Overview of Generalized Additive Models (GAM)
Generalized Additive Models (GAM) are a statistical method used to model the relationships between variables in a dataset. GAM allows us to explore nonlinear relationships between variables, which cannot be achieved using linear models. The method aims to identify the effect of each predictor variable and the outcome variable simultaneously by accounting for both linear and nonlinear relationships.
GAM is a powerful statistical tool that has been widely used in fields such as ecology, biostatistics, and economics. The method is used to fit models to data using mathematical functions, which describe the relationships between variables. The data are fitted with a smooth curve, which can provide a better fit than simpler linear models. Compared to other methods, GAM is relatively easy to use, but it still requires some statistical knowledge to interpret results properly.
How does GAM work?
The basic idea behind GAM is to model a response variable as a collection of functions of one or more predictor variables. A function is a mathematical formula that maps the predictor variables to the expected value of the response variable. Most commonly, the functions are defined as smooth curves, which can capture nonlinear relationships between the variables.
Let's take an example of predicting the price of a house based on the number of bedrooms, the age of the house and the location. We want to model the relationship between these variables and price (the response variable). We can use GAM by creating a model that uses smooth curves to capture the relationships between the variables.
The GAM model can be described as:
Price ~ bedding + s(age) + s(location)
Here, bedding is the number of bedrooms, and age and location are smooth functions of age of the house and location, respectively.
In this model, the relationships between price and the number of bedrooms, age of the house, and location are included in the model as smooth curves. The smooth curves are defined by a small number of adjustable parameters. This helps to reduce the number of unnecessary interactions in the model, resulting in a simpler and more interpretable model.
Advantages of using GAM
GAM is a flexible method, allowing for the inclusion of nonlinear relationships among variables. The method allows for easy identification and interpretation of nonlinear relationships, unlike linear models, which only allow for the inclusion of linear relationships. The use of smooth curves provides enhanced flexibility in representing complicated relationships between multiple variables. This ability of GAM makes it possible to model complicated biological and ecological relationships that would otherwise be too difficult to describe using linear models.
Another advantage of GAM is that it can handle both continuous and categorical variables. In addition, by using a spline function to fit the smooth curves, it can avoid the problem of overfitting that occurs when models are overly complex, which can lead to ineffective models.
Disadvantages of using GAM
Although there are many advantages to using GAM, there are also some disadvantages. One of the main challenges with GAM is that it requires a large sample size. This is because the method is not as good at managing data with fewer observations, which can lead to overfitting problems. Similarly, if there is a high degree of multicollinearity between predictor variables, GAM can struggle to separate out their effects.
Another issue is the selection of which predictor variables to include in the model. Unlike linear regression models, which can be selected by using methods such as AIC, the selection of variables for GAM can be confusing due to the possible interactions between the variables. As a result, researchers have had to develop their own methods for selecting which variables to include.
Applications of GAM
GAM is used in various areas such as ecology, economics, and biostatistics. Applications of GAM include studies of species distribution, resource allocation and management, environmental monitoring, climate change studies, finance and economics, and biomedical research.
For example, in ecological studies, GAM can be used to identify nonlinear relationships between species and habitats. In economics, it can be used to predict the probability of default in financial institutions. Biostatistics researchers use GAM to investigate the interaction between genes and the environment, and to explore the effects of social inequality on health outcomes.
GAM is a powerful statistical method that allows us to explore nonlinear relationships between variables. It is a flexible tool that can handle both continuous and categorical variables, and that can model a wide range of nonlinear relationships. Although the method has some disadvantages, its many advantages and its wide range of applications make it an important tool for researchers in various fields.
