Use of generalized additive mixed models in the comparison of mortar types in different configurations

Authors

DOI:

https://doi.org/10.33448/rsd-v11i6.29160

Keywords:

Generalized additive mixed models; Longitudinal data; Nonparametric regression; P-splines.

Abstract

Generalized additive mixed models (GAMM) are useful when the nature of the data is longitudinal, which include the nonlinearity of the individual trajectories of the subjects, associating these with the assumption of the existence of random effects for each individual. In these models it is possible to rewrite the predictor as a sum of smooth nonparametric functions and then use the smooth technique P-spline. Thus, using the generalized additive mixed models with P-splines, this article aims to verify the impact of the types of mortars and the concentration levels of an additive content on the evolution of mortar weight contained in specimens over time, verifying possible differences between combinations of types and concentration. In relation to the results, it was observed through the analyzes that there were significant differences in the estimated curves of the weight evolution in both types of mortar, concluding that the matured mortar has a water absorption speed by capillarity higher than dry mortar. All the necessary assumptions for the validity of the model have been satisfied.

Author Biographies

Breno Gabriel da Silva, University of São Paulo

Department of Exact Sciences - LCE, University of São Paulo: ESALQ/USP - Piracicaba / SP, Brazil

Willian Luís de Oliveira, State University of Maringá

Department of Statistics, State University of Maringá - Maringá / PR, Brazil

Terezinha Aparecida Guedes, State University of Maringá

Department of Statistics, State University of Maringá - Maringá / PR, Brazil

Vanderly Janeiro, State University of Maringá

Department of Statistics, State University of Maringá - Maringá / PR, Brazil

José Aparecido Canova, State University of Maringá

Department of Civil Engineering, State University of Maringá - Maringá / PR, Brazil

References

Achmad R. F. A., Janssen, P., Sa’adah, U., Solimun, E. A., & Nurjannah A. L. (2018). Comparison of spline estimator at various levels of autocorrelation in smoothing spline non parametric regression for longitudinal data. Communications in Statistics-Theory and Methods, Taylor & Francis 47:5265-5285.

Andrinopoulou, E. R., Eilers, P. H., Takkenberg, J. J., & Rizopoulos, D. (2018). Improved dynamic predictions from joint models of longitudinal and survival data with time-varying effects using P-splines. Biometrics, Wiley Online Library 74:685-693.

Baayen, R. H., van Rij, J., de Cat, C., & Wood, S. (2018). Autocorrelated errors in experimental data in the language sciences: Some solutions offered by Generalized Additive Mixed Models. Mixed-effects regression models in linguistics, Springer, Cham pp. 49-69.

Benedetti, A., Abrahamowicz, M., & Goldberg, M. S. (2009). Accounting for Data-Dependent Degrees of Freedom Selection When Testing the Effect of a Continuous Covariate in Generalized Additive Models. Communications in Statistics - Simulation and Computation 38(5):1115-1135.

Canova, J.A., de Angelis N. G., & Bergamasco, R. (2009). Mortar with unserviceable tire residues. Journal of Urban and Environmental Engineering, JSTOR 3:63-72.

Canova, J.A., de Angelis N. G., & Bergamasco, R. (2015). Pó de borracha de pneus inservíveis em argamassa de revestimento. REEC-Revista Eletrônica de Engenharia Civil 10:41-53.

Corbeil, R. R., & Searle, S. R. (1976). Restricted maximum likelihood (REML) estimation of variance components in the mixed model. Technometrics, Taylor & Francis 18:31-38.

Currie, I. D., & Durbán, M. (2002). Flexible smoothing with P-splines: a unified approach. Statistical Modelling, Sage Publications Sage CA: Thousand Oaks, CA 2:333-349.

Craven, P., & Wahba, G. (1978). Smoothing noisy data with spline functions. Numerische mathematik, Springer 31:377-403.

da Silva, B. G., Guedes, T. A., Janeiro, V., Ferreira, E. C., de Araújo, S. M., & Ciupa, L. (2020). Analyzing weight evolution in mice infected by Trypanosoma cruzi. Acta Scientiarum. Health Sciences 42:e51437- e51437.

de Jong, R., van Buuren, S., & Spiess, M. (2015). Multiple Imputation of Predictor Variables Using Generalized Additive Models. Communications in Statistics - Simulation and Computation 45(3):968-985.

Durbán, M., Harezlak, J., Wand, M.P., & Carroll, R.J. (2005). Simple fitting of subject-specific curves for longitudinal data. Statistics in medicine, Wiley Online Library 24:1153-1167.

Durbán, M. (2007). Splines con penalizaciones: Teoría y aplicaciones. Universidad Pública de Navarra, 60p.

Eilers, P.H.C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical science, JSTOR 89-102.

Friedman, J., Hastie, T., & Tibshirani, R. (2001). The elements of statistical learning. Vol.1. No 10. New York: Springer series in statistics.

Garcia-Hernandez, A., & Rizopoulos, D. (2018). %JM: A SAS Macro to Fit Jointly Generalized Mixed Models for Longitudinal Data and Time-to-Event Responses. Journal of Statistical Software 84:1-29.

Gressani, O., & Lambert, P. (2021). Laplace approximations for fast Bayesian inference in generalized additive models based on P-splines. Computational Statistics & Data Analysis, 154, 107088.

Hastie, T. J., & Tibshirani, R. J. (1990). Generalized additive models. Vol. 43. CRC press.

Hernando V. L., & Paula, G. A. (2016). An extension of log-symmetric regression models: R codes and applications. Journal of Statistical Computation and Simulation 86:1709-1735.

Islamiyati, A., Fatmawati., & Chamidah, N. (2019). Ability of Covariance Matrix in Bi-Response Multi- Prredictor Penalized Spline Model Through Longitudinal Data Simulation. International Journal of Academic and Applied Research 3:8-11.

Keele, L., & Keele, L. (2008). Semiparametric regression statistic for the science. Chichester: Wiley. pp 231.

Lin, X., & Zhang, D. (1999). Inference in generalized additive mixed modelsby using smoothing splines. Journal of the royal statistical society: Series b (statistical methodology), Wiley Online Library 61:381-400.

McKeown, G. J., & Sneddon, I. (2014). Modeling continuous self-report measures of perceived emotion using generalized additive mixed models. Psychological methods, American Psychological Association 19:155-174.

Momen, M., Campbell, M. T., Walia, H., & Morota, G. (2019). Predicting longitudinal traits derived from highthroughput phenomics in contrasting environments using genomic Legendre polynomials and B-splines. G3: Genes, Genomes, Genetics 9:3369-3380.

Nores, M., & Díaz, M. (2016). Bootstrap hypothesis testing in generalized additive models for comparing curves of treatments in longitudinal studies. Journal of Applied Statistics, Taylor & Francis. 43:810-826.

Patterson, H. D., & Thompson, R. (1971). Recovery of inter-block information when block sizes are unequal. Biometrika, Oxford University Press 58:545-554.

Pinheiro, J. C., & Bates, D. M. (2006). Mixed-effects models in S and S-PLUS. Springer Science & Business Media.

Polansky, L., & Robbins, M. M. (2013). Generalized additive mixed models for disentangling long-term trends, local anomalies, and seasonality in fruit tree phenology. Ecology and Evolution, Wiley Online Library 3:3141-3151.

Prawanti, D. D., Budiantara, I. N., & Purnomo, J. D. (2019). Parameter Interval Estimation of Semiparametric Spline Truncated Regression Model for Longitudinal Data. IOP Conference Series: Materials Science and Engineering, IOP Publishing 546:1-10.

R Core Team. (2022). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, https://www.R-project.org/.

Rilem, T.C. (1994). RILEM recommendations for the testing and use of constructions materials. RC 6:218- 220.

Ruppert, D., Wand, M. P., & Carroll, R. J. (2003). Semiparametric regression. No. 12. Cambridge university press, 386p.

Schaeffer, L.R. (2004). Application of random regression models in animal breeding. Livestock Production Science, Elsevier 86:35-45.

Shadish, W. R., Zuur, A. F., & Sullivan, K. J. (2014). Using generalized additive (mixed) models to analyze single case designs. Journal of school psychology, Elsevier 52:149-178.

Sudo, M., Sato, Y., & Yorozuya, H. (2021). Time-course in attractiveness of pheromone lure on the smaller tea tortrix moth: a generalized additive mixed model approach. Ecological Research, 36(4), 603-616.

Toshniwal, D., Speleers, H., Hiemstra, R. R., & Hughes, T. J. (2017). Multi-degree smooth polar splines: A framework for geometric modeling and isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, Elsevier 316:1005-1061.

Wood, S. N. (2017). Generalized additive models: an introduction with R. Chapman and Hall/CRC press, 384p.

Zhang, X., Zhong, Q., & Wang, J. L. (2020). A new approach to varying-coefficient additive models with longitudinal covariates. Computational Statistics & Data Analysis, Elsevier 145:1-15.

Downloads

Published

28/04/2022

How to Cite

SILVA, B. G. da .; OLIVEIRA, W. L. de .; GUEDES, T. A.; JANEIRO, V.; CANOVA, J. A. Use of generalized additive mixed models in the comparison of mortar types in different configurations. Research, Society and Development, [S. l.], v. 11, n. 6, p. e31011629160, 2022. DOI: 10.33448/rsd-v11i6.29160. Disponível em: https://rsdjournal.org/index.php/rsd/article/view/29160. Acesso em: 28 may. 2022.

Issue

Section

Exact and Earth Sciences