Generalized-Linear-Models.md

@@ -26,7 +26,9 @@ When constructing a generalized linear model, three major decisions must be made
 
 1. **Specifying the Random Component:** 
     An appropriate probability distribution for the response variable must be chosen. This 
-    should be any member from the *natural exponential family* distributions:
+    should be any member from the *natural exponential family* distributions. For the 
+    psychological and behavioral research the most important distributions are:
+
     - Continuous variables: 
       * Normal 
       * Gamma 
@@ -35,6 +37,25 @@ When constructing a generalized linear model, three major decisions must be made
       * Poisson 
       * Bernoulli 
       * Binomial 
+
+    We should note that this distribution is not the *true* distribution of the population, 
+    but is a, approximation of the distribution of response variable. Each natural 
+    exponential family distribution can be parameterized by *natural parameter* <a 
+    href="https://www.codecogs.com/eqnedit.php?latex=\theta" target="_blank"><img 
+    src="https://latex.codecogs.com/svg.latex?\theta" title="\theta" /></a> and *dispersion 
+    parameter* <a href="https://www.codecogs.com/eqnedit.php?latex=\phi" target="_blank"> 
+    <img src="https://latex.codecogs.com/svg.latex?\phi" title="\phi" /></a>. Parameter <a 
+    href="https://www.codecogs.com/eqnedit.php?latex=\theta" target="_blank"><img 
+    src="https://latex.codecogs.com/svg.latex?\theta" title="\theta" /></a> has information 
+    about the location of the distribution and in its basic form is a function of 
+    distribution mean <a href="https://www.codecogs.com/eqnedit.php?latex=\mu" 
+    target="_blank"><img src="https://latex.codecogs.com/svg.latex?\mu" title="\mu" /></a>. 
+    On the other hand, the variance of the distribution is a function of <a 
+    href="https://www.codecogs.com/eqnedit.php?latex=\mu" target="_blank"><img 
+    src="https://latex.codecogs.com/svg.latex?\mu" title="\mu" /></a> and <a 
+    href="https://www.codecogs.com/eqnedit.php?latex=\phi" target="_blank"><img 
+    src="https://latex.codecogs.com/svg.latex?\phi" title="\phi" /></a>.
+
 2. **Specifying the Systematic Component (Linear Predictor):**
     A linear combination of predictor variables should be constructed as the linear 
     predictor of the model.