Changes between Version 6 and Version 7 of OfficialTolArchiveNetworkGrzLinModel

Timestamp:

Mar 30, 2011, 2:18:59 PM (14 years ago)

Author:

Víctor de Buen Remiro

Comment:

--

OfficialTolArchiveNetworkGrzLinModel

@@ -25 +25 @@
  * [[LatexEquation( \eta=X\beta\in\mathbb{R}^{n} )]] the linear prediction
  * [[LatexEquation( g )]] the link function
+ * [[LatexEquation( g^-1 )]] the inverse-link or mean function
  * [[LatexEquation( f)]] the density function of a distribution of the 
    [http://en.wikipedia.org/wiki/Exponential_family exponential family]
@@ -35 +36 @@
 The density function becomes as a real valuated function of at least two parameters 
 
-  [[LatexEquation( f\left(y_{k};\mu_{k}\right) )]]
+  [[LatexEquation( f\left(y;\mu\right) )]]
 
-the output [[LatexEquation( y_k )]] and the average 
+For each row [[LatexEquation( k=1 \dots  n)]] we will know the output [[LatexEquation( y_k )]] 
+and the average 
 
   [[LatexEquation( \mu_{k}=g^{-1}\left(\eta_{k}\right)=g^{-1}\left(x_{k}\beta\right) )]] 
 
-for each row [[LatexEquation( k=1 \dots  n)]]:
+Each particular distribution may have its own additional parameters.
 
-This class also implements 
+This class also implements these common features
  * scalar prior information of type normal or uniform, truncated or not in both cases, and 
  * linear constraining inequations over linear parameters [[BR]][[BR]]
@@ -53 +55 @@
 There is a sample of use in [source:/tolp/OfficialTolArchiveNetwork/GrzLinModel/test/test_0001/test.tol test_0001/test.tol]
 
+In this case we have
+
+ * the identity as link function and mean function [[BR]] [[BR]] 
+   [[LatexEquation( \eta = g\left(\mu\right)= \mu = g^{-1}\left(\eta\right) = \eta)]] [[BR]] [[BR]] 
+ * the density function has the variance as extra parameter[[BR]] [[BR]] 
+   [[LatexEquation( f\left(y;\mu, \sigma^2 \right) ) = \frac{1}{\sqrt{2\pi\sigma^{2}}}e^{^{-\frac{1}{2}\frac{\left(y-\mu\right)^{2}}{\sigma^{2}}}} )]]
+
+
 === Weighted Poisson Regresion ===
 
 It will be implemented in [source:/tolp/OfficialTolArchiveNetwork/GrzLinModel/WgtPoisson.tol GrzLinModel::@WgtPoisson] but is not available yet.
+
+In this case we have
+
+ * the link function [[BR]] [[BR]] 
+   [[LatexEquation( \eta g\left(\mu\right)=\ln\left(\mu\right) )]] [[BR]]  [[BR]]
+ * the mean function [[BR]] [[BR]] 
+   [[LatexEquation( \mu = g^{-1}\left(\eta\right)=\exp\left(\eta\right) )]] [[BR]]  [[BR]]
+ * the probability mass function [[BR]] [[BR]] 
+   [[LatexEquation( f\left(y;\mu \right) ) = \frac{1}{y!}e^{-\mu}\mu^{y} )]]
+
 
 === Weighted Qualitative Regresion ===