Table 2 Actual, refitted, and recovered covariance matrices of non-weighted regression coefficients in equations
From: Model errors in tree biomass estimates computed with an approximation to a missing covariance matrix
Eq # | Actual | Refitted | Recovered | Recovered (robust) | P 1 ×100 | P 2×100 | P 3 ×100 |
|---|---|---|---|---|---|---|---|
1 | \(\left( {\begin{array}{*{20}c} {2.62 \times 10^{ - 3} } & { - 0.132} \\ { - 0.132} & {8.67} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {3.30 \times 10^{ - 3} } & { - 0.179} \\ { - 0.179} & {11.4} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {2.75 \times 10^{ - 3} } & { - 0.154} \\ { - 0.154} & {10.2} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {3.01 \times 10^{ - 3} } & { - 0.167} \\ { - 0.167} & {10.9} \\ \end{array} } \right)\) | 0.5 | 64 | 68 |
2 | \(\left( {\begin{array}{*{20}c} {0.267} & { - 0.746} \\ { - 0.746} & {2.25} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {0.316} & { - 0.871} \\ { - 0.871} & {2.53} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {0.240} & { - 0.677} \\ { - 0.677} & {2.33} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {0.264} & { - 0.740} \\ { - 0.740} & {2.19} \\ \end{array} } \right)\) | 99 | 95 | 98 |
5 | \(\left( {\begin{array}{*{20}c} {1.14 \times 10^{ - 3} } & { - 0.605 \times 10^{ - 1} } \\ { - 0.605 \times 10^{ - 1} } & {3.56} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {1.39 \times 10^{ - 3} } & { - 0.598 \times 10^{ - 1} } \\ { - 0.598 \times 10^{ - 1} } & {3.00} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {1.02 \times 10^{ - 3} } & { - 0.436 \times 10^{ - 1} } \\ { - 0.436 \times 10^{ - 1} } & {2.21} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {1.08 \times 10^{ - 3} } & {0.465 \times 10^{ - 1} } \\ {0.465 \times 10^{ - 1} } & {2.35} \\ \end{array} } \right)\) | 4 | 6 | 7 |
6 | \(\left( {\begin{array}{*{20}c} {1.47 \times 10^{ - 1} } & { - 0.383} \\ { - 0.383} & {1.04} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {2.00 \times 10^{ - 1} } & { - 0.469} \\ { - 0.469} & {1.15} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {1.38 \times 10^{ - 1} } & { - 0.319} \\ { - 0.319} & {0.785} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {1.46 \times 10^{ - 1} } & { - 0.338} \\ { - 0.338} & {0.831} \\ \end{array} } \right)\) | 5 | 36 | 36 |
9 | \(\left( {\begin{array}{*{20}c} {5.53 \times 10^{ - 4} } & { - 0.322 \times 10^{ - 1} } \\ { - 0.322 \times 10^{ - 1} } & {2.19} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {1.33 \times 10^{ - 3} } & { - 0.636 \times 10^{ - 1} } \\ { - 0.636 \times 10^{ - 1} } & {3.44} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {5.61 \times 10^{ - 4} } & { - 0.273 \times 10^{ - 1} } \\ { - 0.273 \times 10^{ - 1} } & {1.50} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {6.05 \times 10^{ - 4} } & { - 0.293 \times 10^{ - 1} } \\ { - 0.293 \times 10^{ - 1} } & {1.61} \\ \end{array} } \right)\) | 4 | 3 | 5 |
10 | \(\left( {\begin{array}{*{20}c} {7.84 \times 10^{ - 2} } & { - 0.227} \\ { - 0.227} & {0.697} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {1.27 \times 10^{ - 1} } & { - 0.499} \\ { - 0.499} & {0.86} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {8.20 \times 10^{ - 2} } & { - 0.210} \\ { - 0.210} & {0.561} \\ \end{array} } \right)\) | \(\left( {\begin{array}{*{20}c} {8.82 \times 10^{ - 2} } & { - 0.225} \\ { - 0.225} & {0.599} \\ \end{array} } \right)\) | 12 | 15 | 19 |