Regression Analyses in MerQur: A Review from Linear Models to Mixed-Effects Models
DOI:
https://doi.org/10.53463/merqur.20260448Keywords:
regression, logistic, GLM, ridge, lassoAbstract
Regression analysis is the most comprehensive family of methods in modern statistics, enabling the explanation of a dependent response variable through one or more independent variables. Spanning from linear regression through generalised linear models, regularised regression, and hierarchical mixed-effects models, this family is the most frequently used analytical group in academic research for both prediction and explanation. This study introduces in detail the 12 analyses offered in MerQur’s Regression category: Multiple Linear Regression, Logistic Regression, Poisson/Negative Binomial Regression, Multinomial Logistic Regression, Ordinal Logistic Regression, Ridge Regression, Lasso Regression, Linear Mixed Model (LMM), Nested LMM, Crossed LMM, Generalized Estimating Equations (GEE), and Generalized Linear Mixed Model (GLMM). For each analysis: (i) mathematical form and application context, (ii) required assumptions, (iii) form fields and options in MerQur, (iv) reported coefficients, effect sizes, and diagnostic outputs, and (v) interpretation guidance for a typical research question. Linear regression for continuous response, logistic for binary, Poisson/NB for count, ordinal logistic for ordinal, multinomial logistic for nominal multi-category, Ridge/Lasso for high-dimensional and multicollinear data, LMM/Nested/Crossed LMM for hierarchical structures, GEE for repeated measures, and GLMM for non-normal response with hierarchy — all are within scope. This review provides MerQur users with a decision map for the correct choice among 12 regression methods.
References
Agresti, A. (2013). Categorical data analysis (3rd ed.). Wiley.
Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48. https://doi.org/10.18637/jss.v067.i01
Bolker, B. M., Brooks, M. E., Clark, C. J., Geange, S. W., Poulsen, J. R., Stevens, M. H. H., & White, J.-S. S. (2009). Generalized linear mixed models: A practical guide for ecology and evolution. Trends in Ecology & Evolution, 24(3), 127–135. https://doi.org/10.1016/j.tree.2008.10.008
Cameron, A. C., & Trivedi, P. K. (2013). Regression analysis of count data (2nd ed.). Cambridge University Press.
Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1–22. https://doi.org/10.18637/jss.v033.i01
Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.
Hardin, J. W., & Hilbe, J. M. (2013). Generalized estimating equations (2nd ed.). Chapman & Hall/CRC.
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning (2nd ed.). Springer. https://doi.org/10.1007/978-0-387-84858-7
Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55–67. https://doi.org/10.1080/00401706.1970.10488634
Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied logistic regression (3rd ed.). Wiley.
James, G., Witten, D., Hastie, T., & Tibshirani, R. (2021). An introduction to statistical learning with applications in R (2nd ed.). Springer.
Liang, K.-Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1), 13–22. https://doi.org/10.1093/biomet/73.1.13
McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (2nd ed.). Chapman & Hall.
Nakagawa, S., & Schielzeth, H. (2013). A general and simple method for obtaining R² from generalized linear mixed-effects models. Methods in Ecology and Evolution, 4(2), 133–142. https://doi.org/10.1111/j.2041-210x.2012.00261.x
Pinheiro, J. C., & Bates, D. M. (2000). Mixed-effects models in S and S-PLUS. Springer. https://doi.org/10.1007/b98882
Stigler, S. M. (2016). The seven pillars of statistical wisdom. Harvard University Press.
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B, 58(1), 267–288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x
Zuur, A. F., Ieno, E. N., Walker, N. J., Saveliev, A. A., & Smith, G. M. (2009). Mixed effects models and extensions in ecology with R. Springer. https://doi.org/10.1007/978-0-387-87458-6
Downloads
Published
Issue
Section
License
Copyright (c) 2026 MerQur
This work is licensed under a Creative Commons Attribution 4.0 International License.
This article is published under a Creative Commons Attribution 4.0 International License (CC-BY 4.0). Under this license you may:
- Share: Copy and redistribute the material in any medium or format.
- Adapt: Remix, transform and build upon the material for any purpose, including commercial use.
- Attribution: You must give appropriate credit, provide a link to the license, and indicate if changes were made.
