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Update Assessing Model Goodness of Fit to the Data authored by Mortaheb Sepehr's avatar Mortaheb Sepehr
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Assessing-Model-Goodness-of-Fit-to-the-Data.md
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...@@ -22,3 +22,9 @@ There are two approaches to compare different models: *Likelihood Ratio Test* an ...@@ -22,3 +22,9 @@ There are two approaches to compare different models: *Likelihood Ratio Test* an
#### 3.1 Likelihood Ratio Tests #### 3.1 Likelihood Ratio Tests
Likelihood ratio tests are often used to compare two models that one of them is a special case of the other. For example, in the generalized linear models, they can be used to compare models with different linear predictors; or to compare models with different distributions if the distribution of one of them is a special case of the distribution of the other one. The likelihood ratio tests is a conditional test in that given the full model (the more complex model) fits the data, it tests whether the simpler model also fits the data. If <img src="https://latex.codecogs.com/svg.latex?M_0" title="M_0" /> is the simpler model and <img src="https://latex.codecogs.com/svg.latex?M_1" title="M_1" /> represents the full model, the likelihood ratio statistic equals:
<img src="https://latex.codecogs.com/svg.latex?LR&space;=&space;-2[ln(L(M_0))-ln(L(M_1))]" title="LR = -2[ln(L(M_0))-ln(L(M_1))]" />
where <img src="https://latex.codecogs.com/svg.latex?L(M_0)" title="L(M_0)" /> and <img src="https://latex.codecogs.com/svg.latex?L(M_1)" title="L(M_1)" /> are maximum values of the likelihood function for the simple and full models respectively.