Residual Analysis for Linear Mixed Models

Nobre, Juvêncio S.; Singer, Júlio M.

doi:10.1002/bimj.200610341

Cited by 120 publications

(23 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, unlike standard linear models, the distributional assumptions in mixed-effects models need to be checked at multiple levels, including the distribution of random effect coefficients (Snijders & Bosker, 2011). Data points with high leverage on model estimates can also be an issue, but such leverage can be assessed with influence diagnosis tools (Demidenko & Stukel, 2005;Loy & Hofmann, 2013;Santos Nobre & Singer, 2007;Zare & Rasekh, 2011).…”

Section: Introductionmentioning

confidence: 99%

Robustness of linear mixed‐effects models to violations of distributional assumptions

et al. 2020

View full text Add to dashboard Cite

Linear mixed‐effects models are powerful tools for analysing complex datasets with repeated or clustered observations, a common data structure in ecology and evolution. Mixed‐effects models involve complex fitting procedures and make several assumptions, in particular about the distribution of residual and random effects. Violations of these assumptions are common in real datasets, yet it is not always clear how much these violations matter to accurate and unbiased estimation. Here we address the consequences of violations in distributional assumptions and the impact of missing random effect components on model estimates. In particular, we evaluate the effects of skewed, bimodal and heteroscedastic random effect and residual variances, of missing random effect terms and of correlated fixed effect predictors. We focus on bias and prediction error on estimates of fixed and random effects. Model estimates were usually robust to violations of assumptions, with the exception of slight upward biases in estimates of random effect variance if the generating distribution was bimodal but was modelled by Gaussian error distributions. Further, estimates for (random effect) components that violated distributional assumptions became less precise but remained unbiased. However, this particular problem did not affect other parameters of the model. The same pattern was found for strongly correlated fixed effects, which led to imprecise, but unbiased estimates, with uncertainty estimates reflecting imprecision. Unmodelled sources of random effect variance had predictable effects on variance component estimates. The pattern is best viewed as a cascade of hierarchical grouping factors. Variances trickle down the hierarchy such that missing higher‐level random effect variances pool at lower levels and missing lower‐level and crossed random effect variances manifest as residual variance. Overall, our results show remarkable robustness of mixed‐effects models that should allow researchers to use mixed‐effects models even if the distributional assumptions are objectively violated. However, this does not free researchers from careful evaluation of the model. Estimates that are based on data that show clear violations of key assumptions should be treated with caution because individual datasets might give highly imprecise estimates, even if they will be unbiased on average across datasets.

show abstract

Section: Introductionmentioning

confidence: 99%

Robustness of linear mixed‐effects models to violations of distributional assumptions

et al. 2020

View full text Add to dashboard Cite

show abstract

“…To model the expected value of the response variable (Z-score of W/A, H/A, and W/H), the following variables were considered as fixed effects: living location, weight, length, gestational age, sex, maternal age, parity, HHg levels in the newborn, maternal HHg levels, family income, maternal education in years, frequency of fish consumption, breastfeeding, age of the child, and hemoglobin levels. The random effects (subject and time) were used to model their covariance structure [ 21 ].…”

Section: Methodsmentioning

confidence: 99%

Influence of Maternal Fish Intake on the Anthropometric Indices of Children in the Western Amazon

2018

View full text Add to dashboard Cite

We studied trends in fish intake among pregnant women living in the Madeira River Basin in Rondônia State, Brazil, to investigate the influence of maternal fish intake on anthropometric indices of children followed up to 5 years. Maternal fish intake was assessed using hair mercury concentrations of mothers and children at delivery and 6, 24, and 59 months. Data analysis was performed using a linear mixed-effect model. Mothers were predominantly young, had low incomes and limited schooling, and breastfed for >6 months. Only 1.9% of children had low birth weight. Anthropometric indices in approximately 80% of the study population showed Z-score values ranging from ≥−2 to ≤1. The influence of maternal fish intake on anthropometric indices, including height-to-age (H/A), weight-to-age (W/A), and weight-to-height (W/H) were not statistically significant after model adjustments. However, higher income and larger birth weight had a positive influence on H/A and W/A, whereas W/H gain was favored by higher maternal educational status and breastfeeding duration. Other variables (hemoglobin concentration and maternal age) had a positive significant influence on anthropometric indices. Maternal fish intake (or its attendant MeHg exposure) did not affect children growth. Nevertheless, it is advisable to avoid mercury-contaminated fish during pregnancy and childhood.

show abstract

“…An analysis of the residuals for the selected model revealed a potential violation of the linearity assumption and the assumption of homoscedasticity of the errors (Santos Nobre & Singer, 2007). To remedy the violation of linearity, the natural logarithm of the dependent variable was taken.…”

Section: Methodsmentioning

confidence: 99%

Sports Fans, Identity, and Socialization: Exploring the Fandemonium

Tainsky¹,

Jasielec

2014

JSM

View full text Add to dashboard Cite

This study uses consumer-theory modeling in exploring the broadcasts of games not featuring a local team. Our general linear mixed model controls for the variation in consumption attributable to traditionally employed determinants of demand and highlights factors related to home team loyalty. The study concludes that while traditional shifters are likewise useful in estimating demand for out-of-market games, fan allegiance to their local team plays a central role in the viewership of all games, even those in which the local team is not explicitly involved. The observation of compositional inheritance effects underscores the significance of local identification in league-wide interest, a phenomenon of growing importance with the ever-increasing availability of out-of-market games.Scott Tainsky is with the Department of Recreation, Sport and Tourism and Mateusz Jasielec is with the

show abstract

Residual Analysis for Linear Mixed Models

Cited by 120 publications

References 23 publications

Robustness of linear mixed‐effects models to violations of distributional assumptions

Robustness of linear mixed‐effects models to violations of distributional assumptions

Influence of Maternal Fish Intake on the Anthropometric Indices of Children in the Western Amazon

Sports Fans, Identity, and Socialization: Exploring the Fandemonium

Contact Info

Product

Resources

About