Educational Psychology

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Longitudinal Methods Development (LMD) Lab

LMD Lab members
Members of the LMD lab pose with pillows printed with their first authored papers.


  • Development and extension of statistical methodologies that effectively describe different underlying intrinsically nonlinear patterns of change
  • Evaluation of the robustness (including accuracy and precision) of the methods developed or extended via Monte Carlo Simulation techniques
  • Provide researchers and practitioners with the theoretical underpinnings and empirical guidance on how to effectively utilize these techniques to address important substantive questions in education and psychology.

Current projects

  • Development of Bayesian Piecewise Crossed Random Effects Model
  • Evaluation of Model Identification Issues for Crossed Random Effects Model
  • Incorporating Covariates in Bayesian Piecewise Growth Mixture Models
  • Global Model Fit Indices for Random Effects Models

Research group

Nidhi Kohli headshot

Nidhi Kohli

  • Lab director
  • American Guidance Service, Inc. and John P. Yackel Professor of Educational Measurement and Assessment, Department of Educational Psychology

Current PhD students

Corissa Rohloff headshot
Corissa Rohloff
Curriculum Vitae (PDF)

Corissa's research assesses model fit and estimation for intrinsically nonlinear mixed-effects models. Her main focus is on the analysis of repeated measures data using complex functional forms. More specifically, Corissa has explored how functional form plays into model fit (i.e., overfitting) and whether functional form should be taken into consideration when researchers evaluate the appropriateness of their models. Additionally, she is working on an extension of the piecewise random-effects model with unknown knots to incorporate crossed random effects (for e.g., student and teacher random effects on growth) using Bayesian estimation methods.

In 2022, she received the American Educational Research Association (AERA) Educational Statistics Special Interest Group (SIG) Best Graduate Student Paper Award for her paper, “The Impact of Functional Form Complexity on Model Overfitting for Nonlinear Mixed-Effects Models.”

Rik Lam headshot
Rik Lamm

Rik's research focuses on Bayesian estimation of nonlinear mixed effects models. Mainly his research pertains to piecewise growth mixture models (PGMM) and it's modeling in a variety of contexts. His current project incorporates covariates into the detection of knots for PGMM models with an R package that will allow other researchers to implement the model. Additionally, Rik is part of the Minnesota Youth Development Research Group.

Ziwei Zhang headshot
Ziwei Zhang

Ziwei is interested in topics related to model estimation and evaluation, and model fit indices. Her research is centered on intrinsically nonlinear models for longitudinal data in the frameworks of random-effects modeling (REM) and latent growth curve modeling (LGC). At present, there is a lack of research on global model fit indices for the linear and intrinsically nonlinear models in the REM framework. Researchers can only compare models relatively in the REM framework but cannot assess how well the individual model fits data. Though LGC can achieve this by providing global model fit indices, it requires complex parameter transformations to fit intrinsically nonlinear models. The REM framework, on the other hand, can directly fit the intrinsically nonlinear models. To better evaluate linear and intrinsically nonlinear models, Ziwei aims to translate global fit indices from the SEM framework into the REM framework. The model fit indices allow researchers to detect the discrepancy between the proposed random-effects model and the observed data, and thereby, evaluate the overall fit of the model to data.

Past PhD students

Yadira Peralta-Torres headshot

Yadira Peralta-Torres Current position: Assistant professor in the Department of Economics at the Center for Research and Teaching in Economics (CIDE), Mexico

Recent publications

*Zhang, Z., *Rohloff, C. T., & Kohli, N. (2022). Model fit indices for random effects models: Translating model fit ideas from latent growth curve models. Structural Equation Modeling: A Multidisciplinary Journal, DOI:

*Rohloff, C. T., Kohli, N., & Chung, S. (2022). The impact of functional form complexity on model overfitting for nonlinear mixed-effects models. Multivariate Behavioral Research, DOI:

*Zhang, Z., *Rohloff, C. T., & Kohli, N. (2022). Commentary on “Obtaining interpretable parameters from reparameterized longitudinal models: Transformation matrices between growth factors in two parameter-spaces”. Journal of Educational and Behavioral Statistics. DOI:

*Peralta, Y., Kohli, N., Lock, E. F., and Davison, M. L. (2022). Bayesian modeling of associations in bivariate piecewise linear mixed-effects models. Psychological Methods,27(1), 44–64.

Kohli, N., & Sullivan, A. L. (2019). Linear-Linear piecewise growth mixture models with unknown random knots: A primer for School Psychology. Journal of School Psychology, 73, 89–100.

Kohli, N., *Peralta, Y., & *Bose, M. (2019). Piecewise random-effects modeling software programs. Structural Equation Modeling: A Multidisciplinary Journal, 26(1), 156–164.

*Peralta, Y., Kohli, N., & Wang, C. (2018). A primer on distributional assumptions and model linearity in repeated measures data analysis. The Quantitative Methods for Psychology, 14(3), 199–217, DOI: doi:10.20982/tqmp.14.3.p199.

Lock, E. F., Kohli, N., & *Bose, M. (2018). Detecting multiple random changepoints in Bayesian piecewise growth mixture models. Psychometrika, 83(3), 733–750.

Kohli, N., *Peralta, Y., *Zopluoglu, C., & Davison, M. L. (2018). A note on estimating single-class piecewise mixed effect models with unknown change points. International Journal of Behavioral Development—Method & Measures Section, 42(5), 518–524.

Sullivan, A. L., Kohli, N., Farnsworth, E. M., Jones, L., & Sadeh, S. (2017). Longitudinal models of reading achievement of students with and without learning disabilities. School Psychology Quarterly, 32(3), 336–349.

Kohli, N., Harring, J. R., & *Zopluoglu, C. (2016). A finite mixture of nonlinear random coefficient models for continuous repeated measures data. Psychometrika, 81(3), 851–880.

Wang, C., Kohli, N., & *Henn, L. (2016). A second-order longitudinal model for binary outcomes: Item response theory versus factor analytic framework. Structural Equation Modeling: A Multidisciplinary Journal, 23(3), 455–465.

Kohli, N., Hughes, J., Wang, C., *Zopluoglu, C., & Davison, M. L. (2015). Fitting a linear–linear piecewise growth mixture model with unknown knots: A comparison of two common approaches to inference. Psychological Methods, 20(2), 259–275.

Kohli, N., Koran, J., & *Henn, L. (2015). Relationships among classical test theory and item response theory frameworks via factor analytic models. Educational and Psychological Measurement, 75(3), 389–405.

Kohli, N., Sullivan, A. L., Sadeh, S. S., & *Zopluoglu, C. (2015). Longitudinal mathematics development of students with learning disabilities and students without disabilities: A comparison of linear, quadratic, and piecewise mixed effects models. Journal of School Psychology, 53(2), 105–120. [The first author received the following financial support for the research, authorship, and publication of this article: U of M Grant-in-Aid of Research, Artistry & Scholarship Program]

*Zopluoglu, C., Harring, J. R., & Kohli, N. (2014). FitPMM: An R routine to fit finite mixture of piecewise mixed–effect models with unknown random knots. Applied Psychological Measurement, 38(7), 583–584.

Kohli, N., Harring, J. R., & Hancock, G. R. (2013). Piecewise linear–linear latent growth mixture models with unknown knots. Educational and Psychological Measurement, 73(6), 935–955.

Kohli, N., & Harring, J. R. (2013). Modeling growth in latent variables using a piecewise function. Multivariate Behavioral Research, 48(3), 370–397.

*Indicates co-author was an UMN student during part or all of the work