Modeling Predictors of Latent Classes in Regression Mixture Models

The purpose of this study is to provide guidance on a process for including latent class predictors in regression mixture models. We first examine the performance of current practice for using the 1-step and 3-step approaches where the direct covariate effect on the outcome is omitted. None of the approaches show adequate estimates of model parameters. Given that Step 1 of the 3-step approach shows adequate results in class enumeration, we suggest using an alternative approach: (a) decide the number of latent classes without predictors of latent classes, and (b) bring the latent class predictors into the model with the inclusion of hypothesized direct covariate effects. Our simulations show that this approach leads to good estimates for all model parameters. The proposed approach is demonstrated by using empirical data to examine the differential effects of family resources on students’ academic achievement outcome. Implications of the study are discussed.     

A GIS-based approach for estimating spatial distribution of seasonal temperature in Zhejiang Province,China

INTRODUCTION Spatial distribution estimates of meteorological data are becoming increasing important as inputs to spatially explicit landscape, regional, and global models. Interpolation is a common method translating for estimated spatial distribution of meteorological data that come from distantly scattered meteorologi- cal stations into raster data, which has benefits of simplicity and convenience. The choice of spatial interpolator is especially important in mountainous areas where dat…     

Multilevel Rasch Modeling: Does Misfit to the Rasch Model Impact the Regression Model?

Abstract

Multilevel Rasch models are increasingly used to estimate the relationships between test scores and student and school factors. Response data were generated to follow one-, two-, and three-parameter logistic (1PL, 2PL, 3PL) models, but the Rasch model was used to estimate the latent regression parameters. When the response functions followed 2PL or 3PL models, the proportion of variance explained in test scores by the simulated student or school predictors was estimated accurately with a Rasch model. Proportion of variance within and between schools was also estimated accurately. The regression coefficients were misestimated unless they were rescaled out of logit units. However, item-level parameters, such as DIF effects, were biased when the Rasch model was violated, similar to single-level models.     

Approaches for Specifying the Level-1 Error Structure When Synthesizing Single-Case Data

Multilevel modeling has been utilized for combining single-case experimental design (SCED) data assuming simple level-1 error structures. The purpose of this study is to compare various multilevel analysis approaches for handling potential complexity in the level-1 error structure within SCED data, including approaches assuming simple and complex error structures (heterogeneous, autocorrelation, and both) and those using fit indices to select between alternative error structures. A Monte Carlo study was conducted to empirically validate the suggested multilevel modeling approaches. Results indicate that each approach leads to fixed effect estimates with little to no bias and that inferences for fixed effects were frequently accurate, particularly when a simple homogeneous level-1 error structure or a first-order autoregressive structure was assumed and the inferences were based on the Kenward-Roger method. Practical implications and recommendations are discussed.     

Power Analysis in Two-Level Unbalanced Designs

Previous work on statistical power has discussed mainly single-level designs or 2-level balanced designs with random effects. Although balanced experiments are common, in practice balance cannot always be achieved. Work on class size is one example of unbalanced designs. This study provides methods for power analysis in 2-level unbalanced designs with random effects. Overall, the nesting affects power negatively, the treatment affects power positively, and the Level-2 units affect power more than Level-1 units. Computing power assuming balanced designs provides reasonable estimates only when imbalance is mild or moderate. When imbalance is large or extreme, computing power assuming balanced designs produces larger estimates of power. The use of the harmonic mean provides accurate estimates of power in unbalanced 2-level designs even when imbalance is large.     

Contextual and individual-level predictors of abused children's reentry into out-of-home care: a multilevel mixture survival analysis

Objectives

This study examined the effects of individual and contextual factors on reentry into out-of-home care among children who were discharged from child protective services in fiscal year 2004-2005. The objectives were to: (1) examine individual and contextual factors associated with reentry, (2) explore whether there are meaningful groups of youth who differ in terms of risk for reentry, and (3) determine whether relatively homogeneous clusters of child welfare agencies, based on contextual characteristics, differ significantly in terms of the reentry rates of the children whom they serve.

Method

The study design involved a multilevel longitudinal analysis of administrative data based on an exit cohort. Two Cox proportional hazards multilevel mixture models were tested. The first model included multiple individual level predictors and no agency level predictors. The second model included both levels of predictors.

Results

The results of multilevel Cox regression mixture modeling indicated that at the individual level, younger age, being placed in out-of-home care because of neglect and having physical, health problems corresponded to a decreased likelihood for reentry. At the agency level, lower average expenditures per child and contracting out case management services were associated with faster reentry into out-of-home care.

Conclusions

This study demonstrates that children who reenter out-of-home care appear to be a homogeneous population and that reentry is associated with both contextual factors and individual characteristics.

Practice implications

The most important implication that can be drawn from the study findings is that reentry may be most effectively prevented by focusing on such factors at the organizational level as contracting out case management services and funding allocation. Child welfare agencies that are responsible for an array of services and decide to contract out case management should consider the use of performance-based contracts and emphasize and strengthen quality assurance approaches for contracted services. In addition, to compensate for lower funding allocated for children served in out-of-home care, child welfare workers should become more familiar with community resources and help connect families to these supports.     

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.     

初中生成就目标取向与学业效能感、学业成绩的关系研究

为了解初中生成就目标取向与学业效能感、学业成绩的关系,采用问卷对204名初中生进行了调查,所有数据采用SPSS16.0进行统计分析。结果发现：（1）初中生在成绩接近目标和成绩回避目标上存在显著的性别差异,学业效能感在年级上差异显著。（2）掌握目标取向和成绩接近目标取向与学业效能感和学业成绩之间有显著正相关,对学业效能感和学业成绩有正向预测作用;成绩回避目标取向与学业效能感之间相关不显著,对学业成绩有负向预测作用。（3）学业效能感在成就目标取向与学业成绩之间起着部分中介作用。     

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.     

What Satisfies Students? Mining Student-Opinion Data with Regression and Decision Tree Analysis

To investigate how students' characteristics and experiences affect satisfaction, this study uses regression and decision tree analysis with the CHAID algorithm to analyze student-opinion data. A data mining approach identifies the specific aspects of students' university experience that most influence three measures of general satisfaction. The three measures have different predictors and cannot be used interchangeably. Academic experiences are influential. In particular, faculty preparedness, which has a well-known relationship to student achievement, emerges as a principal determinant of satisfaction. Social integration and pre-enrollment opinions are also important. Campus services and facilities have limited effects, and students' demographic characteristics are not significant predictors. Decision tree analysis reveals that social integration has more effect on the satisfaction of students who are less academically engaged.     

Hierarchical Regression Without Phantom Factors

In a recent note in the Teacher's Corner of this journal, de Jong (1999) proposed a method for computing hierarchical or fixed-order regressions in the context of latent variables. The essence of this approach is to decompose the predictor variables in the regression into orthogonal components based on a Cholesky decomposition and to regress the dependent variable on these orthogonal components. The components may be conceived of as phantom factors that do not have their own indicators. Because the idea of sequential entry of predictors in a latent variable regression framework seems generally to be unknown, the approach was developed by de Jong for latent variable regressions. However, it equally can be used for observed variable regression or path models. In this article we show that the phantom factors are unnecessary to achieve the objectives of a hierarchical regression. We give a direct approach that is equivalent to de Jong's approach.     

The Impact of Misspecifying Class-Specific Residual Variances in Growth Mixture Models

The purpose of this study was to examine the impact of misspecifying a growth mixture model (GMM) by assuming that Level-1 residual variances are constant across classes, when they do, in fact, vary in each subpopulation. Misspecification produced bias in the within-class growth trajectories and variance components, and estimates were substantially less precise than those obtained from a correctly specified GMM. Bias and precision became worse as the ratio of the largest to smallest Level-1 residual variances increased, class proportions became more disparate, and the number of class-specific residual variances in the population increased. Although the Level-1 residuals are typically of little substantive interest, these results suggest that researchers should carefully estimate and report these parameters in published GMM applications.     

Multiple linear regression: Identify potential health care stocks for investments using out-of-sample predictions

College-level statistics courses emphasize the use of the coefficient of determination, R-squared, in evaluating a linear regression model: higher R-squared is better. This often gives students an impression that higher R-squared implies better predictability since textbooks tend to use sample data to support the theory and students rarely have an opportunity to work on real data. In this paper, health care stocks are used as predictors and the result demonstrates that high R-squared does not necessarily mean high predictability and that multiple linear regression can be used in the study of data behavior. In particular, by learning the pattern of the near and far out-of-sample-prediction errors for different time periods throughout a dataset, the near out-of-sample prediction errors can be used to control the prediction errors and identify a subset of predictors that can well reflect the trend of S&P 500.     

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…     

多变量模型参数的贝叶斯估计及其在农业研究中的应用

对于农业研究中多变量线性模型参数的估计,以往常采用经典统计方法。随着计算机技术的进步,贝叶斯统计方法在科学研究的各个领域迅速发展。文章利用贝叶斯统计方法对农业研究中的多变量模型进行参数估计,并与经典统计方法进行比较,验证了贝叶斯方法的有效性。该方法可为农业研究中多变量模型参数的估计提供新的途径和手段。     

Limitations of Analysis of Covariance on Intact Group Quasi-Experimental Designs

Multiple regression models are used to demonstrate that every organismic variable is to some extent a proxy for every pertinent missing organismic variable. For analysis of covariance, clear assessment of treatment effects is possible only when the treatment vector(s) is(are) kept orthogonal to all organismic variables by random assignment of subjects. The “adjusted treatment effects” of covariance analysis on quasi-experimental designs include effects resulting from differences in the adjusted means of the treatment groups on pertinent organismic variables-both those used as covariates and others that are missing from the analysis. Only if the adjusted treatment means, do not differ in any of the organismic variables that are pertinent for predicting the criterion would the assessment of treatment effects be proper.     

Comparing cultural differences in two quality measures in Chinese kindergartens: the Early Childhood Environment Rating Scale-Revised and the Kindergarten Quality Rating System

This study examined the degrees of congruence between two early childhood evaluation systems on various quality concepts: the Early Childhood Environment Rating Scale-Revised (ECERS-R) and Zhejiang’s Kindergarten Quality Rating System (KQRS). Analysis of variance and post hoc least significant difference tests were employed to show the extent to which the ECERS-R ratings predict a kindergarten’s placement on the KQRS. Results found two quality dimensions (Language-reasoning and Interaction) that did not distinguish the quality between any levels of kindergartens, whereas one dimension (Space and furnishing) successfully distinguished the quality between all levels of kindergartens. Activities and Programme structure only distinguished the quality differences between Level-2 and Level-3 kindergartens, whereas Personal care and Routines only distinguished the quality differences between Level-1 and Level-3 kindergartens. Findings based on item-level analysis provided further insights into underlying cultural and contextual reasons for differences found in the concepts of quality in the two evaluation systems.     

The national survey of student engagement as a predictor of undergraduate GPA: a cross‐sectional and longitudinal examination

Data from the National Survey of Student Engagement (NSSE) collected across seven years were used to predict final, cumulative grade point averages (GPA). Cross‐product regression was used to explore the predictive abilities of the NSSE benchmark scores for freshmen (n = 2578) and seniors (n = 2293) collected in cross‐sectional cohorts. Hierarchical regression was also used with 127 longitudinal responses in students’ first and senior years of college. In the cross‐sectional analyses, Level of Academic Challenge emerged as a significant predictor of GPA for freshmen, whereas the Active and Collaborative Learning benchmark was a significant predictor for seniors; both effects were modest. The cross‐sectional data explained 22.6% of the variance with 18.2% of this variance accounted for by pre‐college control factors (American College Test score and high school GPA). For the analysis of longitudinal data, 31.3% of the variance was explained and 27.8% was attributed to the pre‐college indicators. No benchmark scores were significant predictors of GPA in the longitudinal data. Results suggest that cross‐sectional analyses can adequately detect modest effects on final GPA. In contrast, longitudinal models explain more variance, though they lack the power to reveal modest effects. This study suggests approaches for the responsible use of cross‐sectional and longitudinal data in educational research.     

Heterogeneous Subgroup Identification in Observational Studies

Abstract

Despite the overwhelming focus on the overall average treatment effect in the methodological and statistical literature, in many cases the efficacy of an educational program or intervention might vary based on unit background characteristics. The identification of subgroups for which an educational intervention is particularly effective or, on the other hand, has no effect or is possibly harmful, may have important practical implications, especially in terms of allocation of resources. We propose a five-step approach using propensity score matching and regression trees to identify subgroups with heterogeneous treatment effects in observational studies. Results of two Monte Carlo simulation studies demonstrate that the proposed approach can accurately identify heterogeneous subgroups while maintaining Type I error rate. In a case study with Early Childhood Longitudinal Study-Kindergarten cohort data, we find that the effect of exposure to special education services on fifth-grade mathematics achievement varies based on kindergarten mathematics achievement and student gender.