# Limitations of ordinary least squares models in analyzing repeated measures data.

@article{Ugrinowitsch2004LimitationsOO, title={Limitations of ordinary least squares models in analyzing repeated measures data.}, author={Carlos Ugrinowitsch and Gilbert W. Fellingham and Mark D. Ricard}, journal={Medicine and science in sports and exercise}, year={2004}, volume={36 12}, pages={ 2144-8 } }

PURPOSE
To a) introduce and present the advantages of linear mixed models using generalized least squares (GLS) when analyzing repeated measures data; and b) show how model misspecification and an inappropriate analysis using repeated measures ANOVA with ordinary least squares (OLS) methodology can negatively impact the probability of occurrence of Type I error.
METHODS
The effects of three strength-training groups were simulated. Strength gains had two slope conditions: null (no gain), and…

## 94 Citations

Generalized additive models to analyze non-linear trends in biomedical longitudinal data using R: Beyond repeated measures ANOVA and Linear Mixed Models

- EngineeringbioRxiv
- 2022

In biomedical research, the outcome of longitudinal studies has been traditionally analyzed using the repeated measures analysis of variance (rm-ANOVA) or more recently, linear mixed models (LMEMs).…

Using generalized additive models to analyze biomedical non-linear longitudinal data

- Computer Science
- 2021

It is shown that GAMs are able to produce estimates that are consistent with the trends of biomedical non-linear data even in the case when missing observations exist, allowing reliable inference from the data.

Generalized additive models to analyze nonlinear trends in biomedical longitudinal data using R: Beyond repeated measures ANOVA and linear mixed models.

- EngineeringStatistics in medicine
- 2022

In biomedical research, the outcome of longitudinal studies has been traditionally analyzed using the repeated measures analysis of variance (rm-ANOVA) or more recently, linear mixed models (LMEMs).…

The consistency of ordinary least-squares and generalized least-squares polynomial regression on characterizing the mechanomyographic amplitude versus torque relationship

- PsychologyPhysiological measurement
- 2009

Overall, OLS and GLS polynomial regression models were only able to consistently describe the torque-related patterns of response for MMG(RMS) in 27-55% of the subjects across three trials.

Understanding and using time series analyses in addiction research.

- PsychologyAddiction
- 2019

This paper provides addiction researchers with an overview of many of the methods available and guidance on when and how they should be used, sample size determination, reporting, and interpretation, and the importance of pre-registering hypotheses and analysis plans before the analyses are undertaken.

Applications of spatial models to ordinal data

- Environmental SciencebioRxiv
- 2020

None of the eight evaluated models fully removed spatial patterns indicating that there is a need to either adjust existing models or develop novel models for spatial adjustments of ordinal data collected in fields exhibiting discontinuous transitions between heterogeneous patches.

Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines

- MathematicsEmerging Themes in Epidemiology
- 2016

A stepwise approach that builds from simple to complex models, and argues that inference for any problem depends more on the estimated curve or differences in curves rather than the coefficients, provides a set of tools to model longitudinal childhood data for non-statisticians using linear mixed-effect models.

Number of accelerometer monitoring days needed for stable group-level estimates of activity

- BiologyPhysiological measurement
- 2016

Simulation data suggest that stable estimates of group-level means can be obtained from as few as one randomly selected monitoring day from a sampled week, on the other hand, estimates using non-random selection of weekend days may be significantly biased.

Machine learning analytics for predictive breeding

- Environmental Science
- 2020

Overall, algorithmic modeling outperforms data modeling methods for the soybean IDC ordinal data type and machine learning algorithms provide higher prediction accuracy than traditional statistical data models in terms of sensitivity, specificity, and overall.

Monitoring acute effects on athletic performance with mixed linear modeling.

- EducationMedicine and science in sports and exercise
- 2010

Mixed linear modeling can be applied successfully to monitor factors affecting performance in a squad of elite athletes to demonstrate the application of mixed linear modeling for monitoring athletic performance.

## References

SHOWING 1-10 OF 18 REFERENCES

Modelling covariance structure in the analysis of repeated measures data.

- EconomicsStatistics in medicine
- 2000

In many situations, estimates of linear combinations are invariant with respect to covariance structure, yet standard errors of the estimates may still depend on the covariance structures, so inference about fixed effects proceeds essentially as when using PROC GLM.

Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data.

- MathematicsStatistics in medicine
- 1997

The purpose of this tutorial is to provide readers with a sufficient introduction to the theory to understand the method and a more extensive discussion of model fitting and checking in order to provide guidelines for its use.

Random-effects models for longitudinal data.

- MathematicsBiometrics
- 1982

A unified approach to fitting these models, based on a combination of empirical Bayes and maximum likelihood estimation of model parameters and using the EM algorithm, is discussed.

Tests for gaussian repeated measures with missing data in small samples.

- MathematicsStatistics in medicine
- 2000

For small samples of Gaussian repeated measures with missing data, Barton and Cramer recommended using the EM algorithm for estimation and reducing the degrees of freedom for an analogue of Rao's F…

Effects of covariance model assumptions on hypothesis tests for repeated measurements: analysis of ovarian hormone data and pituitary‐pteryomaxillary distance data

- MathematicsStatistics in medicine
- 2001

The characteristics of tests based on these two methods of analysis are described and the performance of these tests is investigated, particularly on tests for group effects and parallelism of response profiles.

Maximum likelihood computations with repeated measures: application of the EM algorithm

- Computer Science, Mathematics
- 1987

The purpose of this article is to consider the use of the EM algorithm for both maximum likelihood (ML) and restrictedmaximum likelihood (REML) estimation in a general repeated measures setting using a multivariate normal data model with linear mean and covariance structure.

Modelling the random effects covariance matrix in longitudinal data

- MathematicsStatistics in medicine
- 2003

This paper proposes an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix, which will allow the parameters that result from this decomposition to depend on subject-specific covariates and also explore ways to parsimoniously model these parameters.

Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data

- Mathematics
- 1988

Abstract We develop an efficient and effective implementation of the Newton—Raphson (NR) algorithm for estimating the parameters in mixed-effects models for repeated-measures data. We formulate the…

Design of Experiments: Statistical Principles of Research Design and Analysis

- Mathematics
- 1999

1. RESEARCH DESIGN PRINCIPLES The Legacy of Sir Ronald A. Fisher / Planning for Research / Experiments, Treatments, and Experimental Units / Research Hypotheses Generate Treatment Designs / Local…

Growth curve model analysis for quality of life data.

- MedicineStatistics in medicine
- 1998

A growth curve model conditional on a time-dependent variable of defined health states is proposed in order to assess the overall treatment effect while taking into account occurrences of missing data and measurements from irregular visits.