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

-### 1. Introduction
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+### 1. Introduction
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+In statistical inferences about a population of the study, it is considered that the data and the model are given. As a result, valid inference depends on using a model that is a good representation of the data. 
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+We should keep in mind that assessing the goodness-of-fit of a model to a dataset should never be based on a single statistic or statistical test. Actually, evaluating a model is a process of gathering evidence for and against a model or a subset of plausible models. Here we discuss three aspects: global measures for goodness-of-fit to the data, comparing competing models, and assessing local lack of fit. 
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+### 2. Global Measures of Fit
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+This is a measure to compare observed values of the response variable with fitted or predicted values. There are two common measures to evaluate global measure of fit: deviance (*Dev*) and the generalized Pearson <img src="https://latex.codecogs.com/svg.latex?\chi^2" title="\chi^2" /> statistic. Deviance compares the maximum value of the likelihood function of a model (<img src="https://latex.codecogs.com/svg.latex?M_1" title="M_1" />) and the maximum possible value of the likelihood function computing using the data (<img src="https://latex.codecogs.com/svg.latex?M_y" title="M_y" />): 
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+<img src="https://latex.codecogs.com/svg.latex?Dev&space;=&space;-2(ln(L(M_1))-ln(L(M_y)))" title="Dev = -2(ln(L(M_1))-ln(L(M_y)))" />
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