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Spectral parameterization for linear mixed models applied to confounding of fixed effects by random effects. (English) Zbl 1421.62090
Summary: Linear mixed models (LMMs) are a commonly-used tool for fitting linear models with correlated errors across a wide variety of fields. However, adding random effects to a linear model can cause unexpected large changes in fixed effect estimates relative to the same model without random effects, and the process by which such changes occur is not well understood. We present the spectral parameterization of LMMs as a tool for understanding such confounding, and develop diagnostics for evaluating the effect on fixed effect estimates of collinearities between columns of the fixed effect and reparameterized random effect design matrices, as well as individual observations. We also present spectral parameterizations of ANOVA-like models, intrinsic conditional autoregressive models, and approximations to Gaussian processes.
MSC:
62J05 Linear regression; mixed models
62J10 Analysis of variance and covariance (ANOVA)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G15 Gaussian processes
Software:
GMRFLib; spectralGP
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