The Likelihood-Ratio Test
<p>The Likelihood-Ratio Test (LRT) is a statistical test used to compare the goodness of fit of two models based on the ratio of their likelihoods. This article will use the LRT to compare two models which aim to predict a sequence of coin flips in order to develop an intuitive understanding of the what the LRT is and why it works. I will first review the concept of <em>Likelihood </em>and<em> </em>how we can find the value of a parameter, in this case the probability of flipping a heads, that makes observing our data the most likely. I will then show how adding independent parameters expands our parameter space and how under certain circumstance a simpler model may constitute a subspace of a more complex model. Finally, I will discuss how to use Wilk’s Theorem to assess whether a more complex model fits data significantly better than a simpler model.</p>
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