Linked Questions
24 questions linked to/from What is the difference between a "link function" and a "canonical link function" for GLM
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Are canonical link functions and link functions the same thing? [duplicate]
Are Canonical link functions and the link functions the same thing?
If not, can anyone tell the difference between them?
I know a link function is a function that links a linear predictor to the ...
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GLM difference between the links [duplicate]
I'd be very grateful if someone could help me understand the idea behind link functions:
I know that the idea is that we want to map the mean to the $\eta$-vector. Also, I know that the canonical ...
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What makes the canonical link function special in GLMs? [duplicate]
Why is the canonical link function used so frequently with GLMs? What makes it "natural"?
Is there any reason to think that, $Q(\theta _i)$ (where $Q$ is the canonical link function, and $\theta _i$ ...
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Difference between logit and probit models
What is the difference between Logit and Probit model?
I'm more interested here in knowing when to use logistic regression, and when to use Probit.
If there is any literature which defines it using ...
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Intuition behind logistic regression
Recently I began studying machine learning, however I failed to grasp the intuition behind logistic regression.
The following are the facts about logistic regression that I understand.
As the basis ...
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Fixed effect Logit with R
I would like to perform a Fixed effect logit estimation in R.
Can someone point out a package that can do the job?
Note: For the time being I'm not really interested in the random effect.
Update;
...
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Problem understanding the logistic regression link function
I am trying to learn the logistic regression model. I came to know that there is no linear relationship between predictor variables and response variables since response variables are binary (...
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Understand Link Function in Generalized Linear Model
I am still trying to learn (may be the terminology issue) what does "link function" mean. For example, in logistic regression, we assume response variable is coming form binomial distribution.
The $\...
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What useful properties does the canonical link function have?
So here I am studying generalized linear models. I know this question is quite naive and simple, but I do not exactly know why the link canonical function is so useful. Could someone provide me an ...
user242554
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Where does the binary logistic regression model equation come from?
In Frank Harrell's Regression Modeling Strategies, he states:
The ordinary linear regression model is:
$$C(Y|X)=E(Y|X)=X\beta$$
and given $X$, $Y$ has a normal distribution with mean $X\beta$ and ...
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Link function in a Gamma-distribution GLM
In a GLM, if the response variable has a Gamma distribution, why is the inverse used as the link function, i.e.: $\mu = -(X\beta)^{-1}$?
In particular, why is the inverse the canonical link? Does it ...
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Two simple questions regarding GLM
I'm currently doing a modelling project. However, I haven't taken a bunch of statistics classes, so I have to teach myself generalized linear models. I'm reading Generalized Linear Models for ...
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Is the link function in Probit model canonical?
If I understand correctly, Probit model is a generalized linear model. I didn't see it listed in the table, so I was wondering if its link function is canonical for some distribution?
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Why do we choose exponential function as the nonlinearity in Possion GLM
In Poisson GLM, the response variable $Y$ follows the Poisson distribution
$$P(Y=y)=\lambda^y\exp(-\lambda)/y!$$
and:
$$\lambda=\exp(\bf \theta^Tx)$$
My question is why do we use exponential as the ...
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Why does the exponential distribution have a canonical link that can yield negative values?
The canonical link for the binomial is the logit. The linear predictor can be anything so it is usable for the probability after the logit transform is used. The case is analogous for the Poisson ...
