Alternative Equation Formats

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MathML

\begin{array}{rcl} \hat{Q} & = & \sum_{h = 1}^{H} \sum_{i = 1}^{n_{h}} \sum_{j = 1}^{m_{h i}} w_{h i j} {\hat{D}}_{h i j} {(diag ({\hat{π}}_{h i j}) - {\hat{π}}_{h i j} {\hat{π}}_{h i j}^{'})}^{- 1} {\hat{D}}_{h i j}^{'} \\ \hat{G} & = & \frac{n - 1}{n - p} \sum_{h = 1}^{H} \frac{n_{h} (1 - f_{h})}{n_{h} - 1} \sum_{i = 1}^{n_{h}} (e_{h i \cdot} - {\bar{e}}_{h \cdot \cdot}) (e_{h i \cdot} - {\bar{e}}_{h \cdot \cdot})^{'} \\ e_{h i \cdot} & = & \sum_{j = 1}^{m_{h i}} w_{h i j} {\hat{D}}_{h i j} {(diag ({\hat{π}}_{h i j}) - {\hat{π}}_{h i j} {\hat{π}}_{h i j}^{'})}^{- 1} (y_{h i j} - {\hat{π}}_{h i j}) \\ {\bar{e}}_{h \cdot \cdot} & = & \frac{1}{n_{h}} \sum_{i = 1}^{n_{h}} e_{h i \cdot} \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} \hat{\mb{Q}} & = & \sum _{h=1}^ H\sum _{i=1}^{n_ h} \sum _{j=1}^{m_{hi}} w_{hij}{ \hat{\mb{D}}_{hij}} \left(\textrm{diag}({\hat\bpi }_{hij})- {\hat\bpi }_{hij}{{\hat\bpi }_{hij}}'\right)^{-1} \hat{\mb{D}}_{hij}'\\ \hat{\mb{G}} & = & \frac{n-1}{n-p} \sum _{h=1}^ H { \frac{n_ h(1-f_ h)}{n_ h-1} \sum _{i=1}^{n_ h} { (\mb{e}_{hi\cdot }-\bar{\mb{e}}_{h\cdot \cdot }) (\mb{e}_{hi\cdot }-\bar{\mb{e}}_{h\cdot \cdot })'}} \\ \mb{e}_{hi\cdot }& =& \sum _{j=1}^{m_{hi}} w_{hij}\hat{\mb{D}}_{hij} \left(\textrm{diag}({\hat\bpi }_{hij})- {\hat\bpi }_{hij}{{\hat\bpi }_{hij}}'\right)^{-1} (\mb{y}_{hij}-{\hat\bpi }_{hij})\\ \bar{\mb{e}}_{h\cdot \cdot } & =& \frac1{n_ h}\sum _{i=1}^{n_ h}\mb{e}_{hi\cdot } \end{eqnarray*}