Parameterization | Latent association | Studiesi |
---|---|---|
A1: Current value (linear predictor) | \( {W}_i(t)={\displaystyle {\sum}_{k=1}^K{\alpha}_k{\mu}_{ik}(t)} \) | [17, 19, 21, 29, 37, 39, 42, 48, 49, 52, 56, 58, 60, 62, 67, 70] |
A2: Current value (expected value)a | \( {W}_i(t)={\displaystyle {\sum}_{k=1}^K{\alpha}_k{h}_k^{-1}\left({\mu}_{ik}\right(t\left)\right)} \) | [62] |
A3: Interactionb | \( {W}_i(t)={\displaystyle {\sum}_{k=1}^K\left\{{\alpha}_k{\mu}_{ik}(t)+{\sum}_{l=1}^p{x}_{il}^{(2)}{\mu}_{ik}(t){\gamma}_{kl}\right\}} \) | [37] |
A4: Lagged timec | \( {W}_i(t)={\displaystyle {\sum}_{k=1}^K{\alpha}_k{\mu}_{ik}\left(t-c\right)} \) | [46] |
A5: General vector functiond | \( {W}_i(t)={a}^T\psi \left(t,,,{b}_i\right) \) | [38] |
A6: Time-dependent slopese | \( {W}_i(t)={\displaystyle {\sum}_{k=1}^K\left\{{\mu}_{ik}(t)+{\displaystyle {\sum}_{v=1}^V{\alpha}_{vk}\frac{d^v}{d{t}^v}{\mu}_{ik}(t)}\right\}} \) | |
A7: Cumulative effects | \( {W}_i(t)={\displaystyle {\sum}_{k=1}^K{\alpha}_k{\displaystyle {\int}_0^t}{\mu}_{ik}(s)ds} \) | [56] |
A8: Random effectsf | \( {W}_i(t)={\displaystyle {\sum}_{k=1}^K{\alpha}_k^T{b}_{ik}} \) | |
A9: Generalised random effects + fixed effectsg | \( {W}_i(t)={\displaystyle {\sum}_{k=1}^K{\alpha}_k^Tr\left({b}_{ik} + {\tilde {\beta}}_k^{(1)}\right)} \) | |
A10: Correlated random effectsh | \( {W}_i(t)={\theta}_i{\textstyle}\mathrm{with}{\textstyle }{\left({b}_i^T,,,{\theta}_i\right)}^T\sim {\mathrm{F}}_{\mathrm{a}} \) | [29] |