Using Mx to Analyze Cross-Level Effects in Two-Level Structural Equation Models

Two-level data sets are frequently encountered in social and behavioral science research. They arise when observations are drawn from a known hierarchical structure, such as when individuals are randomly drawn from groups that are randomly drawn from a target population. Although 2-level data analysis in the context of structural equation modeling can be conducted by easily accessible software such as LISREL, the group- and individual-level effects are usually treated as though they are uncorrelated. When extra group variables are measured and their relationships with individual-level variables are studied, the analysis of cross-level covariance structures is of interest. In this article, we propose a model setup framework in Mx that allows the analysis of cross-level covariance structures. An illustrative example is given and a small-scale simulation study is conducted to examine the performance of the proposed procedure. The results show that the proposed method can produce reliable parameter and standard error estimates, and the goodness-of-fit statistics also follow the chi-square distribution in large samples.     

An Illustration of Second-Order Latent Growth Models

Methods of latent curve analysis (latent growth modeling) have recently emerged as a versatile tool for investigating longitudinal change in measured variables. This article, using higher order factor models as suggested by McArdle (1988) and Tisak and Meredith (1990), illustrates latent curve analysis for the purpose of modeling longitudinal change directly in a latent construct. The construct of interest is assumed to be indicated by several measured variables, all of which are observed at the same multiple time points. Examples with simultaneous estimation of covariance and mean structures are provided for both a single group and a two-group scenario.     

Bayesian Analysis of Multivariate Latent Curve Models With Nonlinear Longitudinal Latent Effects

In longitudinal studies, investigators often measure multiple variables at multiple time points and are interested in investigating individual differences in patterns of change on those variables. Furthermore, in behavioral, social, psychological, and medical research, investigators often deal with latent variables that cannot be observed directly and should be measured by 2 or more manifest variables. Longitudinal latent variables occur when the corresponding manifest variables are measured at multiple time points. Our primary interests are in studying the dynamic change of longitudinal latent variables and exploring the possible interactive effect among the latent variables.

Much of the existing research in longitudinal studies focuses on studying change in a single observed variable at different time points. In this article, we propose a novel latent curve model (LCM) for studying the dynamic change of multivariate manifest and latent variables and their linear and interaction relationships. The proposed LCM has the following useful features: First, it can handle multivariate variables for exploring the dynamic change of their relationships, whereas conventional LCMs usually consider change in a univariate variable. Second, it accommodates both first- and second-order latent variables and their interactions to explore how changes in latent attributes interact to produce a joint effect on the growth of an outcome variable. Third, it accommodates both continuous and ordered categorical data, and missing data.     

Society Gets the Individual it Deserves: Engaging Learners for the Flat World

Historically the individual and society pendulum has swung back and forth between individuals and conformity and individuals and community. Individuals and society are mutually dependent yet conflicts of interest have shown how one has sometimes flourished at the expense of the other. As the world and society changes, learning must follow so individuals or groups can participate in society. And because participation in society inherently involves learning physical educators and kinesiologists (among others) need to address how we can assist students to be engaged learners who transform experiences into fruitful knowledge, skills, attitudes, values, and beliefs and give meaning to their lives. The paper will situate learning and in particular, student engagement, as a vector for the pervasive change and the associated profound challenges that will be presented to individuals and society this century. Student engagement, particularly at a philosophic level, has essentially been ignored within our field.     

Developing and sustaining open communication in action research initiatives: a response to Kemmis (2006)

In a recent issue of Educational Action Research, Stephen Kemmis argued that action research should be participative in nature and involve ‘open communication’ by engaging the voices and perspectives of others besides teachers, such as students, parents/caregivers and other community members. This article explores the implications of this call for open communication, with reference to results from one study conducted within New Zealand that investigated teachers’ action research work from multiple and culturally diverse perspectives. Data analysis from this study revealed a number of barriers to maintaining critical, public dialogue and collective inquiry. Foremost amongst these was a lack of preparation and willingness on the part of school leaders to respond to specific challenges put forward from some stakeholder groups, particularly at a time when race relationships between Maori and non‐Maori groups dominated national news headlines.     

Latent variable models: Applications in education

Most theories in the social sciences involve relationships among constructs which are not directly observable. Behavioral measures exist of all constructs, such as intelligence, creativity, and other cognitive traits, aggressiveness, sociability, and other personality and affective characteristics; but these observed measures are usually assumed to be imperfect indicators of the (presumed) underlying construct. The imperfections exist because of errors of measurement and because the observed behavior may be influenced by other underlying constructs in addition to the one of primary interest. Statistical methods, called latent variable models, have been developed to provide rigorous tests of theories involving unobserved variables. This paper describes the major types of latent variable models, shows how they can be applied in educational research, and gives representative examples of their use from the literature.     

Bayesian Quantile Structural Equation Models

Structural equation modeling is a common multivariate technique for the assessment of the interrelationships among latent variables. Structural equation models have been extensively applied to behavioral, medical, and social sciences. Basic structural equation models consist of a measurement equation for characterizing latent variables through multiple observed variables and a mean regression-type structural equation for investigating how explanatory latent variables influence outcomes of interest. However, the conventional structural equation does not provide a comprehensive analysis of the relationship between latent variables. In this article, we introduce the quantile regression method into structural equation models to assess the conditional quantile of the outcome latent variable given the explanatory latent variables and covariates. The estimation is conducted in a Bayesian framework with Markov Chain Monte Carlo algorithm. The posterior inference is performed with the help of asymmetric Laplace distribution. A simulation shows that the proposed method performs satisfactorily. An application to a study of chronic kidney disease is presented.     

Sensitivity Analysis of Multiple Informant Models When Data Are Not Missing at Random

Missing data are common in studies that rely on multiple informant data to evaluate relationships among variables for distinguishable individuals clustered within groups. Estimation of structural equation models using raw data allows for incomplete data, and so all groups can be retained for analysis even if only 1 member of a group contributes data. Statistical inference is based on the assumption that data are missing completely at random or missing at random. Importantly, whether or not data are missing is assumed to be independent of the missing data. A saturated correlates model that incorporates correlates of the missingness or the missing data into an analysis and multiple imputation that might also use such correlates offer advantages over the standard implementation of SEM when data are not missing at random because these approaches could result in a data analysis problem for which the missingness is ignorable. This article considers these approaches in an analysis of family data to assess the sensitivity of parameter estimates and statistical inferences to assumptions about missing data, a strategy that could be easily implemented using SEM software.     

The analysis of causal models: Some remarks on new techniques

The theme of this article is the convergence between sociological reflection and technical developments in quantitative analysis. The author shows how the use of techniques based upon the general model of regression forces further reflection on phenomena studied, each of the techniques presented implying postulates about the dynamics of the variables measured or about the influence of variables that are not measured. Taking ecological analysis and contextual analysis as a starting point, the author introduces path analysis showing a progression from the former to the latter models in the convergence between techniques and sociological reflection.     

Relationships between colleague ratings and faculty compensation

Rankings of graduate and professional programs have become commonplace since Cartter's study for the American Council on Education was published in 1966. Much of the research up to the present has focused on discovering proxy variables, such as departmental size, which correspond to departmental ratings, as well as observing how the ratings of departments change over time. This study examines the relationship between the peer ratings reported by Roose and Andersen in 1970 and resource allocation patterns, represented by average salary figures, among fifty major American universities. It also shows the relationship of these ratings and other resource allocation measures within one of the fifty institutions. Results indicate that among the fifty universities, average salaries are higher at the highly rated institutions than at the lower rated ones, with senior professors being the chief beneficiaries of the higher wage scales. Similarly, within one institution the senior professors of higher ranked departments are better paid, compared to their junior colleagues, than those of lower rated departments. The higher rated departments share commonalities as to proportion of senior professors and teaching load assignments as well. Both across and within universities, departments found to be prestigious by Roose and Andersen do tend to exhibit common characteristics concerning resource allocation procedures.Presented at the Annual Forum of the Association for Institutional Research, Houston, Texas, May 1978.     

Modeling Self-Regulation as a Process Usinga Multiple Time-Scale Multiphase Latent Basis Growth Model

Measurement burst designs, wherein individuals are measured intensively during multiple periods (i.e., bursts), have created new opportunities for studying change at multiple time scales. This article develops a model that might be useful in situations where the functional form of short-term change is unknown, might consist of multiple phases, and might change over the long term. Specifically, we combine measurement of intraindividual entropy, a latent basis growth model, a multiphase growth model, and a growth model with covariates into a unified framework that could help accommodate the complexity of patterns that emerge in multiple time-scale categorical data streams. Empirical data from a longitudinal study of young children’s behavior during laboratory tasks designed to induce frustration are used to illustrate the utility of the proposed model for simultaneously describing intratask (short-term) change in self-regulation and developmental (long-term) shifts in intratask change.     

Modeling Latent Growth Curves With Incomplete Data Using Different Types of Structural Equation Modeling and Multilevel Software

This article offers different examples of how to fit latent growth curve (LGC) models to longitudinal data using a variety of different software programs (i.e., LISREL, Mx, Mplus, AMOS, SAS). The article shows how the same model can be fitted using both structural equation modeling and multilevel software, with nearly identical results, even in the case of models of latent growth fitted to incomplete data. The general purpose of this article is to provide a demonstration that integrates programming features from different software. The most immediate goal is to help researchers implement these LGC models as a useful way to test hypotheses of growth.     

Educational Accountability in a Regulated Market

Public debate about school choice is often polarized between those who favor and oppose total free markets in education. However, the serious intellectual work on choice focuses on more moderate alternatives that involve a mixture of public and private accountability. A regulated market model of educational accountability would mix government regulation, options for families, and entrepreneurship on the supply side. It would sustain a role for government in licensing schools, protecting children, punishing misrepresentation, and ensuring free flow of information. This article shows how a regulated market in education would work and how one could be created.     

Enabling transformation through critical engagement and reflexivity: a case study of South African academics

ABSTRACT

Scholars writing on agency argue that normally, individuals who experience social structures as comfortable will tend to want to reproduce them while those who experience these structures as oppressive will want to change them. This is a bleak outlook because it suggests that those in positions of power and influence are less likely to seek to overhaul the very system of rewards and punishments that benefits them. However, there are exceptions to this pattern: instances where those who experience the structures as comfortable, nevertheless, work at transforming them. This article introduces an alternative perspective to current transformation discourses by seeking to understand why such exceptions exist. It argues that critical engagement is an important dimension of such transformation, and examines how it interacts with reflexivity to shape individual choices and reformulate interest. Drawing on a hermeneutic phenomenological analysis of in-depth interviews with 10 academics who have been identified as agents of change at one university in South Africa, we reveal how individuals are able to shift their understanding of what is or is not in their interest in a context where raced, gendered and classed interests are deeply embedded in the fabric of the society. In such contexts, reflexivity and critical personal engagement with one’s context can lead to a shift in interest and then consciousness as the individual comes to see and experience things from a different vantage point, opening up the possibility for a changed relationship with the social structure and its constraints and determining influence.     

Emergent Environmental Literacy in the Nonnarrative Compositions of Kindergarten Children

This article shows how links between science and literacy offer kindergarten children the opportunity to create and express their individual understandings about environmental change through emergent environmental literacy. This article reports on one of the science experiences in a kindergarten classroom in which the children explored the phenomenon of environmental change. The kindergarten science program can help children learn how scientists look at the world; young children can express these concepts through nonnarrative compositions. The article concludes with suggestions for teaching practice in the kindergarten science program.     

Change Factors Influencing the Diffusion and Adoption of Green Building Practices

This study aims to improve how human performance improvement (HPI) practitioners manage attributes of change. While there have been numerous studies addressing various aspects of change management, few have examined how the characteristics of the change itself contribute to adoption. This study addresses a change scenario of current importance and interest. Researchers coded applicable survey responses from a previous study and performed factor analysis to identify barriers and incentives to green building, including Leadership in Energy and Environmental Design (LEED) certification, for construction industry professionals in the Pacific Northwest, and how those professionals feel about adopting “green” building practices—among them, the LEED rating system. Findings suggest that (a) the qualities of some changes have far more influence on adoption than others, such as difficulty of transition, and (b) other characteristics combine to exert their influence in concert with one another. Finally, a user's perception of the value of the change was significant. The article's conclusion addresses how HPI practitioners can integrate the findings into green building adoption specifically, as well as within the greater context of change management and implementation practices in general.     

The Stability of IRT b Values

This study investigated possible explanations for an observed change in Rasch item parameters (b values) obtained from consecutive administrations of a professional licensure examination. Considered in this investigation were variables related to item position, item type, item content, and elapsed time between administrations of the item. An analysis of covariance methodology was used to assess the relations between these variables and change in item b values, with the elapsed time index serving to control for differences that could be attributed to average or pool changes in b values over time. A series of analysis of covariance models were fitted to the data in an attempt to identify item characteristics that were significantly related to the change in b values after the time elapsed between item administrations had been controlled. The findings indicated that the change in item b values was not related either to item position or to item type. A small, positive relationship between this change and elapsed time indicated that the pool b values were increasing over time. A test of simple effects suggested the presence of greater change for one of the content categories analyzed. These findings are interpreted, and suggestions for future research are provided.     

School Teachers’ Experiences of Science Curriculum Reform

We examine teachers’ experiences of a major reform of the school science curriculum for 14–16-year olds in England. This statutory reform enhances the range of available science courses and emphasises the teaching of socio-scientific issues and the nature of science, alongside the teaching of canonical science knowledge. This paper examines teachers’ experiences of the reform and the factors that condition these experiences. A designed sample of 22 teachers discussed their experiences of the reform within a semi-structured interview. Our analysis considers how the external and internal structures within which teachers work interact with the personal characteristics of teachers to condition their experiences of the curriculum reform. In many cases, personal/internal/external contexts of teachers’ work align, resulting in an overall working context that is supportive of teacher change. However, in other cases, tensions within these contexts result in barriers to change. We also explore cases in which external curriculum reform has stimulated the development of new contexts for teachers’ work. We argue that curriculum reformers need to recognise the inevitability of multiple teaching goals within a highly differentiated department and school workplace. We also show how experiences of curriculum reform can extend beyond the learning of new knowledge and associated pedagogies to involve challenges to teachers’ professional identities. We argue for the extended use of teacher role models within local communities of practice to support such ‘identity work’.     

Education for Sustainability in Scottish Secondary Schools: boundary maintenance or professional reorientation?

This article reports on a study of education for sustainability in Scottish secondary schools. The study was based at the Institute of Education, University of Stirling, and was sponsored (between November 1997 and March 1998) by the Sustainable Schools Partnership, with funding from the Royal Society for the Protection of Birds Scotland, Scottish Natural Heritage and the Worldwide Fund for Nature Scotland and (between April 1998 and July 1998) by the University of Stirling. It comprised three research strands: a trawl of documentary evidence relating to policy and practice within the field of education for sustainability; interviews with key personnel in secondary schools identified as developing good practice in the field of education for sustainability; and a series of discussions with policy makers having a national and/or international perspective on education for sustainability and its development in schools. Although the prime focus was on Scottish schools, each of these strands also covered as a secondary concern relevant work in the other national regions of the UK. Having briefly clarified some issues of definition, the article offers an analysis of the central problem faced by schools (secondary schools in particular) involved in cross‐curriculum developments of this kind. That analysis focuses upon the aspiration of these schools to bring about whole‐school change within an institutional context characterised by strong boundary maintenance. The article then outlines the first of two findings: where education for sustainability is being developed within a secondary school setting, whole‐school change is likely to be conceived as modest modifications to existing structures. The article goes on, however, to outline some of the changing practices within these schools and, in doing so, introduces the second finding: where education for sustainability is being developed within a secondary school setting, whole‐school change is likely to be conceived in terms of a reorientation of professional interest and practice towards the local community and wider community concerns. These two findings, we argue, should be seen neither as complementary nor as existing in creative tension. They point to a school system seriously at odds with itself: pulled by one set of professional and managerial priorities towards piecemeal change within fixed parameters and by a very different set of professional and educational responses towards the reconceptualisa‐tion of teaching and learning and the closer involvement of schools in the local communities. This increased interest in the outward‐looking school community extends to issues of global concern. The article concludes with some thoughts on how this tension might be resolved through a radical reordering of educational priorities in favour of boundary realignment and community participation.