Changes between Version 1 and Version 2 of OfficialTolArchiveNetworkGrzLinModel

Timestamp:

Jan 26, 2011, 2:09:30 PM (14 years ago)

Author:

Víctor de Buen Remiro

Comment:

--

OfficialTolArchiveNetworkGrzLinModel

@@ -11 +11 @@
 [source:/tolp/OfficialTolArchiveNetwork/GrzLinModel/WgtReg.tol @WgtReg] 
 is the base to inherit weighted generalized linear regressions as poisson, 
-binomial, logit, probit or any other, given just the scalar distribution 
-function [[LatexEquation( F )]] and the corresponding density function 
-[[LatexEquation( f )]]. In a weighted regression each row of input data 
-has a distinct weight in the likelihood function. For example, it can be 
-very usefull to handle with data extrated from an stratified sample.
+binomial, normal or any other, given just the scalar link 
+function [[LatexEquation( g )]] and the density function [[LatexEquation( f )]]. 
+
+For boolean and qualitative response outputs like logit or probit there is an 
+specialization on package [wiki:OfficialTolArchiveNetworkQltvRespModel QltvRespModel]
+
+In a weighted regression each row of input data has a distinct weight in the 
+likelihood function. For example, it can be very usefull to handle with data extrated 
+from an stratified sample.
 
 Let be 
@@ -23 +27 @@
  * [[LatexEquation( \beta\in\mathbb{R}^{n} )]] the regression coefficients 
  * [[LatexEquation( \eta=X\beta\in\mathbb{R}^{n} )]] the linear prediction
- * [[LatexEquation( \eta=X\beta\in\mathbb{R}^{n} )]] the linear prediction
  * [[LatexEquation( g )]] the link function
- * [[LatexEquation( f )]] the density fuciton of a distribution of the 
-[http://en.wikipedia.org/wiki/Exponential_family exponential family]
+ * [[LatexEquation( f)]] the density function of a distribution of the 
+   [http://en.wikipedia.org/wiki/Exponential_family exponential family]
 
 Then we purpose that the average of the output is the inverse of the link function 
@@ -33 +36 @@
   [[LatexEquation( E\left[y\right]=\mu=g^{-1}\left(X\beta\right) )]]
 
+The density function becomes as a real valuated function of at least two parameters 
+
+  [[LatexEquation( f\left(y_{k};\mu_{k}\right) )]]
+
+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)]]:
+
+If there are more unknown parameters about the density we will supose 
+  
+
+=== Weighted Poisson Regresion ===