Properties of an R2 statistic for fixed effects in the linear mixed model for longitudinal data Public Deposited

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  • March 21, 2019
  • Matuszewski, Jeanine M.
    • Affiliation: Gillings School of Global Public Health, Department of Biostatistics
  • The R2 statistic has become a widely used tool when analyzing data in the linear univariate setting. Many R2 statistics for the linear mixed model exist but their properties are not well established. The purpose of this dissertation is to examine the properties and performance of R2[beta] for fixed effects in the linear mixed model. Two approaches are considered in deriving approximations for the mean and variance of R2[beta] under the null and alternative hypotheses which include using the Beta distribution and a Taylor series approximation. Test statistics based on these two approximations of the mean and variance are proposed and compared to the overall F test for fixed effects in the linear mixed model. Using simulations, the Type I error rate of the proposed R2[beta] test statistics derived from the Beta distribution was equivalent to the Type I error rate for the overall F test. The Type I error rates for the test statistic based on the Taylor series approximation moments were slightly inflated. The impact of covariance structure misspecification, estimation technique, and denominator degrees of freedom method on the asymptotic properties of R2[beta] are explored. For the simulation studies examined, the estimation technique does not impact the values of R2[beta]. The values and asymptotic properties of R2[beta] using Kenward-Roger, containment and Satterthwaite methods are greatly impacted by covariance structure misspecification whereas R2[beta] using the residual method is not. Simulations illustrate the impact of underspecification of the covariance structure as compound symmetric when the true structure is more complex. The asymptotic R2[beta]'s for the underspecified models using Kenward-Roger degrees of freedom are smaller than the true asymptotic R2[beta]'s. Conversely, the asymptotic R2[beta]'s for the underpecified models using residual methods are larger than the true asymptotic R2[beta]. The semi-parital R2[beta] for the four denominator degrees of freedom are computed and compared to the corresponding model R2[beta] in both a real world example and simulation study. The semi-partial R2[beta] using residual degrees of freedom never exceeded the model R2[beta], but the semi-partial R2[beta] using the other three methods sometimes exceeded the model R2[beta]. R2[beta] is also evaluated as a fixed effects model selection tool. The performance of R2[beta] is poor; so an adjusted R2[beta] is created for purposes of fixed effects model selection. The adjusted R2[beta] using residual degrees of freedom outperformed the adjusted R2[beta] defined using the other methods.
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  • "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biostatistics, Gillings School of Global Public Health."
  • Edwards, Lloyd
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  • Chapel Hill, NC
  • Open access

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