Simulation studies comparing fixed effect and mixed models in data sets with multiple measurements in individual sampling units

Abstract

Use of mixed models is advocated almost ubiquitously when regression analysis is applied in data sets that contain multiple measurements in individual sampling units that lead to intercorrelation amongst the residuals. Using two examples, simulation studies were undertaken comparing models that contained fixed effects only with mixed models in which random effects identified the sampling units within the data set. Both approaches resulted in unbiased estimates of the parameters. The choice of a suitable parameterization for the mixed model proved difficult. It was found that use of either an appropriate mixed model or a lesser-known method (‘adjusted ordinary least squares regression’) to fit models with fixed effects only could yield unbiased estimates of the standard errors of the parameter estimates. However, difficulties remain with computational methods in both cases and it cannot be assumed, a priori, that either approach is necessarily superior to the other for any particular data set.

KEYWORDS:

• Regression
• fixed effects
• mixed models
• multiple measurements
• longitudinal data

Acknowledgements

We thank Professor Tim Gregoire (School of Environment, Yale University) for valuable discussion of certain aspects of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Documentation for the SAS statistical package is available at https://support.sas.com/en/documentation.html (accessed April 2021).