Contemplative Pedagogy: Frequently Asked Questions

Contemplative Pedagogy is a new and sometimes controversial pedagogical practice. Faculty often have basic questions about how to implement the pedagogy in their classrooms, in addition to questions that challenge the educational value and appropriateness of the practice. Assembled here are the most frequently asked questions about Contemplative Pedagogy, with responses from six contemplative professors, each from a different institutional and philosophical location. The respondents are founding members of the Contemplative Studies Consultation of the American Academy of Religion. The diversity of views expressed by the respondents invites the reader to see that there is no single theory or praxis of contemplative pedagogy.     

Outlying Observation Diagnostics in Growth Curve Modeling

Growth curve models are widely used for investigating growth and change phenomena. Many studies in social and behavioral sciences have demonstrated that data without any outlying observation are rather an exception, especially for data collected longitudinally. Ignoring the existence of outlying observations may lead to inaccurate or even incorrect statistical inferences. Therefore, it is crucial to identify outlying observations in growth curve modeling. This study comparatively evaluates six methods in outlying observation diagnostics through a Monte Carlo simulation study on a linear growth curve model, by varying factors of sample size, number of measurement occasions, as well as proportion, geometry, and type of outlying observations. It is suggested that the greatest chance of success in detecting outlying observations comes from use of multiple methods, comparing their results and making a decision based on research purposes. A real data analysis example is also provided to illustrate the application of the six outlying observation diagnostic methods.     

评欧阳修《易童子问》

欧阳修《易童子问)认为,《易》之“十翼”各有瑕疵,其中纵有孔子之言,但非孔子之文章。本文认为。此论并非无可嘉许之处．但亦不免言过其实,而致疑于其所不应疑者。本文通过对“十翼”的逐一分析。得出结论《序卦传》与《杂卦传》确如欧阳修所言。既不具微官大义．也与孔子无关。《说卦传》与《周易》关系渺茫,以《说卦传》为孔子之所作,更属无稽之谈。大小《象传》之内容,则不离乎秦汉时代、以功名利禄为人生目的的俗儒之胸襟,亦可能为邹衍一派阴阳家言。而《彖传》乃《周易》哲学精义之所在,其中若干部分必在孔子之前已经集结。惟《文言传》与《系辞传》中所录孔子之言,必皆出于孔子及门弟子之手。欧阳修呼《系辞传》为“僭妄之书”,且具有“害经惑世”之罪愆．未免有褊狭愚昧之失。文章还对欧阳修所指《系辞传》中三种成卦之法的不相容进行了辨析,指出．究实此三者所指不同,可以并存而不害。     

Diagnostics of Robust Growth Curve Modeling Using Student's t Distribution

Growth curve models with different types of distributions of random effects and of intraindividual measurement errors for robust analysis are compared. After demonstrating the influence of distribution specification on parameter estimation, 3 methods for diagnosing the distributions for both random effects and intraindividual measurement errors are proposed and evaluated. The methods include (a) distribution checking based on individual growth curve analysis; (b) distribution comparison based on Deviance Information Criterion, and (c) post hoc checking of degrees of freedom estimates for t distributions. The performance of the methods is compared through simulation studies. When the sample size is reasonably large, the method of post hoc checking of degrees of freedom estimates works best. A web interface is developed to ease the use of the 3 methods. Application of the 3 methods is illustrated through growth curve analysis of mathematical ability development using data on the Peabody Individual Achievement Test Mathematics assessment from the National Longitudinal Survey of Youth 1997 Cohort (Bureau of Labor Statistics, U.S. Department of Labor, 2005).     

Incorporating Student Mobility in Achievement Growth Modeling: A Cross-Classified Multiple Membership Growth Curve Model

Multiple membership random effects models (MMREMs) have been developed for use in situations where individuals are members of multiple higher level organizational units. Despite their availability and the frequency with which multiple membership structures are encountered, no studies have extended the MMREM approach to hierarchical growth curve modeling (GCM). This study introduces a cross-classified multiple membership growth curve model (CCMM-GCM) for modeling, for example, academic achievement trajectories in the presence of student mobility. Real data are used to demonstrate and compare growth curve model estimates using the CCMM-GCM and a conventional GCM that ignores student mobility. Results indicate that the CCMM-GCM represents a promising option for modeling growth for multiple membership data structures.     

Modeling Incomplete Longitudinal Substance Use Data Using Latent Variable Growth Curve Methodology

Longitudinal data sets typically suffer from attrition and other forms of missing data. When this common problem occurs, several researchers have demonstrated that correct maximum likelihood estimation with missing data can be obtained under mild assumptions concerning the missing data mechanism. With reasonable substantive theory, a mixture of cross-sectional and longitudinal methods developed within multiple-group structural equation modeling can provide a strong basis for inference about developmental change. Using an approach to the analysis of missing data, the present study investigated developmental trends in adolescent (N = 759) alcohol, marijuana, and cigarette use across a 5-year period using multiple-group latent growth modeling. An associative model revealed that common developmental trends existed for all three substances. Age and gender were included in the model as predictors of initial status and developmental change. Findings discuss the utility of latent variable structural equation modeling techniques and missing data approaches in the study of developmental change.     

A Latent Growth Curve Modeling Approach to Pooled Interrupted Time Series Analyses

This paper presents a latent variable approach for the estimation of treatment effects within a pooled interrupted time series (ITS) design. Although considered quasi-experimental, the ITS design has been noted as representing one of the strongest alternatives to the randomized experiment, making it highly appropriate for use in documenting the presence of effects that might warrant further evaluation in a large-scale randomized study. Results suggest that the latent variable growth modeling (LGM) is capable of detecting simultaneous differences in both level and slope, and provides tests of significance for these two necessary indicators of an ITS intervention effect. As shown in the analyses, the LGM framework provides a comprehensive and flexible approach to research design and data analysis, making available to a wide audience of researchers an analytical framework for a variety of analyses of growth and developmental processes.     

Asking the Right Questions About g

It is our position that a complete understanding of human intellectual development is of ultimate interest to researchers and of great import to society. In this article, we ask questions that reflect common themes seen in the debate regarding the nature and importance of general cognitive ability (i.e., the g factor), sources of individual and group differences, and the viability of arguments against g theory. We also examine questions reflecting aspects of these debates that are commonly ignored or misconstrued. Our goal is to help researchers and debaters continue or begin to ask clear, critical, and dispassionate questions about g that will stimulate productive research and promote informed public policy.     

Examining Spirituality Over Time: Latent Growth Curve and Individual Growth Curve Analyses

SUMMARY

Research on spirituality and religiousness has gained growing attention in recent years; however, most studies have used cross-sectional designs. As research on this topic evolves, there has been increasing recognition of the need to examine these constructs and their effects through the use of longitudinal designs. Beyond repeated-measures ANOVA and OLS regression models, what tools are available to examine these constructs over time? The purpose of this paper is to provide an overview of two cutting-edge statistical techniques that will facilitate longitudinal investigations of spirituality and religiousness: latent growth curve analysis using structural equation modeling (SEM) and individual growth curve models. The SEM growth curve approach examines change at the group level, with change over time expressed as a single latent growth factor. In contrast, individual growth curve models consider longitudinal change at the level of the person. While similar results may be obtained using either method, researchers may opt for one over the other due to the strengths and weaknesses associated with these methods. Examples of applications of both approaches to longitudinal studies of spirituality and religiousness are presented and discussed, along with design and data considerations when employing these modeling techniques.     

Beyond Curve Fitting to Inferences About Learning

In this commentary, the authors elaborate on the issue of going beyond curve fitting to the drawing of inferences about motor learning. They argue that the agenda of A. Heathcote and S. Brown (2004) is largely a theory-free, curve-fitting enterprise that can be useful for certain aspects of describing behavior change, but that its gold standard of percentage of variance accounted for can also be misleading in its relevance to the theory of learning. Clearly, analysis methods are necessary and some are better than others, but the researcher can more fully exploit the relevance of methods to the construct with a priori theorizing than with a data-driven strategy of maximizing percentage of variance accounted for in curve fitting.     

Nine Critical Questions About Selective College Admissions

The misgivings of college faculty, college administrators, and high school counselors about selective admissions are focused on 9 issues. Data relevant to those issues reveal that: (1) prediction of grades is sufficiently accurate to be useful; (2) prediction equations from one year are sound for use in the immediately succeeding years; (3) predictions of first-year grades are related to performance over the 2-year period at a junior college and the 4-year career at a senior college; (4) there may need to be separate prediction procedures for widely different majors, such as science and nonscience; (5) accurate predictions can be made before the student has completed high school; (6) the nonacademic courses students take do not reduce prediction accuracy; (7) introduction of selectivity has not been found to decrease diversity in educational opportunity; (8) grading practices in an institution will tend to fluctuate with the degree of selectivity; and (9) procedures are available to set admissions cutoffs, to provide students with sound counseling information, and to provide a second chance for those who do net meet minimum admissions standards.     

Longitudinal Associations Between Parental SES and Adolescent Health-Related Quality of Life Using Growth Curve Modeling

We evaluate how two aspects of socioeconomic status, parental objective and subjective social status, are associated with health-related quality of life in three racial/ethnic groups during pre- to mid-adolescent development, using growth curve modeling. In a longitudinal cohort study, 4,048 Black, Latinx, or White adolescents were assessed in 5th, 7th and 10th grade. Objective social status (OSS) was based on parent-reported highest household educational attainment and total household income, and subjective social status (SSS) was measured with the MacArthur Scale, through which parents indicated their social standing in reference to community and national norms. Adolescents completed the Pediatric Quality of Life Inventory to measure their physical and psychosocial health-related quality of life. Based on growth curve modeling of the intercept, adolescents whose parents have higher OSS levels reported better health-related quality of life, whereas parental SSS was not associated with adolescent health-related quality of life in 5^th grade. These findings were largely consistent across racial/ethnic groups. Based on growth curve modeling of the developmental slopes (or growth curves), higher objective social status was associated with a slower positive growth of health-related quality of life from 5^th to 10^th grade, which was largely consistent across racial/ethnic groups. The opposite appeared for parental SSS and physical health-related quality of life, and only for Latinx, where higher parental perceived social status was associated with an acceleration of positive change. Family income and education may influence health-related quality of life at the start of adolescence, but its effect appears to diminish as youth mature. However, in Latinx youth, parents’ perceived social status may continue to influence improvement in their physical health-related quality of life as they mature.

     

Measuring Patterns of Change in Personality Assessments: An Annotated Application of Latent Growth Curve Modeling

Latent growth curve (LGC) modeling within the framework of structural equation modeling (SEM) is now highly regarded as one of the most powerful and informative approaches to the analysis of longitudinal data (see, e.g., Curran &; Hussong, 2003 Curran, P. J. and Hussong, A. M. 2003. The use of latent trajectory models in psychopathology research. Journal of Abnormal Psychology, 112: 526–544. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Whereas LGC modeling enables researchers to test for differences in developmental trajectories across time, conventional repeated measures analyses do not provide this opportunity. Nonetheless, a review of studies reported in most psychology journals reveals scant application of this methodological approach. One possible explanation for this limited use of LGC modeling is a lack of knowledge related to its application. The intent of this article, then, is to address this deficiency by presenting an annotated application of LGC modeling to health psychology data. Based on a sample of 405 Hong Kong Chinese women who recently underwent breast cancer surgery, we walk the readers through SEM modeling procedures that test for differences in both the initial status and rate of change in Psychological Morbidity and Social Adjustment at 1, 4, and 8 months postsurgery. We interpret findings from both a methodological and a substantive perspective.     

老年人认知功能的变化轨迹：基于潜变量增长模型的分析

摘 要 本研究采用中国老年健康影响因素跟踪调查（CLHLS）的4次数据（2002,2005,2008,2011）,对老年人认知功能的变化趋势以及影响因素进行了探讨。结果显示：（1）老年人认知功能在4次测查中呈非线性的下降趋势。（2）日常生活活动能力较低的个体其认知功能也较低;老年人读书年限越高,其认知功能水平越高;女性的认知功能水平低于男性;不饮酒的老年人认知功能低于饮酒的老年人。（3）读书年限与饮酒会正向预测模型的斜率。