## What are Generalized Additive Models used for?

Generalised Additive Models (GAMs) are an adaptation that allows us to model non-linear data while maintaining explainability.

## What is a generalized additive mixed model?

A generalized additive mixed model is a generalized linear mixed model in which the linear predictor depends linearly on unknown smooth functions of some of the covariates (‘smooths’ for short). Estimating the degree of smoothness of the term amounts to estimating the variance parameter for the term.

**What do you mean by additive model?**

The additive model is the arithmetic sum of the predictor variables’ individual effects. For a two factor experiment (X, Y), the additive model can be represented by: Y = B0 + B1 X1 + B2 X2 + ε Similarly, a multiplicative model can be represented by: Y = B0 * B1 X1 * B2 X2 + ε

**Why do we use mixed models?**

Mixed effects models are useful when we have data with more than one source of random variability. For example, an outcome may be measured more than once on the same person (repeated measures taken over time). When we do that we have to account for both within-person and across-person variability.

### What is an additive model in statistics?

In statistics, an additive model (AM) is a nonparametric regression method. The AM uses a one-dimensional smoother to build a restricted class of nonparametric regression models. Because of this, it is less affected by the curse of dimensionality than e.g. a p-dimensional smoother.

### What is an additive model in machine learning?

10.2 Additive Models Additive models are specific application of projection pursuit. They are more useful in scientific applications. In additive models we assume that the response is linear in the predictors effects. and that there is an additive error. This allows us to study the effect of each.

**Are splines GAMs?**

The issue arises because GAMs use splines to learn from the data using basis functions. The splines themselves are built from basis functions that are typically setup in terms of the data used to fit the model.

**Why is it called an additive model?**

#### What is additive model in time series?

Additive model analysis is a newly emerged approach for time-series modeling. Under this setting, the given time-series would be decomposed into four components: trend, seasonality, cyclic patterns, and a random component. The formula is as follows: 𝑦(𝑡)=𝑔(𝑡)+𝑠(𝑡)+ℎ(𝑡)+ϵ(𝑡).

#### When would you use a mixed effects model?

Mixed Effects Models are used when there is one or more predictor variables with multiple values for each unit of observation. This method is suited for the scenario when there are two or more observations for each unit of observation.

**What is a random effect in a mixed model?**

Random effects factors are fields whose values in the data file can be considered a random sample from a larger population of values. They are useful for explaining excess variability in the target.

**What is additive model in Anova?**

The two possible means models for two-way ANOVA are the additive model and the interaction model. The additive model assumes that the effects on the outcome of a particular level change for one explana- tory variable does not depend on the level of the other explanatory variable.

Generalized additive mixed models. Following the extension from linear mixed models to additive mixed models, extension from generalized linear mixed models to generalized additive mixed models is made, Algorithms are developed to compute the MLE’s of the nonlinear effects and the covariance structures based on the penalized marginal likelihood.

## What are generalized addictive models (GAMs)?

An alternative approach is provided by Generalized Addictive Models, which allows us to fit models with non-linear smoothers without specifying a particular shape a priori. I will not go into much details about the theory behind GAMs.

## Are there generalised Poisson models for underdispersed data?

We briefly discuss generalised Poisson models for underdispersed data. In Chapters 6 and 7 two-dimensional smoothers are applied on zero-inflated guillemots and harbour porpoise datasets. A short revision of zero-inflated models is included. Gamma GAMMs are applied on two-way nested tree data in Chapter 8.

**What is the difference between the two R squared models?**

As you can see there is not much difference in the two models in terms of R Squared, so both model are able to explain pretty much the same level of variation in yield.