Goodness-of-fit tests in mixed models

Claeskens, Gerda; Hart, Jeffrey D.

doi:10.1007/s11749-009-0148-8

Cited by 34 publications

(20 citation statements)

References 41 publications

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“…In the second case, the characteristics of interest both have a normal-mixture distribution that consists of 90% of N (4, 0.1) and 10% of N (−4, 0.1). This is the same distribution considered by [17], with mean 3.2 and variance 5.86. The distribution is then standardized to satisfy the requirements set up at the beginning of the section.…”

Section: Simulation Studiesmentioning

confidence: 91%

Simple estimation of hidden correlation in repeated measures

Nguyen

Jiang

2011

Statistics in Medicine

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In medical and social studies, it is often desirable to assess the correlation between characteristics of interest that are not directly observable. In such cases, repeated measures are often available, but the correlation between the repeated measures is not the same as that between the true characteristics that are confounded with the measurement errors. The latter is called the hidden correlation. Previously, the problem has been treated by assuming prior knowledge about the measurement errors, or by using relatively complex statistical models, such as the mixed effects models, with no closed-form expression for the estimated hidden correlation. We propose a simple estimator of the hidden correlation that is very much like the Pearson correlation coefficient, with a closed-form expression, under assumptions much weaker than the mixed effects model. Simulation results show that the proposed simple estimator performs similarly as the restricted maximum likelihood (REML) estimator in mixed models, but is computationally much more efficient than REML. Simulation comparison with the Pearson correlation is also made. A real data example is considered.

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Section: Simulation Studiesmentioning

confidence: 91%

Simple estimation of hidden correlation in repeated measures

Nguyen

Jiang

2011

Statistics in Medicine

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“…Three different models for the distribution of the true intake fat density X were tried. These were normal, uniform and a non‐parametric estimate obtained via a minimum distance approach, as used in Claeskens and Hart (2009). The p ‐values from the local test are 0.7808, 0.6885 and 0.9849, indicating that a quadratic function is not favoured over a linear function.…”

Section: Simulations and An Empirical Examplementioning

confidence: 99%

Local and Omnibus Goodness-of-Fit Tests in Classical Measurement Error Models

Hart

Janicki

et al. 2010

Journal of the Royal Statistical Society Series B: Statistical Methodology

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SummaryWe consider functional measurement error models, i.e. models where covariates are measured with error and yet no distributional assumptions are made about the mismeasured variable. We propose and study a score-type local test and an orthogonal series-based, omnibus goodness-of-fit test in this context, where no likelihood function is available or calculated-i.e. all the tests are proposed in the semiparametric model framework. We demonstrate that our tests have optimality properties and computational advantages that are similar to those of the classical score tests in the parametric model framework. The test procedures are applicable to several semiparametric extensions of measurement error models, including when the measurement error distribution is estimated non-parametrically as well as for generalized partially linear models. The performance of the local score-type and omnibus goodness-of-fit tests is demonstrated through simulation studies and analysis of a nutrition data set.

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“…In the literature, a number of diagnostic tools have been suggested for assessing the random-effects distribution in linear mixed models [14,13,5] and also in generalized linear mixed models [20,18,25,22,3,12]. However, to the best of our knowledge, there is only one diagnostic tool available for checking the random-effects distribution in nonlinear mixed-effects models.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear mixed-effects models for pharmacokinetic data analysis: assessment of the random-effects distribution

Drikvandi

2017

J Pharmacokinet Pharmacodyn

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Nonlinear mixed-effects models are frequently used for pharmacokinetic data analysis, and they account for inter-subject variability in pharmacokinetic parameters by incorporating subject-specific random effects into the model. The random effects are often assumed to follow a (multivariate) normal distribution. However, many articles have shown that misspecifying the random-effects distribution can introduce bias in the estimates of parameters and affect inferences about the random effects themselves, such as estimation of the inter-subject variability. Because random effects are unobservable latent variables, it is difficult to assess their distribution. In a recent paper we developed a diagnostic tool based on the so-called gradient function to assess the random-effects distribution in mixed models. There we evaluated the gradient function for generalized liner mixed models and in the presence of a single random effect. However, assessing the random-effects distribution in nonlinear mixed-effects models is more challenging, especially when multiple random effects are present, and therefore the results from linear and generalized linear mixed models may not be valid for such nonlinear models. In this paper, we further investigate the gradient function and evaluate its performance for such nonlinear mixed-effects models which are common in pharmacokinetics and pharmacodynamics. We use simulations as well as real data from an intensive pharmacokinetic study to illustrate the proposed diagnostic tool.

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Goodness-of-fit tests in mixed models

Abstract: Hypothesis test, Mixed model, Minimum distance, Nonparametric test, Order selection, 62G10,

Cited by 34 publications

References 41 publications

Simple estimation of hidden correlation in repeated measures

Simple estimation of hidden correlation in repeated measures

Local and Omnibus Goodness-of-Fit Tests in Classical Measurement Error Models

Nonlinear mixed-effects models for pharmacokinetic data analysis: assessment of the random-effects distribution

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