What is Log Likelihood?
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Define Log likelihood in layman terms
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In statistics, the likelihood function (often simply called the likelihood) measures the goodness of fit of a statistical model to a sample of data for given values of the unknown parameters. It is formed from the joint probability distribution of the sample, but viewed and used as a function of the parameters only, thus treating the random variables as fixed at the observed values.
The likelihood function describes a hypersurface whose peak, if it exists, represents the combination of model parameter values that maximize the probability of drawing the sample obtained. The procedure for obtaining these arguments of the maximum of the likelihood function is known as maximum likelihood estimation, which for computational convenience is usually done using the natural logarithm of the likelihood, known as the log-likelihood function.
A likelihood function is a function that estimates how likely it is that the model at hand represents the real underlying relationship of the variables.
In simple terms, suppose we have two variables X and Y where X is an independent variable and Y is the dependent variable. From the given dataset, we can form a relationship between the two variables by developing a linear regression equation. In the process of forming a linear regression equation, we need to estimate the coefficients. Having calculated the coefficients, we can see how likely it is to obtain a dataset like the one we used to form the regression equation. This likeliness is calculated with the help of the likelihood function.
Every algorithm that works on calculating the regression coefficients for the given model is based on maximizing the likelihood of the function itself. The higher the value of the likelihood function, the better our model is. Once the regression equation has been formed, the likelihood of the estimates can be measured by taking the log of the likelihood values.
This is called Log Likelihood.