A transformation of a parameter governing a response distribution that is used as a crucial part of the generalized linear model to map that parameter's range (which may be from 0 to 1, or only positive values, e.g.) to the real number line $(-\infty, +\infty)$.

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### How can I use the link(g, lam) function from "psyphy" package to adjuste asymptotes?

I need to customize the asymptotes of the model, and I am trying with psyphy package which provides parameters for adjusting asymptotes in its ...
36 views

### Transforming the expected value of $Y_i$ in binomial regression

Currently, I'm learning generalized linear regression (GLM). There is something troubling me concerning binomial regression. In this text, in the part about the structure of a GLM, the random ...
102 views

### Mean finger volume: Is a GLM with log link function appropriate?

I have a model where the volume ($V$) of a finger is normally distributed, with mean $\mu = \beta_0 L^{\beta_1}D^{\beta_2}$ (where $L=$ length, $D=$ diameter and $\beta_i \in \Bbb R$ for $i=0,1,2$) ...
28 views

### Is this the correct way to compute confidence intervals on the original scale for GLM(M)s?

Suppose I have fitted a GLM and want to produce a confidence interval (or a prediction interval) on the original scale of the outcome. What I would do is estimate it on the link scale and then inverse ...
27 views

### Why is the canonical parameter linearly related to the input x in GLMs and why does it give the link function?

In Andrew Ng's CS229 notes, one of the three assumptions he makes for constructing GLM models is: The natural parameter $\eta$ and the inputs x are related linearly: $\eta=\theta^Tx$ He goes on to ...
32 views

### Link functions in poisson regression

I've recently started studying statistics and a question came up to my mind while reading about poisson regression: If we have to exponentiate all terms in order to have only positive values, why do ...
199 views

### Interpretation difference between log link and log transformation

I have a question about the interpretation difference between log link of GLM and log transformation of LM. I know that log transformation is for target variable but log link is for mean .But related ...
78 views

### How to Interpret Parameter Estimates (B) in GLM With Different Link Functions (inverse, 1/mu^2)

I'm experimenting with different PDF (gamma, inverse gaussian, quasi binomial) as well as different link functions (inverse, 1/mu^2, log, logit) in order to find out which generalized linear ...
21 views

### Which type of distribution and link function for quasi-proportion and proportion data in a GLM with high variance in DV?

First of all, I hope my question is not too broad for Cross Validated. If it should be, I'm sorry, and it would be nice if someone could tell me another statistics forum, but this one seemed most ...
27 views

### Which type of distribution and link function for quasi-proportion and proportion data in a multilevel/longitudinal GLM?

First of all, I hope my question is not too broad for Cross Validated. If it should be, I'm sorry, and it would be nice if someone could tell me another statistics forum, but this one seemed most ...
10 views

### Is the following Bayesian GLM reasonable?

Let $Y\geq 0$ count dependent variable following a $Poisson$ distribution with parameter $\lambda$. Also, let $X_{1}\geq 0,...,X_{q}\geq 0$ counts treated as independent variables. I want to fit the ...
30 views

### Is log-link function important in this case?

I have a positive count response $Y$ (number of times that a particular pattern was observed within a single day) and positive count independent variables $X_{1}, X_{2}$ (that are associated with the ...
17 views

### Why the p-value of the interaction term changes when changing the link function of binomial Generalised Linear Model

I have fitted three binomial generalised linear models with three different link functions in order to investigate the relative risk/odds ratio/probability difference of the data. fiverelapse: an ...
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### Geometric distribution: finding canonical link and proving it is part of the natural exponential family?

Looking for some help on my statistics homework question! The background to the question is: suppose that you toss a biased coin repeatedly (and independently) until you get a head. Let Y denote the ...
176 views

### The identity link not used for binary response

Questions: The identity link is the standard one with normal responses but is not often used with binary or count responses. Why do you think this is? My idea: The range for a linear predictor, and ...
395 views

### Logistic regression with actual probabilities $\in(a,b)$ where $0<a<b<1$

When modelling probabilities with a logistic regression$^1$, the range of fitted probabilities is $(0,1)$. The logit function$^2$ asymptotes at $0$ and $1$, so this is a good match. However, in some ...
50 views

### Would this modification accelerate convergence of generalized linear model, or break it?

This page describes the following iteratively reweighted linear least-squares (IRLS) method for solving a generalized linear model (GLM): let $x_1=0$ for $j=1,2,...$ do linear ...
297 views

### Negative Value Gamma GLM Inverse Link

I want to calculate a log-likelihood score for a gamma glm with inverse link function. The score will be used to find optimal parameters ($\beta$) for the model. I'm fixing the shape parameter and ...
42 views

### Log-likelihood using the link identity for poisson?

I understood the Log-likelihood using the link “log” for poisson, λ=exp(α+βx). But I can’t get the Log-likelihood in the case of “identity”, λ=α+βx. How do I get it?. The example is the following data....
163 views

### How do I interpret generalized linear regression with continues independent variable with Gaussian family and log link

I am running generalized linear regression Gaussian family and log link. Independent variable is Time (continues variable). Dependent variables: years of practice (continues variable). ...
450 views

### Valid GLM with square root link

I came across the following answer to a problem, and I couldn't reconcile the answer with what I found. I'm sure I did something wrong, but I'm not sure where my mistake is. The model is of the ...
197 views

### Understanding glm and link functions: how to generate data?

I'm trying to take the approach for understanding how certain concepts work, by trying to generate data for them and checking how the output behaves. Currently, I thus realized I don't quite get what'...
32 views

### How to interpret the beta estimates of a generalized linear model with a square root power link?

I'm running a generalized linear model (GLM) in SAS with a gamma distribution (since my Y response variable is skewed to the right) and a specified square root power link (since I found that ...
822 views

### Why are Poisson regression coefficients biased?

Suppose I run a simple Poisson regression, where $$Y \sim \text{Pois} (5X)$$ If I run a Poisson regression of $Y$ on $X$, I am expecting to get back $5$. Instead I get numbers much higher. Why is ...
I have the following model $$Y \sim \operatorname{Poisson}\left(\frac{1}{1+\exp(\beta X)} E\right)$$ In other words, I have count data for Poisson process with exposure E and rate given by the ...