## What is goodness-of-fit statistics and maximum likelihood estimates?

Super Contributor
Posts: 482

# What is goodness-of-fit statistics and maximum likelihood estimates?

Can someone tell me in simple terms?

Thanks.

SAS Employee
Posts: 340

## Re: What is goodness-of-fit statistics and maximum likelihood estimates?

Goodness of fit is just a number that measures how a model fits the data (the data that was used to fit the model).

There are many types of GoF statistics. RSquare is one of the most famous.

You can use GoF statistics to select the best model (if you have more then one) or to judge the fit of one single model. Sometimes this is difficult, because this number depend on the model, and also on how much noise you have in your data. (Good model + High noise -> GoF still „looks bad”.)

There are many ways to fit a parametric model to the data. For example OLS (ordinary least squares) is a popular (and simple) method. Another one is ML (maximum likelihood). While OLS estimates parameters by minimizing sum of squared distances, ML maximizes the probability of observing the data given the estimated model.

When we do ML estimation, we also get this probability, it is called the likelihood. I is usually a very small number, so we rather look at its logarithm: LL (log likelihood). LL is also a GoF statistic. And also AIC, SBC, AICC that are derived from LL.

Sorry, reading all this again, I don’t think it is “in simple terms”. To understand it, I would search for a simple concrete example.