Introduction to MEMWAS
Installation | Purpose | Why random effects and serial correlation are different? | [\operatorname{Cov}\left(b_{0i}+t_{ij}b_{1i},b_{0i}+t_{ik}b_{1i}\right) | [\operatorname{Cov}(u_{ij},u_{ik}) | What does the MEMWAS work on? | Penalized smooth mean functions | Statistical framework | Notation | [\eta_r | [T_c(u) | [\operatorname | Gaussian outcomes | [V | Non-Gaussian outcomes | [L(\psi) | [E(Y_r\mid x_r) | [\operatorname{Cov}(Y) | Family-specific conditional models | Overview on family-specific models | Choosing families and interpreting coefficients | Likelihood and approximation methods | Gaussian models | [\left(X^\top V^{-1}X+\lambda_2D_\beta\right)\widehat\beta | Non-Gaussian models | [h(a;\psi) | Laplace approximation | [H | [\log L(\psi)\approxh(\widehat a;\psi)+\frac{d}{2}\log(2\pi) | Variational inference | [\mathcal{L}(q,\psi) | E_q | Adaptive Gauss--Hermite quadrature | Saddlepoint approximation | Penalized quasi-likelihood | Fixed-effect and serial penalties | [P(\beta) | How does the MEMWAS work? | Data requirements and identifiability | Workflows | Core functions | Key parameters | Approximation diagnostics and uncertainty | Within-subject correlation structures | Overview on autocorrelation structures in MEMWAS | [\rho_1 | Unequally spaced measurements | [\operatorname{Corr}(u_{ij},u_{ik}) | Model comparison and nonlinear screening | [\Lambda | 2{\ell(\widehat\psi_{\mathrm{full}}) | Predictions and random-effect estimates | [\widehat y_r^ | [\widehat\mu_r^ | Examples | Minimal educational example | Minimal healthcare example | Non-Gaussian example and approximation check | Predictor-specific serial coefficient example | Reporting recommendations | References
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