Description: Quasi-likelihood is a statistical method used to estimate parameters in models that do not meet the assumptions of full likelihood. Unlike traditional likelihood, which requires the exact distribution of the data to be known, quasi-likelihood allows for working with distributions that are approximate or based on moments of the distribution. This approach is particularly useful in situations where the data are complex or where model specification is uncertain. Quasi-likelihood is based on the idea that, although an exact form of the likelihood function may not be available, estimates based on moments or other characteristics of the data can be used to make inferences about the model parameters. This method is widely used in applied statistics, especially in fields such as econometrics and biology, where models can be difficult to fully specify. Quasi-likelihood provides a flexible and robust way to tackle estimation problems, allowing researchers to obtain meaningful results even under uncertainty about the data distribution.
History: The concept of quasi-likelihood was introduced by statistician David Cox in 1975. Its development arose as a response to the limitations of traditional likelihood, especially in contexts where model specification was uncertain or where data did not follow well-defined distributions. Over the years, quasi-likelihood has evolved and been integrated into various areas of statistics, being fundamental in the development of generalized linear models and in the analysis of complex data.
Uses: Quasi-likelihood is used in various statistical applications, especially in generalized linear models, where parameter estimation is required without knowing the exact distribution of errors. It is also applied in survival analysis and in longitudinal data models, where the data structure can be complex and does not fit the assumptions of traditional models.
Examples: A practical example of quasi-likelihood can be found in the analysis of count data, such as the number of calls to a call center in a day. In this case, a Poisson model, which is based on quasi-likelihood, can be used to estimate the call rate without needing to know the exact distribution of the data. Another example is in public health studies, where disease incidence rates can be modeled using quasi-likelihood to handle data that do not follow normal distributions.
