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Assessing the impact of variance heterogeneity and misspecification in mixed-effects location-scale models

Vincent Jeanselme, Marco Palma, Jessica K Barrett

TL;DR

This paper tackles the problem of variance heterogeneity in longitudinal analyses by evaluating mixed-effects location-scale models (MELSM) as an alternative to traditional linear mixed models (LMM). Through a comprehensive simulation study based on PBC covariates, it demonstrates that ignoring heteroscedasticity in LMMs leads to undercoverage and biased variance components, while MELSM can recover location estimates more reliably when the scale is correctly specified. The results reveal nuanced effects of misspecification: scale misspecification hurts the precision of location estimates, location misspecification biases scale estimates, and there is a dynamic interplay between random effects and residual variance. The case study on the PBC dataset reinforces the practical value of MELSM for detecting heteroscedasticity and informs methodological guidance for extending these ideas to GLMMs and joint models in survival settings.

Abstract

Linear Mixed Model (LMM) is a common statistical approach to model the relation between exposure and outcome while capturing individual variability through random effects. However, this model assumes the homogeneity of the error term's variance. Breaking this assumption, known as homoscedasticity, can bias estimates and, consequently, may change a study's conclusions. If this assumption is unmet, the mixed-effect location-scale model (MELSM) offers a solution to account for within-individual variability. Our work explores how LMMs and MELSMs behave when the homoscedasticity assumption is not met. Further, we study how misspecification affects inference for MELSM. To this aim, we propose a simulation study with longitudinal data and evaluate the estimates' bias and coverage. Our simulations show that neglecting heteroscedasticity in LMMs leads to loss of coverage for the estimated coefficients and biases the estimates of the standard deviations of the random effects. In MELSMs, scale misspecification does not bias the location model, but location misspecification alters the scale estimates. Our simulation study illustrates the importance of modelling heteroscedasticity, with potential implications beyond mixed effect models, for generalised linear mixed models for non-normal outcomes and joint models with survival data.

Assessing the impact of variance heterogeneity and misspecification in mixed-effects location-scale models

TL;DR

This paper tackles the problem of variance heterogeneity in longitudinal analyses by evaluating mixed-effects location-scale models (MELSM) as an alternative to traditional linear mixed models (LMM). Through a comprehensive simulation study based on PBC covariates, it demonstrates that ignoring heteroscedasticity in LMMs leads to undercoverage and biased variance components, while MELSM can recover location estimates more reliably when the scale is correctly specified. The results reveal nuanced effects of misspecification: scale misspecification hurts the precision of location estimates, location misspecification biases scale estimates, and there is a dynamic interplay between random effects and residual variance. The case study on the PBC dataset reinforces the practical value of MELSM for detecting heteroscedasticity and informs methodological guidance for extending these ideas to GLMMs and joint models in survival settings.

Abstract

Linear Mixed Model (LMM) is a common statistical approach to model the relation between exposure and outcome while capturing individual variability through random effects. However, this model assumes the homogeneity of the error term's variance. Breaking this assumption, known as homoscedasticity, can bias estimates and, consequently, may change a study's conclusions. If this assumption is unmet, the mixed-effect location-scale model (MELSM) offers a solution to account for within-individual variability. Our work explores how LMMs and MELSMs behave when the homoscedasticity assumption is not met. Further, we study how misspecification affects inference for MELSM. To this aim, we propose a simulation study with longitudinal data and evaluate the estimates' bias and coverage. Our simulations show that neglecting heteroscedasticity in LMMs leads to loss of coverage for the estimated coefficients and biases the estimates of the standard deviations of the random effects. In MELSMs, scale misspecification does not bias the location model, but location misspecification alters the scale estimates. Our simulation study illustrates the importance of modelling heteroscedasticity, with potential implications beyond mixed effect models, for generalised linear mixed models for non-normal outcomes and joint models with survival data.

Paper Structure

This paper contains 34 sections, 14 equations, 12 figures, 18 tables.

Table of Contents

  1. Background
  2. Mixed-effect location-scale model
  3. Simulation study
  4. Data generation
  5. Estimands of interest
  6. Software
  7. Results
  8. Practice 1: Ignoring heteroscedasticity
  9. Scale misspecification impacts the precision of location estimates.
  10. Coverage is low in misspecified settings.
  11. Larger numbers of individuals and encounters reduce error.
  12. Practice 2: Misspecifying location and scale in MELSM
  13. Adding superfluous parameters does not invalidate inference.
  14. Not all scale misspecification types affect the location in the same way.
  15. Location misspecification impacts scale.
  16. ...and 19 more sections

Figures (12)

  • Figure 1: Estimated age effect on location (left panel) and scale (right panel) for increasing number of individuals. For each model, coverage is reported as a percentage next to the corresponding boxplot.
  • Figure 2: Estimated age effect on location (left panel) and scale (right panel) for increasing average number of observations per individual. For each model, coverage is reported as a percentage next to the corresponding boxplot.
  • Figure 3: Estimated age effect for location (left panel) and scale (right panel). For each model, coverage is reported as a percentage next to the corresponding boxplot.
  • Figure 4: Estimated standard deviation of random intercepts for location (left panel) and scale (right panel). For each model, coverage is reported as a percentage next to the corresponding boxplot.
  • Figure 5: Estimated age effect for location (left panel) and scale (right panel). For each model, coverage is reported as a percentage next to the corresponding boxplot.
  • ...and 7 more figures