Latent Class Trees with the Three-Step Approach

Latent class (LC) analysis is widely used in the social and behavioral sciences to find meaningful clusters based on a set of categorical variables. To deal with the common problem that a standard LC analysis may yield a large number classes and thus a solution that is difficult to interpret, recently an alternative approach has been proposed, called Latent Class Tree (LCT) analysis. It involves starting with a solution with a small number of “basic” classes, which may subsequently be split into subclasses at the next stages of an analysis. However, in most LC analysis applications, we not only wish to identify the relevant classes, but also want to see how they relate to external variables (covariates or distal outcomes). For this purpose, researchers nowadays prefer using the bias-adjusted three-step method. Here, we show how this bias-adjusted three-step procedure can be applied in the context of LCT modeling. More specifically, an R-package is presented that performs a three-step LCT analysis: it builds a LCT and allows checking how splits are related to the relevant external variables. The new tool is illustrated using a cross-sectional application with multiple indicators on social capital and demographics as external variables and with a longitudinal application with a mood variable measured multiple times during the day and personality traits as external variables.     

Latent Class Modeling with A Time-To-Event Distal Outcome: A Comparison of One,Two and Three-Step Approaches

Latent class methods can be used to identify unobserved subgroups which differ in their observed data. Researchers are often interested in outcomes for the identified subgroups and in some disciplines time-to-event outcome measures are common, e.g., overall survival in oncology. In this study Monte Carlo simulation is used to evaluate the empirical properties of latent class effect estimates on a time-to-event distal outcome using one, two and three-step approaches. Both standard and inclusive bias-corrected three-step approaches are considered. One-step latent class effect estimates are shown to be superior to the evaluated alternatives. Both the two-step approach and a standard three-step approach, where subjects are partially assigned to latent classes, produced unbiased estimates with nominal confidence interval coverage when latent classes were well separated, but not otherwise.

     

A Comparison of Three-Step Approaches for Auxiliary Variables in Latent Class and Latent Profile Analysis

In this article, 3-step methods to include predictors and distal outcomes in commonly used mixture models are evaluated. Two Monte Carlo simulation studies were conducted to compare the pseudo class (PC), Vermunt’s (2010), and the Lanza, Tan, and Bray (LTB) 3-step approaches with respect to bias of parameter estimates in latent class analysis (LCA) and latent profile analysis (LPA) models with auxiliary variables. For coefficients of predictors of class membership, results indicated that Vermunt’s method yielded more accurate estimates for LCA and LPA compared to the PC method. With distal outcomes of latent classes and latent profiles, the LTB method produced the lowest relative bias of coefficient estimates and Type I error rates close to nominal levels.     

Prediction from Latent Classes: A Demonstration of Different Approaches to Include Distal Outcomes in Mixture Models

Including auxiliary variables such as antecedent and consequent variables in mixture models provides valuable insight in understanding the population heterogeneity embodied by a latent class variable. The model building process regarding how to include predictors/correlates and outcomes of the latent class variables into mixture models is an area of active research. As such, new methods of including these variables continue to emerge and best practices for the application of these methods in real data settings (including simple guidelines for choosing amongst them) are still not well established. This paper focuses on one type of auxiliary variable—distal outcomes—providing an overview of the methods currently available for estimating the effects of latent class membership on subsequent distal outcomes. We illustrate the recommended methods in the software packages Mplus and Latent Gold using a latent class model to capture population heterogeneity in students’ mathematics attitudes, linking latent class membership to two distal outcomes.     

A Structural Equation Model of Second Language Acquisition for Adult Learners

Abstract

This study constructs and empirically evaluates a model of second language acquisition for adult learners. The proposed structural equation model describes the relationships between latent variables representing sociocultural background, cognitive ability (in the first language), functional language proficiency, cognitive language proficiency, attitudes, motivation, and instructional approach. Tentative empirical estimates, which are somewhat unreliable due to a small sample size, were obtained using a methodology developed by JÖreskog known as the linear structural relationship (LISREL) model. The data used for estimation are drawn from a Chicago bilingual teacher training program that utilized two radically different English as a Second Language (ESL) teaching methods. Though primarily illustrative in nature, the results showed that an “integrative” approach to second language instruction was shown to be more effective than a strictly “behaviorist” approach, and functional language ability was shown to be an important component of the language acquisition process.     

Measurement Uncertainty in Racial and Ethnic Identification Among Adolescents of Mixed Ancestry: A Latent Variable Approach

In this article, we operationalize identification of mixed racial and ethnic ancestry among adolescents as a latent variable to (a) account for measurement uncertainty, and (b) compare alternative wording formats for racial and ethnic self-categorization in surveys. Two latent variable models were fit to multiple mixed-ancestry indicator data from 1,738 adolescents in New England. The first, a mixture factor model, accounts for the zero-inflated mixture distribution underlying mixed-ancestry identification. Alternatively, a latent class model allows classification distinction between relatively ambiguous versus unambiguous mixed-ancestry responses. Comparison of individual indicators reveals that the Census 2000 survey version estimates higher prevalence of mixed ancestry but is less sensitive to relative certainty of identification than are alternate survey versions (i.e., offering a “mixed” check box option, allowing a written response). Ease of coding and missing data are also considered in discussing the relative merit of individual mixed-ancestry indicators among adolescents.     

Factors Affecting the Item Parameter Estimation and Classification Accuracy of the DINA Model

To better understand the statistical properties of the deterministic inputs, noisy “and” gate cognitive diagnosis (DINA) model, the impact of several factors on the quality of the item parameter estimates and classification accuracy was investigated. Results of the simulation study indicate that the fully Bayes approach is most accurate when the prior distribution matches the latent class structure. However, when the latent classes are of indefinite structure, the empirical Bayes method in conjunction with an unstructured prior distribution provides much better estimates and classification accuracy. Moreover, using empirical Bayes with an unstructured prior does not lead to extremely poor results as other prior-estimation method combinations do. The simulation results also show that increasing the sample size reduces the variability, and to some extent the bias, of item parameter estimates, whereas lower level of guessing and slip parameter is associated with higher quality item parameter estimation and classification accuracy.     

On estimating finite mixtures of multivariate regression and simultaneous equation models

We propose a maximum likelihood framework for estimating finite mixtures of multivariate regression and simultaneous equation models with multiple endogenous variables. The proposed “semi‐parametric” approach posits that the sample of endogenous observations arises from a finite mixture of components (or latent‐classes) of unknown proportions with multiple structural relations implied by the specified model for each latent‐class. We devise an Expectation‐Maximization algorithm in a maximum likelihood framework to simultaneously estimate the class proportions, the class‐specific structural parameters, and posterior probabilities of membership of each observation into each latent‐class. The appropriate number of classes can be chosen using various information‐theoretic heuristics. A data set entailing cross‐sectional observations for a diverse sample of businesses is used to illustrate the proposed approach.     

A Non-arbitrary Method of Identifying and Scaling Latent Variables in SEM and MACS Models

A non-arbitrary method for the identification and scale setting of latent variables in general structural equation modeling is introduced. This particular technique provides identical model fit as traditional methods (e.g., the marker variable method), but it allows one to estimate the latent parameters in a nonarbitrary metric that reflects the metric of the measured indicators. This technique, therefore, is particularly useful for mean and covariance structures (MACS) analyses, where the means of the indicators and latent constructs are of key interest. By introducing this alternative method of identification and scale setting, researchers are provided with an additional tool for conducting MACS analyses that provides a meaningful and nonarbitrary scale for the estimates of the latent variable parameters. Importantly, this tool can be used with single-group single-occasion models as well as with multiple-group models, multiple-occasion models, or both.     

Evaluation of True Criterion Validity for Unidimensional Multicomponent Measuring Instruments in Longitudinal Studies

Longitudinal studies offer unique opportunities to identify the specificity variance in the components of a psychometric scale that is administered repeatedly. This article discusses a procedure for evaluation of the relationship between true scale scores and criterion variables uncorrelated with measurement errors in longitudinally presented measures comprising unidimensional multicomponent instruments. The approach provides point and interval estimates of the true scale criterion validity with respect to a criterion that is assessed once or repeatedly, as well as a means for testing temporal stability in this validity. The outlined method is based on an application of the latent variable modeling methodology, is readily applicable with popular software, and is illustrated using empirical data.     

Managing knowledge performance: testing the components of a knowledge management system on organizational performance

The main purpose of the current study is to validate the framework of knowledge management (KM) capabilities created by Gold (Towards a theory of organizational knowledge management capabilities. Doctoral dissertation, University of North Carolina, Chapel Hill) 2001) in a study of South Korean companies. However, the original framework did not provide a thorough explanation of the effect of incentives, which motivate and encourage the knowledge management process. In this study, the modified framework that includes incentives in the knowledge infrastructure capability was tested. Moreover, since there is a weak linkage between KM and organizational performance, this study used empirical evidence to identify the relationship between KM capabilities (KMC) and four perspectives of organizational performance. Since structural equation modeling (SEM) is mostly used to describe causal relationships among unobserved (latent) and observed variables, this study used SEM procedures to determine whether there were any structural relationships between knowledge management capabilities and four perspectives of organizational performance. Moreover, the SEM procedure is “a statistical test to find whether a model fits a set of data, whether it matches a theoretical expectation” (Vogt, Dictionary of statistics & methodology. Sage Publications Inc., Thousand Oaks, CA, p 135, 2005). Therefore, this study also used SEM procedures to test a hypothesized model that had a good fit indicates that the model adequately describes the sample data. This study assumed that knowledge management capabilities could be divided into two types: knowledge infrastructure and process capabilities. The original hypothesized model showed that there was a positive relationship between knowledge management capabilities and organizational performance, but the overall model fit was insufficient to be accepted, because knowledge infrastructure and process capabilities were highly correlated. This study proposed two alternative models to find the best fit and found that knowledge infrastructure and process capabilities should be combined under the higher-order latent variable as subordinate latent variables. Lastly, there was a positive relationship between KMC and organizational performance. This study might not be free from common method bias to some degrees. It would be better to divide participants into two groups to respond to either the knowledge management capabilities survey or the organizational performance survey and to investigate the correlation between them. There are two main contributions for the field of knowledge management. First, this study attempted to integrate the fragmented literature of knowledge management into a holistic view and develop a framework for knowledge management. Moreover, this study found that there is a strong and positive relationship between KM infrastructure and process, which could refer that, to improve organizational performance, an organization should support KM processes, as well as build decent KM infrastructure. The results of this study would help KM practitioners to advocate the importance of KM to top managements.     

Exploring the Utility of Background and Cognitive Variables in Explaining Latent Differential Item Functioning: An Example of the PISA 2009 Reading Assessment

Differential item functioning (DIF) may be caused by an interaction of multiple manifest grouping variables or unexplored manifest variables, which cannot be detected by conventional DIF detection methods that are based on a single manifest grouping variable. Such DIF may be detected by a latent approach using the mixture item response theory model and subsequently explained by multiple manifest variables. This study facilitates the interpretation of latent DIF with the use of background and cognitive variables. The PISA 2009 reading assessment and student survey are analyzed. Results show that members in manifest groups were not homogenously advantaged or disadvantaged and that a single manifest grouping variable did not suffice to be a proxy of latent DIF. This study also demonstrates that DIF items arising from the interaction of multiple variables can be effectively screened by the latent DIF analysis approach. Background and cognitive variables jointly well predicted latent class membership.     

Latent Curve Models and Latent Change Score Models Estimated in R

When using multiple imputation in the analysis of incomplete data, a prominent guideline suggests that more than 10 imputed data values are seldom needed. This article calls into question the optimism of this guideline and illustrates that important quantities (e.g., p values, confidence interval half-widths, and estimated fractions of missing information) suffer from substantial imprecision with a small number of imputations. Substantively, a researcher can draw categorically different conclusions about null hypothesis rejection, estimation precision, and missing information in distinct multiple imputation runs for the same data and analysis with few imputations. This article explores the factors associated with this imprecision, demonstrates that precision improves by increasing the number of imputations, and provides practical guidelines for choosing a reasonable number of imputations to reduce imprecision for each of these quantities.     

A structural equation model of the writing process in typically-developing sixth grade children

The purpose of this study was to evaluate how sixth grade children planned, translated, and revised written narrative stories using a task reflecting current instructional and assessment practices. A modified version of the Hayes and Flower (1980) writing process model was used as the theoretical framework for the study. Two hundred one sixth-grade students participated in a three-day writing task. On the first day they generated ideas for their story, on the second day they produced a first draft, and on the third day they revised their draft to produce a final copy. Scores from each day’s writing were used as measured variables representing the latent variables of planning, translating, and revising. Confirmatory structural equation modeling results suggested that the latent variable of planning had a moderate relationship to translating and that translating had a stronger than expected relationship with revising. Significant paths between measured and latent variables demonstrated the relative contribution of skills towards the writing process. The approach used in this study highlighted the linear manner in which intermediate grade children write. Findings suggest that planning had a direct effect on translating, but no direct effect on revising. There was a strong relationship between translating and revising, suggesting few differences between students’ first and final drafts.     

CAUSES OF STUDENT ABSENTEEISM IN COMMUNITY COLLEGE CLASSES

In an era of declining college enrollments it is vital to identify potential causes of absenteeism and implement strategies for reducing it. To accomplish this two open‐ended approaches were used to generate a list of reasons for missing social science classes. The combination of these two ultimately led to 51 reasons for missing class that appeared on the Class Attendance Survey in Likert scale format. This survey was shown to have both internal reliability and validity. The dependent variable on the survey was the number of absences reported by each student for the class in which the survey was taken. It was administered in class on or about the last class day by 24 social science professors to 25 classes. This resulted in 402 usable surveys, of which 351 were complete. A factor analysis of the independent variables yielded six factors with eigenvalues greater than 1.0 and factor loadings higher than .50. Four of the six entered a stepwise multiple regression equation. They combined to produce a highly significant F value. In descending order of their beta weights they were labeled “fatigue associated with excessive socializing,” “low attendance incentives,” “irresponsible pursuit of leisure,” and “external responsibilities.” F values for each of the beta weights were significant. Several recommendations for reducing absenteeism were made.     

谈陇东方言中“得来”、“得”的用法

陇东方言中助词“得来”、“得”跟普通话中助词“得”相比较具有不同的用法,它们不但做助词,而且还凝固成词。本文就陇东方言中“得来”、“得”的语法现象做了一定的探讨。     

Testing Criterion Correlations With Scale Component Measurement Errors Using Latent Variable Modeling

A latent variable modeling method for testing criterion correlations with measurement error terms in multicomponent measuring instruments is outlined. The approach is based on an application of the Benjamini–Hochberg multiple testing procedure and can be used when assumptions of validity estimation related procedures need to be examined. The method also allows studying the extent to which criterion validity coefficients might be due to the relationship between a presumed underlying latent construct evaluated by a psychometric scale and a criterion variable, or could be a consequence of the relation between measurement error in the overall scale score and the criterion. The discussed procedure is widely applicable with popular latent variable modeling software, and is illustrated using a numerical example.     

Avoiding and Correcting Bias in Score-Based Latent Variable Regression With Discrete Manifest Items

This article considers models involving a single structural equation with latent explanatory and/or latent dependent variables where discrete items are used to measure the latent variables. Our primary focus is the use of scores as proxies for the latent variables and carrying out ordinary least squares (OLS) regression on such scores to estimate parameters in the structural equation. We are concerned with the bias in these OLS estimates; we present two approaches to deal with this bias. Extending the work of Skrondal and Laake (2001) Skrondal, A. and Laake, P. 2001. Regression among factor scores. Psychometrika, 66: 563–576. [Crossref], [Web of Science ®] , [Google Scholar] on continuous items, we derive sufficient conditions under which the use of scores based on item response theory leads to unbiased OLS estimates at the population level; we deem this approach “bias avoiding.” We also consider Croon's (2002) Croon, M. 2002. “Using predicted latent scores in general latent structure models”. In Latent variable and latent structure models, Edited by: Marcoulides, G. A. and Moustaki, I. 195–223. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.  [Google Scholar] bias correction methodology for continuous items and explore its efficacy on discrete items; we deem this approach “bias correcting.” We illustrate the performance of the 2 approaches through numerical examples of large simulated data sets.     

The role of plausible values in large-scale surveys

In large-scale assessment programs such as NAEP, TIMSS and PISA, students' achievement data sets provided for secondary analysts contain so-called plausible values. Plausible values are multiple imputations of the unobservable latent achievement for each student. In this article it has been shown how plausible values are used to: (1) address concerns with bias in the estimation of certain population parameters when point estimates of latent achievement are used to estimate those population parameters; (2) allow secondary data analysts to employ standard techniques and tools (e.g., SPSS, SAS procedures) to analyse achievement data that contains substantial measurement error components; and (3) facilitate the computation of standard errors of estimates when the sample design is complex. The advantages of plausible values have been illustrated by comparing the use of maximum likelihood estimates and plausible values (PV) for estimating a range of population statistics.     

Using Fixed Thresholds with Grouped Data in Structural Equation Modeling

Valuable methods have been developed for incorporating ordinal variables into structural equation models using a latent response variable formulation. However, some model parameters, such as the means and variances of latent factors, can be quite difficult to interpret because the latent response variables have an arbitrary metric. This limitation can be particularly problematic in growth models, where the means and variances of the latent growth parameters typically have important substantive meaning when continuous measures are used. However, these methods are often applied to grouped data, where the ordered categories actually represent an interval-level variable that has been measured on an ordinal scale for convenience. The method illustrated in this article shows how category threshold values can be incorporated into the model so that interpretation is more meaningful, with particular emphasis given to the application of this technique with latent growth models.