fit with poor measurement quality (e.g., standardized factors loadings of around 0.40). Conversely, an RMSEA value of 0.20 (conventionally thought to indicate very poor fit) can indicate acceptable fit with very high measurement quality (standardized factor loadings around 0.90). Despite the wide-ranging effect on applications of latent variable models, the high level of technical detail involved with this phenomenon has curtailed the exposure of these important findings to empirical researchers who are employing these methods. This article briefly reviews these methodological studies in minimal technical detail and provides a demonstration to easily quantify the large influence measurement quality has on fit index values and how greatly the cutoffs would change if they were derived under an alternative level of measurement quality. Recommendations for best practice are also discussed.     

The Impacts of Ignoring a Crossed Factor in Analyzing Cross-Classified Data

Cross-classified random-effects models (CCREMs) are used for modeling nonhierarchical multilevel data. Misspecifying CCREMs as hierarchical linear models (i.e., treating the cross-classified data as strictly hierarchical by ignoring one of the crossed factors) causes biases in the variance component estimates, which in turn, results in biased estimation in the standard errors of the regression coefficients. Analytical studies were conducted to provide closed-form expressions for the biases. With balanced design data structure, ignoring a crossed factor causes overestimation of the variance components of adjacent levels and underestimation of the variance component of the remaining crossed factor. Moreover, ignoring a crossed factor at the kth level causes underestimation of the standard error of the regression coefficient of the predictor associated with the ignored factor and overestimation of the standard error of the regression coefficient of the predictor at the (k?1)th level. Simulation studies were also conducted to examine the effect of different structures of cross-classification on the biases. In general, the direction and magnitude of the biases depend on the level of the ignored crossed factor, the level with which the predictor is associated at, the magnitude of the variance component of the ignored crossed factor, the variance components of the predictors, the sample sizes, and the structure of cross-classification. The results were further illustrated using the Early Childhood Longitudinal Study-Kindergarten Cohort data.     

Correction for Item Response Theory Latent Trait Measurement Error in Linear Mixed Effects Models

Psychometrika - When latent variables are used as outcomes in regression analysis, a common approach that is used to solve the ignored measurement error issue is to take a multilevel perspective on...     

Misspecification in Latent Change Score Models: Consequences for Parameter Estimation,Model Evaluation,and Predicting Change

Latent change score models (LCS) are conceptually powerful tools for analyzing longitudinal data (McArdle & Hamagami, 2001). However, applications of these models typically include constraints on key parameters over time. Although practically useful, strict invariance over time in these parameters is unlikely in real data. This study investigates the robustness of LCS when invariance over time is incorrectly imposed on key change-related parameters. Monte Carlo simulation methods were used to explore the impact of misspecification on parameter estimation, predicted trajectories of change, and model fit in the dual change score model, the foundational LCS. When constraints were incorrectly applied, several parameters, most notably the slope (i.e., constant change) factor mean and autoproportion coefficient, were severely and consistently biased, as were regression paths to the slope factor when external predictors of change were included. Standard fit indices indicated that the misspecified models fit well, partly because mean level trajectories over time were accurately captured. Loosening constraint improved the accuracy of parameter estimates, but estimates were more unstable, and models frequently failed to converge. Results suggest that potentially common sources of misspecification in LCS can produce distorted impressions of developmental processes, and that identifying and rectifying the situation is a challenge.     

Assessing the reliability of Curriculum-Based Measurement: an application of Latent Growth Modeling

The purpose of this study was to demonstrate the use of Latent Growth Modeling (LGM) as a method for estimating reliability of Curriculum-Based Measurement (CBM) progress-monitoring data. The LGM approach permits the error associated with each measure to differ at each time point, thus providing an alternative method for examining of the reliability of CBM reading aloud data over repeated measurements. The analysis revealed that the reliability of CBM data was not a fixed property of the measure, but it changed with time. The study demonstrates the need to consider reliability in new ways with respect to the use of CBM data as repeated measures.     

The Rediscovery of Bifactor Measurement Models

Bifactor latent structures were introduced over 70 years ago, but only recently has bifactor modeling been rediscovered as an effective approach to modeling construct-relevant multidimensionality in a set of ordered categorical item responses. I begin by describing the Schmid-Leiman bifactor procedure (Schmid &; Leiman, 1957 Schmid, J. 1957. The comparability of the bi-factor and second-order factor patterns. Journal of Experimental Education, 25: 249–253. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and highlight its relations with correlated-factors and second-order exploratory factor models. After describing limitations of the Schmid-Leiman, 2 newer methods of exploratory bifactor modeling are considered, namely, analytic bifactor (Jennrich &; Bentler, 2011 Jennrich, R. I. and Bentler, P. M. 2011. Exploratory bi-factor analysis. Psychometrika, 76: 537–549. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and target bifactor rotations (Reise, Moore, &; Maydeu-Olivares, 2011 Reise, S. P., Moore, T. M. and Maydeu-Olivares, A. 2011. Targeted bifactor rotations and assessing the impact of model violations on the parameters of unidimensional and bifactor models. Educational and Psychological Measurement, 71: 684–711. [Crossref], [Web of Science ®] , [Google Scholar]). Then I discuss limited- and full-information estimation approaches to confirmatory bifactor models that have emerged from the item response theory and factor analysis traditions, respectively. Comparison of the confirmatory bifactor model to alternative nested confirmatory models and establishing parameter invariance for the general factor also are discussed. Finally, important applications of bifactor models are reviewed. These applications demonstrate that bifactor modeling potentially provides a solid foundation for conceptualizing psychological constructs, constructing measures, and evaluating a measure's psychometric properties. However, some applications of the bifactor model may be limited due to its restrictive assumptions.     

The Effects of Educational Diversity in a National Sample of Law Students: Fitting Multilevel Latent Variable Models in Data With Categorical Indicators

Controversy surrounding the use of race-conscious admissions can be partially resolved with improved empirical knowledge of the effects of racial diversity in educational settings. We use a national sample of law students nested in 64 law schools to test the complex and largely untested theory regarding the effects of educational diversity on student outcomes. Social scientists who study these outcomes frequently encounter both latent variables and nested data within a single analysis. Yet, until recently, an appropriate modeling technique has been computationally infeasible, and consequently few applied researchers have estimated appropriate models to test their theories, sometimes limiting the scope of their research question. Our results, based on disaggregated multilevel structural equation models, show that racial diversity is related to a reduction in prejudiced attitudes and increased perceived exposure to diverse ideas and that these effects are mediated by more frequent interpersonal contact with diverse peers. These findings provide support for the idea that administrative manipulation of educational diversity may lead to improved student outcomes. Admitting a racially/ethnically diverse student body provides an educational experience that encourages increased exposure to diverse ideas and belief systems.     

The Determinants and Consequences of Intragroup Respect: An Examination Within a Sporting Context1

Although the term respect is widely used in society, its determinants and consequences on group‐related factors are unclear. In 4 studies (2 pilot studies, validation study, main study), we examined these issues. In the main study, high‐level rowing crew members completed measures of respect, liking, and group identification pre‐ and post‐competition; and attribution items post‐competition. Although respect and liking did not predict team success, success was associated with subsequent levels of respect, but not liking. The effect of success on group identification was mediated by respect. Moderation analyses indicated that intragroup liking, but not respect, increased the likelihood of group‐serving attributions. Results highlight the determinants of respect and its role in group processes and outcomes, and distinguish respect from liking.     

当代大学生自比型价值观数据的潜在结构

本研究对采自3796名在校大学生的Rokeach Value Survey自比型数据进行了因素分析和多维尺度分析。因素分析从两组价值观选项中分别获得6个双极因素,虽然内容各不相同,但均体现出个人指向-亲社会指向的特点。多维尺度分析所获得的两组选项的2维空间距离分布结果也体现类似特点,结果显示终极性价值观可分为四类,工具性价值观可分为五类。当前大学生价值观中存在着舒适的物质生活、兴奋的生活、幸福、快乐和自尊以及雄心壮志的、勇敢的和诚实的等个人取向内容占优势的可能性。在两种分析方法中,多维尺度分析更适合对自比型价值观数据潜在结构的探究。     

The Recovery of Correlation Between Latent Abilities Using Compensatory and Noncompensatory Multidimensional IRT Models

This research examined correlation estimates between latent abilities when using the two-dimensional and three-dimensional compensatory and noncompensatory item response theory models. Simulation study results showed that the recovery of the latent correlation was best when the test contained 100% of simple structure items for all models and conditions. When a test measured weakly discriminated dimensions, it became harder to recover the latent correlation. Results also showed that increasing the sample size, test length, or using simpler models (i.e., two-parameter logistic rather than three-parameter logistic, compensatory rather than noncompensatory) could improve the recovery of latent correlation.     

基于增长模型的非随机缺失数据处理:选择模型和极大似然方法

对含有非随机缺失数据的潜变量增长模型,为了考察基于不同假设的缺失数据处理方法:极大似然(ML)方法与DiggleKenward选择模型的优劣,通过Monte Carlo模拟研究,比较两种方法对模型中增长参数估计精度及其标准误估计的差异,并考虑样本量、非随机缺失比例和随机缺失比例的影响。结果表明,符合前提假设的Diggle-Kenward选择模型的参数估计精度普遍高于ML方法;对于标准误估计值,ML方法存在一定程度的低估,得到的置信区间覆盖比率也明显低于Diggle-Kenward选择模型。     

童年早期社会能力的发展：一个潜变量增长模型

对119名幼儿进行历时两年的三次追踪测试, 采用潜变量增长建模, 检验童年早期的社会能力是否呈线性增长, 并考察气质、性别、母亲受教育程度及其交互作用对社会能力发展水平与速度的预测作用。结果发现：(1)社会能力在两年中呈线性增长, 起始水平及发展速度均存在显著的个体差异; (2)女孩起始的社会能力水平高于男孩; 母亲受教育程度越高, 儿童起始的社会能力水平就越高; (3)气质节律性对社会能力增长速度的预测因儿童性别而异：节律性能够负向预测女孩社会能力的增长速度、正向预测男孩社会能力的增长速度。