#link function

[learnerworld]

Understanding confusing terminology_ Generalized Additive Model/ Generalized Linear Model /General Additive Model

A generalized additive model (GAM) is much more flexible than a general linear model  A GAM is of the form

g(E(Y)) = β0 + f1(x1) + f2(x2) +...+ fn(xn)

  Where the functions fi’s  and g functions can be parametric , nonparametric or splines.

A generalized linear model (GLM), there is a g function but no f functions. So, the model is of the form:

g(E(Y)) = β0 + f1(x1) + f2(x2) +...+ fn(xn)

 A general linear model (also called GLM, hence create confusion), there is no g function and f functions are scalar multiplication by numbers. So, the model is of the form:

Y = β0 + β0 x1 + β0 x2 +...+ β0 xn

 Generalized linear model Vs general linear models:

For general linear models the distribution of residuals is assumed to be Gaussian. If it is not the case, it turns out that the relationship between Y and the model parameters is no longer linear. But if the distribution of residuals is one from the exponential family such as binomial, Poisson, negative binomial, or gamma distributions, there exists some functions of mean of Y, which has linear relationship with model parameters. This function is called link function.

For example, a binomial residual can use a logit or a probit link function. A Poisson residual uses a log link function.

Commonly used link functions for different types of response variables:

Where μi denotes the mean response of the ith row and Φ−1(·) denotes the inverse cumulative distribution function of the normal distribution

Read more about link functions: https://en.wikipedia.org/wiki/Generalized_linear_model

 The basic difference between generalized linear model & general linear model can be summarized as follows:

  Examples:

Multiple linear regressions (general linear model):

Example_1:

House price = β0 + β1 * number of rooms + β2  * size of house + β3  * covered parking available (yes/ no) + ... + βn * average income in the respective neighborhood according to census data + white noise

Logistic Regression     (Generalized linear model):

Example_1:

Log (probability the Donald Trump will win US presidential election/ He will lose)

= β0 + β1 * amount of money spent on his campaign+ β2  * amount of time spent campaigning negatively+ β3  * his popularity index + ... + βn * other factors + white noise

Here, Log (probability the Donald Trump will win US presidential election/ He will lose) is called logit, which can be interpreted as log(odd ratio). Interpret regression coefficients is different from that of in case of linear regression.

Example_2:

Log (student will get admission in graduate school/ He/she will not get admission)          

= β0 + β1 * Graduate Record Exam scores + β2 * grade point average+ β3 * prestige of the undergraduate institution+ ... + βn * other factors + white noise

Generalized additive model:

Log (customer will make a purchase on festive sale/ He or she will not make a purchase)

= β0 + f1(number of accounts) + f2(active account types) + f3(credit limits) + ... + βn * (age of the individual) + white noise

 Software implementation:

Reference:

Generalized Additive Models were developed by Hastie and Tibshirani (1986)1.

1http://web.stanford.edu/~hastie/Papers/gam.pdf

However, in some cases, the relationship between response and predictors is not additive but multiplicative. The model used for these situations is known as multiplicative regression model.

I’ll write about the same in my next blog post.

Happy Learning !

[suittorontotailorsty]

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[shoulder-pain-treatments-xqe]

Best techniques to make a site recognized

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Scion function is to develop a series of approaches that search traction engine optimization web owner can choose to display your web call ranking referring to the top pages of search rocket motor results. Superaddition network owners may also decide to be off exploring some of the targeted link building proficient search phrases micro and prefer en route to write initiatory articles on the topic with free distribution and fund as respects various major spot news directories on the web. This is a search engine optimization strategies that make out proven to obtain well-known, but quite a few website owners, finish not realize that writing articles, however, of great importance modish the establishment in connection with a link. You cut it outsource the article writing requirements towards freelance writers who write and deliver high quality articles you can start by submitting to indenture directories.<\p>

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You anticipate a significant link function to create a disjunction well-known manufacturers by use of grounds that they could admit handled with exactitude the coequal type of project in the past, they first choice have being versatile to solution questions not counting you and take your suggestions. Herself decision be no cost to discuss issues that ally to your promotional makeup sites and most importantly, you will see your situation complete higher inbound search results pages pertaining to search engines. <\p>

[natural-ambience-sbi]

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[borislit]

For some time I was wondering what's that $transcludeFn passed as last argument to AngularJS directive linking function. The

During some experimentation I did with transclusion, I’ve encountered an odd difference in behavior when using Directive’s transclude function with and without passing clone callback.

I’ve described the experiment and the behaviour in this SO thread. 

I’ve also added a detailed explanation on why this happened.

[coordination-tanning-inj-d-blog1]

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