A Simulation Comparison of Approximate Tests for Fixed Effects in Random Coefficients Growth Curve Models

Vólaufová, Júlia; LaMotte, Lynn Roy

doi:10.1080/03610918.2011.635254

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…If A = Z we have a so called random coefficient regression model. References related to random coefficient regression models can, for example, be found in an article by Rutter and Elashoff (1994), and in more recent work by Volaufova and Lamotte (2013) who considered the testing of fixed effects of the model. A multivariate version of Eq.…”

Section: Introductionmentioning

confidence: 99%

Growth Curve Model with Bilinear Random Coefficients

2020

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In the present paper, we derive a new multivariate model to fit correlated data, representing a general model class. Our model is an extension of the Growth Curve model (also called generalized multivariate analysis of variance model) by additionally assuming randomness of regression coefficients like in linear mixed models. Each random coefficient has a linear or a bilinear form with respect to explanatory variables. In our model, the covariance matrices of the random coefficients is allowed to be singular. This yields flexible covariance structures of response data but the parameter space includes a boundary, and thus maximum likelihood estimators (MLEs) of the unknown parameters have more complicated forms than the ordinary Growth Curve model. We derive the MLEs in the proposed model by solving an optimization problem, and derive sufficient conditions for consistency of the MLEs. Through simulation studies, we confirmed performance of the MLEs when the sample size and the size of the response variable are large.

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Section: Introductionmentioning

confidence: 99%

Growth Curve Model with Bilinear Random Coefficients

2020

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“…We recommend a slight improvement to the asymptotic test suggested in [7]. In particular, accuracy of p -values [2, 13] will be assessed.…”

Section: Introductionmentioning

confidence: 99%

Approximate testing in two-stage nonlinear mixed models

Burton¹,

Vólaufová²

2014

Journal of Statistical Computation and Simulation

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We investigate here small sample properties of approximate F-tests about fixed effects parameters in nonlinear mixed models. For estimation of population fixed effects parameters as well as variance components, we apply the two-stage approach. This method is useful and popular when the number of observations per sampling unit is large enough. The approximate F-test is constructed based on large sample approximation to the distribution of nonlinear least squares estimates of subject-specific parameters. We recommend a modified test statistic that takes into consideration approximation to the large sample Fisher information matrix (See [1]). Our main focus is on comparing finite sample properties of broadly used approximate tests (Wald test and likelihood ratio test) and the modified F-test under the null hypothesis, especially accuracy of p-values (See [2]). For that purpose two extensive simulation studies are conducted based on pharmacokinetic models (See [3, 4]).

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Approximate Small-Sample Tests of Fixed Effects in Nonlinear Mixed Models

Vólaufová

2014

Communications in Statistics - Simulation and Computation

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A Simulation Comparison of Approximate Tests for Fixed Effects in Random Coefficients Growth Curve Models

Cited by 3 publications

References 19 publications

Growth Curve Model with Bilinear Random Coefficients

Growth Curve Model with Bilinear Random Coefficients

Approximate testing in two-stage nonlinear mixed models

Approximate Small-Sample Tests of Fixed Effects in Nonlinear Mixed Models

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