Assessing-Model-Goodness-of-Fit-to-the-Data.md

@@ -14,4 +14,11 @@ If the model fits the data perfectly, <img src="https://latex.codecogs.com/svg.l
 
 <img src="https://latex.codecogs.com/svg.latex?\chi^2&space;=&space;\sum_i{\frac{(\mu_i-\hat{\mu}_i)^2}{\sqrt{var(\hat{\mu}_i)}}}" title="\chi^2 = \sum_i{\frac{(\mu_i-\hat{\mu}_i)^2}{\sqrt{var(\hat{\mu}_i)}}}" />
 
-### 3. Comparing Models 
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+### 3. Comparing Models 
+
+There is always a trade off between goodness-of-fit of a model and its complexity. Too simple models have very low complexity but is not a good representation of the information in the data. On the other hand, too complex models do not provide enough of a summary of the information in the data and may capture the noise noise in the data as information. 
+
+There are two approaches to compare different models: *Likelihood Ratio Test* and *Information Criteria*. Likelihood ratio test is used to compare two models that one of them is nested inside the other (is a simpler version of the other one). Information criteria, weigh both goodness-of-fit of the model to the data and its complexity. They can be used for both nested and non-nested models. 
+
+#### 3.1 Likelihood Ratio Tests 
+