Changes between Version 22 and Version 23 of OfficialTolArchiveNetworkGrzLinModel

Timestamp:

Feb 20, 2012, 7:46:39 PM (13 years ago)

Author:

Víctor de Buen Remiro

Comment:

--

OfficialTolArchiveNetworkGrzLinModel

@@ -138 +138 @@
 There is an example of use in [source:/tolp/OfficialTolArchiveNetwork/GrzLinModel/test/test_0004/test.tol test_0004/test.tol]
 
-This a mixture of Bernouilli and Poisson that inflates the probability of zero occurrences in a certain value
+This a mixture of Bernouilli and Poisson that inflates the probability of zero occurrences in a certain value[[BR]]
  
-[[LatexEquation(\pi\in\left[0,1\right] )]] 
+[[LatexEquation(\lambda\in\left[0,1\right] )]] 
 
 that will be called zero inflation and will be an extra parameter used to fit overdispersion.
 
-When [[LatexEquation(\pi=0 )]] we have a Poisson and when [[LatexEquation(\pi=1 )]] it's a Bernouilli.
+When [[LatexEquation(\lambda=0 )]] we have a Poisson and when [[LatexEquation(\lambda=1 )]] it's a Bernouilli.
 
  * the link function is the same than Poisson one[[BR]] [[BR]] 
@@ -151 +151 @@
    [[LatexEquation( \mu = g^{-1}\left(\eta\right)=\exp\left(\eta\right) )]] [[BR]]  [[BR]]
  * the probability mass function [[BR]] [[BR]] 
-   [[LatexEquation( f\left(y;\mu,\pi\right)=\begin{cases}\pi+\left(1-\pi\right)e^{-\mu} & \forall y=0\\\left(1-\pi\right)\frac{1}{y!}e^{-\mu}\mu^{y} & \forall y>0\end{cases} )]] [[BR]] [[BR]] 
+   [[LatexEquation( f\left(y;\mu,\lambda\right)=\begin{cases}\lambda+\left(1-\lambda\right)e^{-\mu} & \forall y=0\\\left(1-\lambda\right)\frac{1}{y!}e^{-\mu}\mu^{y} & \forall y>0\end{cases} )]] [[BR]] [[BR]] 
  * and its logarithm will be [[BR]] [[BR]] 
-   [[LatexEquation( \ln f\left(y;\mu,\pi\right)=\begin{cases}\ln\left(\pi+\left(1-\pi\right)e^{-\mu}\right) & \forall y=0\\\ln\left(1-\pi\right)-\ln\left(\Gamma\left(y+1\right)\right)+y\ln\mu-\mu & \forall y>0\end{cases} )]] [[BR]] [[BR]] 
- * the partial derivatives of log-density function respect to the linear prediction are equals than in a pure Poisson [[BR]] [[BR]]
-   [[LatexEquation( \frac{\partial\ln f}{\partial\eta}=y-e^{\eta} )]] [[BR]] [[BR]]
+   [[LatexEquation( \ln f\left(y;\mu,\lambda\right)=\begin{cases}\ln\left(\lambda+\left(1-\lambda\right)e^{-\mu}\right) & \forall y=0\\\ln\left(1-\lambda\right)-\ln\left(\Gamma\left(y+1\right)\right)+y\ln\mu-\mu & \forall y>0\end{cases} )]] [[BR]] [[BR]] 
+ * the partial derivatives of log-density function respect to the linear prediction are [[BR]] [[BR]]
+   [[LatexEquation( \frac{\partial\ln f}{\partial\eta}=\frac{\partial\ln f}{\partial\mu}\frac{\partial\mu}{\partial\eta}=\begin{cases}\frac{1-\lambda}{\lambda+\left(1-\lambda\right)e^{-\mu}}\mu & \forall y=0\\ \left(\frac{y}{\mu}-1\right)\mu & \forall y>0\end{cases}=\begin{cases} \frac{\left(1-\lambda\right)e^{\eta}}{\lambda+\left(1-\lambda\right)e^{-e^{\eta}}} & \forall y=0\\ y-e^{\eta} & \forall y>0\end{cases} )]] [[BR]] [[BR]]
    [[LatexEquation( \frac{\partial^{2}\ln f}{\partial\eta^{2}}=-e^{\eta} )]] [[BR]] [[BR]]
-