Difference between revisions of "User:Ulf Rehmann/sandbox statprob/"
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| − | + | This code produces some nested array image. | |
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'''Table 1.''' A class of stationary correlation models for longitudinal count data | '''Table 1.''' A class of stationary correlation models for longitudinal count data | ||
and basic properties. | and basic properties. | ||
<center> | <center> | ||
| − | \begin{array}{ccc} | + | $$\begin{array}{ccc} |
| − | Model & Dynamic relationship & Mean-variance \\ | + | \text{Model} & \text{Dynamic relationship} & \text{Mean-variance} \\ |
| − | && \& Correlations \\ \hline | + | && \text{\& Correlations} \\ \hline |
AR(1) & y_{it}=\rho * y_{i,t-1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ | AR(1) & y_{it}=\rho * y_{i,t-1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ | ||
& y_{i1}\sim Poi(\mu_{i\cdot}) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ | & y_{i1}\sim Poi(\mu_{i\cdot}) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ | ||
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& y_{i1}=d_{i1} \sim Poi(\mu_{i\cdot}/(1+\rho)) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ | & y_{i1}=d_{i1} \sim Poi(\mu_{i\cdot}/(1+\rho)) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ | ||
& d_{it} \sim P(\mu_{i\cdot}/(1+\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ | & d_{it} \sim P(\mu_{i\cdot}/(1+\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ | ||
| − | && | + | && = |
\left\{ \begin{array}{ll} | \left\{ \begin{array}{ll} | ||
\frac{\rho}{1+\rho} & \mbox{for } \ell=1\\ | \frac{\rho}{1+\rho} & \mbox{for } \ell=1\\ | ||
0 & \mbox{otherwise}, | 0 & \mbox{otherwise}, | ||
| − | \end{array} \right. | + | \end{array} \right. |
\\ \hline | \\ \hline | ||
EQC & y_{it}=\rho * y_{i1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ | EQC & y_{it}=\rho * y_{i1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ | ||
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& d_{it} \sim P(\mu_{i\cdot}(1-\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ | & d_{it} \sim P(\mu_{i\cdot}(1-\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ | ||
&& =\rho \\ \hline | && =\rho \\ \hline | ||
| − | \end{array} | + | \end{array}$$ |
</center> | </center> | ||
| − | |||
Latest revision as of 11:12, 12 March 2015
This code produces some nested array image.
Table 1. A class of stationary correlation models for longitudinal count data and basic properties.
$$\begin{array}{ccc} \text{Model} & \text{Dynamic relationship} & \text{Mean-variance} \\ && \text{\& Correlations} \\ \hline AR(1) & y_{it}=\rho * y_{i,t-1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ & y_{i1}\sim Poi(\mu_{i\cdot}) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ & d_{it} \sim P(\mu_{i\cdot}(1-\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ && =\rho^{\ell} \\ \hline MA(1) & y_{it}=\rho * d_{i,t-1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ & y_{i1}=d_{i1} \sim Poi(\mu_{i\cdot}/(1+\rho)) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ & d_{it} \sim P(\mu_{i\cdot}/(1+\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ && = \left\{ \begin{array}{ll} \frac{\rho}{1+\rho} & \mbox{for } \ell=1\\ 0 & \mbox{otherwise}, \end{array} \right. \\ \hline EQC & y_{it}=\rho * y_{i1}+d_{it}, t=2,\ldots & E[Y_{it}]=\mu_{i\cdot} \\ & y_{i1}\sim Poi(\mu_{i\cdot}) & \mbox{var}[Y_{it}]=\mu_{i\cdot} \\ & d_{it} \sim P(\mu_{i\cdot}(1-\rho )), t=2,\ldots & \mbox{corr}[Y_{it},Y_{i,t+\ell}]=\rho_{\ell} \\ && =\rho \\ \hline \end{array}$$
Ulf Rehmann/sandbox statprob/. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ulf_Rehmann/sandbox_statprob/&oldid=36325