Published

2022-01-01

Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors

Modelos mixtos para estudios pretest-posttest en poblaciones finitas con error en la respuesta

DOI:

https://doi.org/10.15446/rce.v45n1.93196

Keywords:

BLUP, Optimal estimator, Random permutation model, Analysis of covariance (en)
BLUP, Estimador óptimo, Modelo de permutación aleatoria, Análisis de covarianza (es)

Downloads

Authors

  • Luz Mery Gonzalez Universidad Nacional de Colombia
  • Julio M. Singer Universidade de São Paulo
  • Edward J. Stanek III University of Massachusetts

We consider a finite population mixed model that accommodates response errors and show how to obtain optimal estimators of the finite population parameters in a pretest-posttest context. We illustrate the method with the estimation of the difference in gain between two interventions and consider a simulation study to compare the empirical version of the proposed estimator (obtained by replacing variance components with estimates) with the estimator obtained via covariance analysis usually employed in such settings. The results indicate that in many instances, the proposed estimator has a smaller mean squared error than that obtained from the standard analysis of covariance model.

Se considera un modelo mixto para población finita que tiene en cuenta el error de respuesta y que arroja estimadores óptimos de los  parámetros de la población finita, para analizar datos de estudios con estructura del tipo pretest-posttest. Se ilustra el método estimando la diferencia en ganancia entre dos intervenciones y se considera un estudio de simulación para comparar la versión empírica del estimador propuesto (obtenido al reemplazar las componentes de varianza con sus estimativas) con el estimador obtenido vía análisis de covarianza, que es usualmente empleado en este tipo de estudios. Los resultados indican que en muchas circunstancias, el estimador propuesto tiene menor error cuadrático medio que el obtenido del análisis estándar usando el modelo de covarianza.

References

Alencar, A., Singer, J. M. & Rocha, F. (2012), ‘Competing regression models for longitudinal data’, Biometrical Journal 54, 214–229. DOI: https://doi.org/10.1002/bimj.201100056

Aoki, R., Achcar, J. A., Bolfarine, H. & Singer, J. M. (2003), ‘Bayesian analysis of null intercept errors-in-variables regression for pretest-posttest data’, Journal of Applied Statistics 30, 3–12. DOI: https://doi.org/10.1080/0266476022000018466

Bonate, P. L. (2000), Analysis of pretest-posttest designs, Chapmann & Hall/CRC, Boca Raton. DOI: https://doi.org/10.1201/9781420035926

Brogan, D. R. & Kutner, M. H. (1980), ‘Comparative analysis of pretest-posttest research designs’, The American Statistician 34, 229–232. DOI: https://doi.org/10.1080/00031305.1980.10483034

Efron, B. & Tibshirani, R. (1993), An Introduction to the Bootstrap, Chapman & Hall, New York. DOI: https://doi.org/10.1007/978-1-4899-4541-9

Harville, D. A. (1997), Matrix Algebra from a Statistician’s Perspective, Springer, New York. DOI: https://doi.org/10.1007/b98818

Knoke, J. (1991), ‘Nonparametric analysis of covariance for comparing change in randomized studies with baseline values subject to error’, Biometrics 47, 523–533. DOI: https://doi.org/10.2307/2532143

Laird, N. (1983), ‘Further comparative analyses of pretest-posttest research designs’, The American Statistician 37, 329–330. DOI: https://doi.org/10.1080/00031305.1983.10483133

Leon, S., Tsiatis, A. & Davidian, M. (2003), ‘Semiparametric estimation of treatment effect in a pretest-posttest study’, Biometrics 59, 1046–1055. DOI: https://doi.org/10.1111/j.0006-341X.2003.00120.x

Pfeffermann, D. (2017), ‘Bayes-based non-bayesian inference on finite populations from non-representative samples: A unified approach’, Calcutta Statistical Association Bulletin 69, 35–63. DOI: https://doi.org/10.1177/0008068317696546

R Core Team (2021), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. https://www.Rproject.org/

Rubin, D. (2005), ‘Causal inference using potential outcomes: Design, modeling, decisions’, Journal of the American Statistical Association 100, 322–331. DOI: https://doi.org/10.1198/016214504000001880

Singer, J. & Andrade, D. (1997), ‘Regression models for the analysis of pretest/posttest data’, Biometrics 53, 729–735. DOI: https://doi.org/10.2307/2533973

Stanek III, E. (1988), ‘Choosing a pretest-posttest analysis’, The American Statistician 42, 178–183. DOI: https://doi.org/10.1080/00031305.1988.10475557

Stanek III, E. J. & Singer, J. M. (2004), ‘Predicting random effects from finite population clustered samples with response error’, Journal of the American Statistical Association 99, 1119–1130. DOI: https://doi.org/10.1198/016214504000001718

Stanek III, E. J., Singer, J. M. & Lencina, V. B. (2004), ‘A unified approach to estimation and predition under simple random sampling’, Journal of Statistical Planning and Inference 121, 325–338. DOI: https://doi.org/10.1016/S0378-3758(03)00114-9

Yang, L. & Tsiatis, A. (2001), ‘Efficiency study of estimators for a treatment effect in a pretest-posttest trial’, The American Statistician 55, 314–321. DOI: https://doi.org/10.1198/000313001753272466

How to Cite

APA

Gonzalez, L. M., Singer, J. M. and Stanek III, E. J. (2022). Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors. Revista Colombiana de Estadística, 45(1), 125–148. https://doi.org/10.15446/rce.v45n1.93196

ACM

[1]
Gonzalez, L.M., Singer, J.M. and Stanek III, E.J. 2022. Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors. Revista Colombiana de Estadística. 45, 1 (Jan. 2022), 125–148. DOI:https://doi.org/10.15446/rce.v45n1.93196.

ACS

(1)
Gonzalez, L. M.; Singer, J. M.; Stanek III, E. J. Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors. Rev. colomb. estad. 2022, 45, 125-148.

ABNT

GONZALEZ, L. M.; SINGER, J. M.; STANEK III, E. J. Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors. Revista Colombiana de Estadística, [S. l.], v. 45, n. 1, p. 125–148, 2022. DOI: 10.15446/rce.v45n1.93196. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/93196. Acesso em: 28 mar. 2025.

Chicago

Gonzalez, Luz Mery, Julio M. Singer, and Edward J. Stanek III. 2022. “Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors”. Revista Colombiana De Estadística 45 (1):125-48. https://doi.org/10.15446/rce.v45n1.93196.

Harvard

Gonzalez, L. M., Singer, J. M. and Stanek III, E. J. (2022) “Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors”, Revista Colombiana de Estadística, 45(1), pp. 125–148. doi: 10.15446/rce.v45n1.93196.

IEEE

[1]
L. M. Gonzalez, J. M. Singer, and E. J. Stanek III, “Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors”, Rev. colomb. estad., vol. 45, no. 1, pp. 125–148, Jan. 2022.

MLA

Gonzalez, L. M., J. M. Singer, and E. J. Stanek III. “Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors”. Revista Colombiana de Estadística, vol. 45, no. 1, Jan. 2022, pp. 125-48, doi:10.15446/rce.v45n1.93196.

Turabian

Gonzalez, Luz Mery, Julio M. Singer, and Edward J. Stanek III. “Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors”. Revista Colombiana de Estadística 45, no. 1 (January 19, 2022): 125–148. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/93196.

Vancouver

1.
Gonzalez LM, Singer JM, Stanek III EJ. Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors. Rev. colomb. estad. [Internet]. 2022 Jan. 19 [cited 2025 Mar. 28];45(1):125-48. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/93196

Download Citation

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).