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.     

Robustness of Stepwise Latent Class Modeling With Continuous Distal Outcomes

Recently, several bias-adjusted stepwise approaches to latent class modeling with continuous distal outcomes have been proposed in the literature and implemented in generally available software for latent class analysis. In this article, we investigate the robustness of these methods to violations of underlying model assumptions by means of a simulation study. Although each of the 4 investigated methods yields unbiased estimates of the class-specific means of distal outcomes when the underlying assumptions hold, 3 of the methods could fail to different degrees when assumptions are violated. Based on our study, we provide recommendations on which method to use under what circumstances. The differences between the various stepwise latent class approaches are illustrated by means of a real data application on outcomes related to recidivism for clusters of juvenile offenders.     

Detection of Differential Item Functioning with Nonlinear Regression: A Non‐IRT Approach Accounting for Guessing

In this article we present a general approach not relying on item response theory models (non‐IRT) to detect differential item functioning (DIF) in dichotomous items with presence of guessing. The proposed nonlinear regression (NLR) procedure for DIF detection is an extension of method based on logistic regression. As a non‐IRT approach, NLR can be seen as a proxy of detection based on the three‐parameter IRT model which is a standard tool in the study field. Hence, NLR fills a logical gap in DIF detection methodology and as such is important for educational purposes. Moreover, the advantages of the NLR procedure as well as comparison to other commonly used methods are demonstrated in a simulation study. A real data analysis is offered to demonstrate practical use of the method.     

A General 3-Step Maximum Likelihood Approach to Estimate the Effects of Multiple Latent Categorical Variables on a Distal Outcome

The 3-step approach has been recently advocated over the simultaneous 1-step approach to model a distal outcome predicted by a latent categorical variable. We generalize the 3-step approach to situations where the distal outcome is predicted by multiple and possibly associated latent categorical variables. Although the simultaneous 1-step approach has been criticized, simulation studies have found that the performance of the two approaches is similar in most situations (Bakk & Vermunt, 2016). This is consistent with our findings for a 2-LV extension when all model assumptions are satisfied. Results also indicate that under various degrees of violation of the normality and conditional independence assumption for the distal outcome and indicators, both approaches are subject to bias but the 3-step approach is less sensitive. The differences in estimates using the two approaches are illustrated in an analysis of the effects of various childhood socioeconomic circumstances on body mass index at age 50.     

Not quite normal: Consequences of violating the assumption of normality in regression mixture models

Regression mixture models are a new approach for finding differential effects which have only recently begun to be used in applied research. This approach comes at the cost of the assumption that error terms are normally distributed within classes. The current study uses Monte Carlo simulations to explore the effects of relatively minor violations of this assumption, the use of an ordered polytomous outcome is then examined as an alternative which makes somewhat weaker assumptions, and finally both approaches are demonstrated with an applied example looking at differences in the effects of family management on the highly skewed outcome of drug use. Results show that violating the assumption of normal errors results in systematic bias in both latent class enumeration and parameter estimates. Additional classes which reflect violations of distributional assumptions are found. Under some conditions it is possible to come to conclusions that are consistent with the effects in the population, but when errors are skewed in both classes the results typically no longer reflect even the pattern of effects in the population. The polytomous regression model performs better under all scenarios examined and comes to reasonable results with the highly skewed outcome in the applied example. We recommend that careful evaluation of model sensitivity to distributional assumptions be the norm when conducting regression mixture models.     

Comparison of Approaches to Constructing Confidence Intervals for Mediating Effects Using Structural Equation Models

Regression mixture models, which have only recently begun to be used in applied research, are a new approach for finding differential effects. This approach comes at the cost of the assumption that error terms are normally distributed within classes. This study uses Monte Carlo simulations to explore the effects of relatively minor violations of this assumption. The use of an ordered polytomous outcome is then examined as an alternative that makes somewhat weaker assumptions, and finally both approaches are demonstrated with an applied example looking at differences in the effects of family management on the highly skewed outcome of drug use. Results show that violating the assumption of normal errors results in systematic bias in both latent class enumeration and parameter estimates. Additional classes that reflect violations of distributional assumptions are found. Under some conditions it is possible to come to conclusions that are consistent with the effects in the population, but when errors are skewed in both classes the results typically no longer reflect even the pattern of effects in the population. The polytomous regression model performs better under all scenarios examined and comes to reasonable results with the highly skewed outcome in the applied example. We recommend that careful evaluation of model sensitivity to distributional assumptions be the norm when conducting regression mixture models.     

Generalized Linear Factor Score Regression: A Comparison of Four Methods

Factor score regression has recently received growing interest as an alternative for structural equation modeling. However, many applications are left without guidance because of the focus on normally distributed outcomes in the literature. We perform a simulation study to examine how a selection of factor scoring methods compare when estimating regression coefficients in generalized linear factor score regression. The current study evaluates the regression method and the correlation-preserving method as well as two sum score methods in ordinary, logistic, and Poisson factor score regression. Our results show that scoring method performance can differ notably across the considered regression models. In addition, the results indicate that the choice of scoring method can substantially influence research conclusions. The regression method generally performs the best in terms of coefficient and standard error bias, accuracy, and empirical Type I error rates. Moreover, the regression method and the correlation-preserving method mostly outperform the sum score methods.     

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.

     

GIS-based logistic regression method for landslide susceptibility mapping in regional scale

INTRODUCTION Landslide is one of the most serious geological hazards in mountain areas. Globally, they cause hundreds of billions of dollars in damage, and hun- dreds of thousands of deaths and injuries each year (Aleotti and Chowdhury, 1999). Over the past fewdecades, scientists have shown an ever increasing interest in this natural hazard. One of the study fields is to produce landslide susceptibility map, i.e. a map portraying the spatial distribution of the future susceptibility of s…     

Die Bedeutung signifikanter Anderer für eine Erklärung sozial differenzierter Bildungsaspirationen

The Wisconsin Model of Status Attainment (WSC) predicts that students’ socially differentiated aspirations can be explained by differences in their school performance and the aspirations and expectations of their social environment. The appropriateness of these assumptions has been called into doubt for highly stratified secondary level educational systems such as the German one. Using data from the National Educational Panel Study (NEPS), with grade 5 as the starting cohort, the relationship between parents’ social class position, the school performance, achievement expectations of teachers and other pupils, aspirations of friends, educational expectations of parents, and the educational aspirations of 4896 learners were analyzed. The results of the conditional logistic regression analysis confirmed the assumptions derived from theory. Social differences in the educational aspirations of learners can be partially explained by differences in their school performance and fully explained by the influences of their reference group, in particular, those of their parents.     

多层线性建模在CSCL研究中的应用

CSCL研究中常需要处理小组变量和学习者个体变量两种数据,而个体嵌套在小组中,形成两层结构数据。传统的方差分析或线性回归模型仅能针对单层数据,处理多层数据时,易出现标准误差偏移,影响分析的可信度。多层线性建模尽管受CSCL领域样本数的限制,在组层次可能产生偏移量,但能处理稀疏数据,能比较、评估不同层次变异对总变异的贡献度,确定不同层次变量对因变量的影响程度,反映因变量测量随时间变化的发展轨迹,是CSCL领域比较合适的研究方法。     

A Comparison of Method Effects in Two Confirmatory Factor Models for Structurally Different Methods

It is well known that measurement error in observable variables induces bias in estimates in standard regression analysis and that structural equation models are a typical solution to this problem. Often, multiple indicator equations are subsumed as part of the structural equation model, allowing for consistent estimation of the relevant regression parameters. In many instances, however, embedding the measurement model into structural equation models is not possible because the model would not be identified. To correct for measurement error one has no other recourse than to provide the exact values of the variances of the measurement error terms of the model, although in practice such variances cannot be ascertained exactly, but only estimated from an independent study. The usual approach so far has been to treat the estimated values of error variances as if they were known exact population values in the subsequent structural equation modeling (SEM) analysis. In this article we show that fixing measurement error variance estimates as if they were true values can make the reported standard errors of the structural parameters of the model smaller than they should be. Inferences about the parameters of interest will be incorrect if the estimated nature of the variances is not taken into account. For general SEM, we derive an explicit expression that provides the terms to be added to the standard errors provided by the standard SEM software that treats the estimated variances as exact population values. Interestingly, we find there is a differential impact of the corrections to be added to the standard errors depending on which parameter of the model is estimated. The theoretical results are illustrated with simulations and also with empirical data on a typical SEM model.     

Estimating Causal Effects in Mediation Analysis using Propensity Scores

Mediation is usually assessed by a regression-based or structural equation modeling (SEM) approach that we will refer to as the classical approach. This approach relies on the assumption that there are no confounders that influence both the mediator, M, and the outcome, Y. This assumption holds if individuals are randomly assigned to levels of M but generally random assignment is not possible. We propose the use of propensity scores to help remove the selection bias that may result when individuals are not randomly assigned to levels of M. The propensity score is the probability that an individual receives a particular level of M. Results from a simulation study are presented to demonstrate this approach, referred to as Classical + Propensity Model (C+PM), confirming that the population parameters are recovered and that selection bias is successfully dealt with. Comparisons are made to the classical approach that does not include propensity scores. Propensity scores were estimated by a logistic regression model. If all confounders are included in the propensity model, then the C+PM is unbiased. If some, but not all, of the confounders are included in the propensity model, then the C+PM estimates are biased although not as severely as the classical approach (i.e. no propensity model is included).     

Quasi-experimental estimates of class size effect in primary schools in Poland

In this paper we analyze class size effects in the case of primary schools in Poland. We use two empirical strategies to avoid endogeneity bias. First, we use average class size in a grade as an instrumental variable for actual class size. This allows us to control for within school selection of pupils with different abilities to classes of different sizes. Additionally, we estimate fixed effects for schools to control for differences between them. Second, we exploit the fact that there is an informal maximum class size rule. We estimate class size effect only for those enrollment levels where some schools decide to add a new class and thus dramatically lower class sizes. For such enrollment levels variance of class size is mainly exogenous and we argue that this allows estimation of quasi-experimental class size effects. In this case we again use average class size as an instrument with enrollment as a key control variable. Using both strategies we obtain similar findings. We found that the positive effects observed with OLS regression disappear when we use instrumental variables. If we avoid endogeneity bias, then class size negatively affects student achievement. However, this effect is rather small. We discuss methodology, possible bias of results and the importance of our findings to current policy issues in Poland.     

Applying Kaplan-Meier to Item Response Data

Some IRT models can be equivalently modeled in alternative frameworks such as logistic regression. Logistic regression can also model time-to-event data, which concerns the probability of an event occurring over time. Using the relation between time-to-event models and logistic regression and the relation between logistic regression and IRT, this article outlines how the nonparametric Kaplan-Meier estimator for time-to-event data can be applied to IRT data. Established Kaplan-Meier computational formulas are shown to aid in better approximating “parametric-type” item difficulty compared to methods from existing nonparametric methods, particularly for the less-well-defined scenario wherein the response function is monotonic but invariant item ordering is unreasonable. Limitations and the potential for Kaplan-Meier within differential item functioning are also discussed.     

Local Observed‐Score Kernel Equating

Three local observed‐score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias—as defined by Lord's criterion of equity—and percent relative error. The local kernel item response theory observed‐score equating method, which can be used for any of the common equating designs, had a small amount of bias, a low percent relative error, and a relatively low kernel standard error of equating, even when the accuracy of the test was reduced. The local kernel equating methods for the nonequivalent groups with anchor test generally had low bias and were quite stable against changes in the accuracy or length of the anchor test. Although all proposed methods showed small percent relative errors, the local kernel equating methods for the nonequivalent groups with anchor test design had somewhat larger standard error of equating than their kernel method counterparts.     

Effects of sample size and nonnormality on the estimation of mediated effects in latent variable models

A Monte Carlo approach was used to examine bias in the estimation of indirect effects and their associated standard errors. In the simulation design, (a) sample size, (b) the level of nonnormality characterizing the data, (c) the population values of the model parameters, and (d) the type of estimator were systematically varied. Estimates of model parameters were generally unaffected by either nonnormality or small sample size. Under severely nonnormal conditions, normal theory maximum likelihood estimates of the standard error of the mediated effect exhibited less bias (approximately 10% to 20% too small) compared to the standard errors of the structural regression coefficients (20% to 45% too small). Asymptotically distribution free standard errors of both the mediated effect and the structural parameters were substantially affected by sample size, but not nonnormality. Robust standard errors consistently yielded the most accurate estimates of sampling variability.     

Covariate Measurement Error Correction for Student Growth Percentiles Using the SIMEX Method

In this study, we examined the impact of covariate measurement error (ME) on the estimation of quantile regression and student growth percentiles (SGPs), and find that SGPs tend to be overestimated among students with higher prior achievement and underestimated among those with lower prior achievement, a problem we describe as ME endogeneity in this article. We proceeded to assess the effect of covariate ME correction on SGP estimation at two levels—the individual (student) and the aggregate (classroom). Our ME correction approach was limited to the simulation‐extrapolation method known as SIMEX. For both the individual and aggregate SGP, we find SIMEX effective in bias reduction. Further, because SIMEX is especially effective in reducing SGP bias for students with very high or very low prior achievement, it significantly weakens the ME endogeneity. SIMEX is also effective in reducing the MSE of aggregate SGP, provided that the students are sorted to some extent on their latent prior achievement. Our empirical study confirms the pattern of the simulation results: SIMEX mainly affects the mean SGP of classes in the highest and lowest quintiles of the prior score distribution, and significantly lowers the correlation between class SGP and prior achievement.     

Detecting selection bias,using propensity score matching,and estimating treatment effects: an application to the private returns to a master’s degree

Most research in the area of higher education is plagued by the problem of endogeneity or self-selection bias. Unlike ordinary least squares (OLS) regression, propensity score matching addresses the issue of self-selection bias and allows for a decomposition of treatment effects on outcomes. Using panel data from a national survey of bachelor’s degree recipients, this approach is illustrated via an analysis of the effect of receiving a master’s degree, in various program areas, on wage earning outcomes. The results of this study reveal that substantial self-selection bias is undetected when using OLS regression techniques. This article also shows that, unlike OLS regression, propensity score matching allows for estimates of the average treatment effect, average treatment on the treated effect, and the average treatment on the untreated effect on student outcomes such as wage earnings.     

A too liberal religious education? A thought experiment for teachers and theorists

This paper proposes that the ideas of political philosopher John Rawls could be adapted to offer a new starting point for a pedagogy of religious education (RE) in the non‐denominational sector. It is argued that contemporary approaches to RE may infringe the liberal principle of freedom of belief by favouring certain methods of interpreting religions. In response to this criticism, it is suggested that teachers can construct a just and fair pedagogy, which is truly liberal in its assumptions, by following a procedure similar to that advocated by Rawls. Readers are invited to don a ‘veil of ignorance’ and imagine that from this perspective they are to enter into a hypothetical contract outlining the founding principles of a pedagogical approach. It is argued that those entering into such a contract would opt for a form of critical RE not dissimilar to Wright’s that aims to present religions and competing ideologies without distortion. It is hoped that this hypothetical contract can thus characterise and legitimise the first principles of a truly liberal RE, and provide a convenient conceptual apparatus that eliminates bias and promotes balance.