Table 6 Operations required to calculate the correction factor
Step | Component | Number of operations |
|---|---|---|
1 | \((\mathbf{X}_1' \mathbf{X}_1)^{-1}\) | \(p_1\) |
2 | \({\mathbf{X}_1'{} \mathbf{X}_2}{Var}(\hat{{\varvec{\upbeta }}}_2){\mathbf{X}_2'{} \mathbf{X}_1}\) | \(p_1p_2^2+p_1^2p_2\) |
3 | Multiplying \((\mathbf{X}_1'{} \mathbf{X}_1 )^{-1}\) on both sides of step 2 | \(2p_1^2\) |
4 | \({\mathbf{X}_1'{} \mathbf{X}_2}{Var}(\hat{{\varvec{\upbeta }}}_2, \hat{{\varvec{\upbeta }}}_1)\) | \(p_1^2p_2\) |
5 | Multiplying \((\mathbf{X}_1'{} \mathbf{X}_1 )^{-1}\) on the left side of step 4 | \(p_1^2\) |
6 | Addition to obtain correction factor for other fixed effects | \(2p_1^2\) |
7 | Addition of step 6 to \({Var}(\hat{{\varvec{\upbeta }}}_1)\) | \(p_1^2\) |
8 | Completing PEVMean | \(p_1\) |
Total calculations | \(2p_1+6p_{1}^{2} +p_1p_2(2p_1+p_2)\) |