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
The equation linking the height and weight of the children between the ages of 5 and 13 and given as follows   here w is the mean weight in kilograms and h the mean height in

The distribution free or technique which is the analogue of the analysis of variance for the design with two factors. It can be applied to data sets which do not meet the assumptio

An approach to investigations designed to recognize a particular medical condition in the large population, usually by means of a blood test, which might result in the considerable

The scatter plots of SRES1, RESI1 versus totexp demonstrates that there is non-linear relationship that exists as most of the points are below and above zero. The scatter plots sho

can you help specify the model for an event study and to interpret the results/

Kendall's tau statistics : The measures of the correlation between the two sets of rankings. Kendall's tau itself (τ) is the rank correlation coefficient based on number of inversi

Behrens Fisher problem : The difficulty of testing for the equality of the means of the two normal distributions which do not have the equal variance. Various test statistics have

the problem that demonstrates inference from two dependent samples uses hypothetical data from TB vaccinations and the number of new cases before and after vaccinations for cases o

3. a. A researcher in Hong Kong computes the correlation between the percentage of employee turnover and the local unemployment rate (also expressed as a percentage) over a 20-mont

The division of a sample of observations into several classes, together with the number of observations in each of them.  It acts as a useful summary of the main features of the da