Generalized additive model, Advanced Statistics

  • The linear component ηi, de?ned just in the traditional way: ηi = x'1
  • A monotone differentiable link function g that describes how E(Yi) = µi is related to the linear component:1590_Generalized additive model.png
  • Yi are independent (i = 1, 2, . . . , n) (but not identically distributed) and each has a distribution from the exponential family. For the purpose of Generalized Linear Models theory, the usual exponential family is parametrized in a bit more speci?c way. Let us focus for simplicity to the case where θ is one-dimensional. It is assumed that the probability density of the response Y can be expressed as

2165_Generalized additive model1.png

for some functions ai(Φ) = Φ/wi, b and ci = c(yi, Φ/wi), where wi is a known weight for each observation. Hereby, θi is called canonical parameter whereas Φ is called the dispersion parameter.

Note: For most models, the weight is the same for each i (that is, wi = 1 for all i) and then the scaling simpli?es to ai(Φ) = Φ), whereas ci(yi, Φ) becomes just c(yi, Φ) and (1) simpli?es to

1714_Generalized additive model2.png

It can be shown from a standard theory for these distributions that

1652_Generalized additive model3.png

Posted Date: 2/27/2013 12:45:32 AM | Location : United States







Related Discussions:- Generalized additive model, Assignment Help, Ask Question on Generalized additive model, Get Answer, Expert's Help, Generalized additive model Discussions

Write discussion on Generalized additive model
Your posts are moderated
Related Questions
sales per day for a product are as follows: x= 10, 11, 12, 13 (p)= 0.2, 0.4, 0.3, 0.1 obtain mean and variance of daily sale. if the profit is described by the following equation p

Option-3 scheme is a scheme of measurement used in the situations investigating possible changes over the time in longitudinal data. The scheme is planned to prevent measurement o

Dr. Stallter has been teaching basic statistics for many years. She knows that 80% of the students will complete the assigned problems. She has also determined that among those who

Write a c++ program to find the sum of 0.123 ? 10 3 and 0.456 ? 10 2 and write the result inthree significant digits.

What is a Generalized Linear Model? A traditional linear model is of the form where Yi is the response variable for the ith observation, xi is a column vector of explanator

Missing values : The observations missing from the set of data for some of the reason. In longitudinal studies, for instance, they might occur because subjects drop out of the stud

Pascal's triangle  is an arrangement of numbers described by Pascal in his Traité du Triangle Arithmétique published in the year 1665 as 'The number in each cell is equal to in the

Response surface methodology (RSM): The collection of the statistical and mathematical methods useful for improving, developing, and optimizing processes with significant applicat

Graphical deception : Statistical graphics which are not as honest as they should be. It is relatively simple. To mislead the unwary with the graphical material. For instance, c

Canonical correlation analysis : A process of analysis for investigating the relationship between the two groups of variables, by ?nding the linear functions of one of the sets of