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Page 2
From: Evaluating the robustness of repeated measures analyses: The case of small sample sizes and nonnormal data
| Compound symmetric (CS) (2 parameters) \( {\sigma^2}\left[ {\begin{array}{*{20}c} 1 \hfill & \rho \hfill & \rho \hfill & \rho \hfill \\ {} \hfill & 1 \hfill & \rho \hfill & \rho \hfill \\ {} \hfill & {} \hfill & 1 \hfill & \rho \hfill \\ {} \hfill & {} \hfill & {} \hfill & 1 \hfill \\ \end{array}} \right] \) | Random coefficients (RC) (4 parameters) \( \left[ {\begin{array}{*{20}c} 1 & 0 \\ 1 & 1 \\ 1 & 2 \\ \vdots & \vdots \\ 1 & {K-1} \\ \end{array}} \right]\left[ {\begin{array}{*{20}c} {{\sigma_{11 }}} & {{\sigma_{12 }}} \\ {{\sigma_{12 }}} & {{\sigma_{22 }}} \\ \end{array}} \right]\left[ {\begin{array}{*{20}c} 1 & 0 \\ 1 & 1 \\ 1 & 2 \\ \vdots & \vdots \\ 1 & {K-1} \\ \end{array}} \right]+\left[ {\begin{array}{*{20}c} {\sigma^2 } & {} & {} & {} \\ {} & {\sigma^2 } & {} & {} \\ {} & {} & \ddots & {} \\ {} & {} & {} & {\sigma^2 } \\ \end{array}} \right] \) |
| Unstructured (UN) (\( {{{K\left[ {K+1} \right]}} \left/ {2} \right.} \) parameters) \( \begin{array}{*{20}c} {\sigma_{11}^2} & {{\sigma_{12 }}} & {{\sigma_{13 }}} & \cdots & {{\sigma_{1K }}} \\ {} & {\sigma_{22}^2} & {{\sigma_{23 }}} & \cdots & {{\sigma_{2K }}} \\ {} & {} & {\sigma_{33}^2} & \cdots & {{\sigma_{3K }}} \\ {} & {} & {} & \ddots & \vdots \\ {} & {} & {} & {} & {\sigma_{KK}^2} \\ \end{array} \) | Heterogeneous first-order autoregressive [ARH(1)] (K + 1 parameters) \( \begin{array}{*{20}c} {\sigma_1^2} & {\sigma_1 {\sigma_2}\rho } & {\sigma_1 {\sigma_3}{\rho^3}} & \cdots & {\sigma_1 {\sigma_K}{\rho^{K-1 }}} \\ {} & {\sigma_2^2} & {\sigma_2 {\sigma_3}\rho } & \cdots & {\sigma_2 {\sigma_K}{\rho^{K-2 }}} \\ {} & {} & {\sigma_3^2} & \cdots & {\sigma_3 {\sigma_K}{\rho^{K-3 }}} \\ {} & {} & {} & \ddots & \vdots \\ {} & {} & {} & {} & {\sigma_K^2} \\ \end{array} \) |
- Only the upper diagonal of the symmetric matrices is shown. The CS structure is displayed for four factor levels (K = 4). For higher K, the K × K correlation matrix again has 1 on the main diagonal and ρ elsewhere.