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Statistical and Research Methodology in Education


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FY Awards

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Cross-Classified Structural Equations Model: Development of an OpenMX Module and its Application to Multiyear Assessment and Intervention Data in Literacy Research

Year: 2009
Name of Institution:
University of Houston
Goal: Methodological Innovation
Principal Investigator:
Mehta, Paras
Award Amount: $702,393
Award Period: 3 years
Award Number: R305D090024


Purpose: The proposed project aimed to: (1) develop a software library for fitting cross-classified structural equations models (CC-SEM); (2) analyze a number of large literacy-related datasets with common methodological issues; and (3) document and disseminate the software library.

Multilevel modeling (MLM) is the preferred approach for modeling longitudinal and nested educational datasets. However, multiyear student data are no longer hierarchically nested within a single teacher, but are partially cross-classified due to dispersion of students from the same classroom to multiple different classrooms. In addition, student outcomes may be partially clustered within multiple teachers. Although current MLM software packages allow cross-classified data to a certain extent, estimation is computationally challenging for such nonhierarchically nested data. In addition, current MLM software packages allow outcome data only at the lowest level of hierarchy. Multi-level structural equations modeling (ML-SEM) has more recently become available and it allows for latent variables at each level measured by multiple indicators at that level. The project team developed a ML-SEM software library that allows latent variable models for arbitrarily cross-classified and multiple-membership data.

Project Activities: The CC-SEM library was developed as an extension to OpenMx, an open source SEM project integrated into the R statistical modeling language. Integration of CC-SEM with R and OpenMX is to make the software: (1) fully programmable and extensible; (2) free and opensource; (3) multiprocessor and cluster enabled; and (4) user-friendly with multiple front-ends (e.g., matrix, simple script based and graphical interfaces). The library used sparse matrix methods for formulating CC-SEM models as restricted linear mixed-effects models and for computing the likelihood and its derivatives. Potential users of CC-SEM include substantive users interested in analyzing data, methodologists interested in evaluating models and methods, and statistical developers interested in further extending its functionality.

In addition, the project team analyzed a number of large educational datasets with common methodological issues that are of interest to educational researchers. The methodological issues include: (1) longitudinal (multiple years, grades, and cohorts) student language and literacy outcome data with multiple within-year and end-of-year assessments with cross-classification of responses within teachers from different grades; (2) multiple teachers within a grade; (3) repeated teachers across years;(4) pullout instruction for a subset of students; (5) multiple latent student constructs of interest; and (6) teacher, school and district level constructs of interest.

The project fully documented every aspect of the software library as well as the CC-SEM modeling framework using the R documentation standards. A user-friendly manual for the CC-SEM software was developed that includes examples from publicly available datasets as well as the datasets used in the secondary data analysis.

Related IES Projects: Language and Literacy Abilities in Spanish Language Speaking Children (R305A100272); The Roles of Instruction and Component Skills in Reading Achievement (R305A120785)

Products and Publications

Book chapter

Branum-Martin, L. (2013). Multilevel Modeling: Practical Examples to Illustrate a Special Case of SEM. In Y. Petscher, C. Schatschneider, and D. Compton (Eds.), Applied Quantitative Analysis in the Social Sciences (pp. 95–124). New York: Routledge.

Mehta, P.D. (2013). nLevel Structural Equation Modeling. In Y. Petscher, C. Schatschneider, and D.L. Compton (Eds.), Applied Quantitative Analysis in Education and the Social Sciences (pp. 329–362). New York: Routledge.

Mehta, P. D., & Petscher, Y. (2016). N-level structural equation model of student achievement data nested with repeated teachers, schools, and districts. In J. R. Harring, L. M. Stapleton, & S. N. Beretvas (Eds.), Advances in multilevel modeling for educational research: Addressing practical issues found in real-world applications (pp. 193–228). IAP Information Age Publishing.

Journal article, monograph, or newsletter

Brunson, J.A., Øverup, C.S., and Mehta, P.D. (2016). A Social Relations Examination of Neuroticism and Emotional Support. Journal of Research in Personality, 63, 67–71.

Mehta, P. D. (2018). Virtual Levels and Role Models: N-Level Structural Equations Model of Reciprocal Ratings Data. Multivariate Behavioral Research, 1–20.

Øverup, C. S., Brunson, J. A., & Mehta, P. D. (2021). A Social Relations Model of need supportiveness. Journal of Research in Personality, 94, 104142.

Porter, B., Øverup, C. S., Brunson, J. A., & Mehta, P. D. (2018). Meta-accuracy and perceived reciprocity from the perception-meta-perception social relations model. Social Psychology, 50, 24–37.