Questions tagged [link-function]

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 ...
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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 ...
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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 $i=0,1,2$) ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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49 views

Finding a confidence interval for difference of proportions

Let two independent random variables, $Y_1$ and $Y_2$ that have binomial distribution have parameters $n_1 = n_2 = 100$, $p_1$ and $p_2$, respectively, be observed to be equal to $y_1 = 50$ and $y_2 = ...
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Help understand the virtue of generalized linear models

On page 4 of https://www.sagepub.com/sites/default/files/upm-binaries/21121_Chapter_15.pdf, the authors state the following strength of generalized models, which I don't quite understand. Indeed, one ...
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197 views

Which link function could be used for a glm where the response is per cent (0 - 100%)?

I am thinking about building a model (glm) where the response variable (y) is the cover (in per cent) of a plant species in a defined area, dependant of environmental variables. However, I don't think ...
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49 views

Conway-Maxwell-Poisson (CMP) - Coefficient interpretation (Log/IRR)

I'm using the Conway-Maxwell-Poisson (CMP) distribution to model the amount of nouns in a clause (data is under-dispersed). I've run the model using glmmTMB (family= "compois") but I'm ...
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Why are we entitled to use the link function we prefer the most?

For a project, we have been trying to fit different models. When we used a Poisson regression, so a glm with a Poisson family, initially our fit was quite bad. But once we used the identity link ...
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Definition of a link function (brms or multilevel model -associated)

I have one question related to a link function defined in BRM. According to the reference (Bürkner, Paul-Christian. "brms: An R package for Bayesian multilevel models using Stan." Journal of ...
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Why do we link the rate parameter of the Gamma distribution for a Gamma GLM?

I've seen several explanations of GLMs that link the linear combination of coefficients to the rate parameter, and assume the shape parameter is constant for all values of $y_i$ (for example, here: ...
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180 views

chi square GLM inference

Suppose at $m$ different positions on a line $a_1,....,a_m$, we sample from a i.i.d normal distribution $N(\mu_i,\sigma_i^2)$, $n_i$ times for each of the $1\le i\le m$ different points. Here of ...
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How do we do GEE with a dataset having a lot of zeroes? (Statistics doubts regarding exploring climate data)

I am working on relationship between climate variables available per zip code and a certain disease incidence over 3 years. I found that Gini index and Generalized estimating equations (GEE) are the ...
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177 views

Fit at zero inflated poisson GAM

I am trying to fit at zero inflated poisson GAM to my count data, and I want a log link. ziP() from the mgcv package does not support the log link. what can I do?
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198 views

Appropriate link function for beta distribution

I am fitting a continuous proportion as my response in a beta distribution model.( I am using rstanarm to implement this model). For context the continuous proportion is the amount of time out of 30 ...
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How does link function work in GLM?

I have several questions regarding the link function of generalized linear regression. I know how link function changes range of the distribution function's mean to the complete real line. But is that ...
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91 views

Modeling both mean and variance in a linear model

I have a variable $X$ that decays log-normally with time, and I have estimated the mean and the SD of that log-linear relationship. I also have a (categorical) variable $Y$ which—I hypothesize—will ...
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Link functions and interpreting credible intervals

I am pretty new to statistics, and was trying to interpret credible intervals from a bayesian analysis I had preformed. Some of my models are glms, and so have a link function. I know that to ...
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453 views

Log transformation in GLM and model fit

For a negative binomial GLM, are we allowed to write the log transformation in the following way? ...
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1k views

glm with log link in binomial family

I was reading this post https://r-posts.com/simulations-comparing-interaction-for-adjusted-risk-ratios-versus-adjusted-odds-ratios/ and found that the author adjusted a glm with binomial family and ...
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1answer
366 views

Gamma GLM: why log-link is more common than canonical link

"The canonical link of Gamma GLM is $g(x)=1/x$ is often not very practical. Log-link is more appropriated in most cases." One reason I can think of is that log-link makes sure $\mu$, the ...
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GLM: effect of link function on choice of transformation of covariate

It struck me that if I have data of the form below, ...
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94 views

Should you standardize when using a Log link?

If I use a model with a log link function should I still standardize independent variables (since they differ in the scales range) or the log transformation is enough?
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350 views

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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Generalized Linear Model and Identity link, what's its benefit?

I found a paper saying that a Generalized linear model with an identity link function was used. They standardize some continuous independent variable as well as the continuous dependent variable and ...
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103 views

Generalised Linear Model help

Kind of new to coding using Rstudio here. I have data for a survey for 600 individuals, over 4 years (150 p/year), for 30 categories being an absence or presence (0/1) resulting in a total score /30 ...
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Is the following a GLM?

We know that the standard linear model is a partial case of the GLM scenario by taking the identity link function, i.e. $$g(μ)=μ=η=x_i^Tβ$$ However, in one of our past papers we are asked to ...
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Why does the canonical parameter give a link function? Why does this relate $E[Y]$ to $x^T \beta$?

If I have a pdf in the form $f(y|\theta,\phi)=\text{exp}\bigg(\frac{y\theta-b(\theta)}{a(\phi)}+c(y,\phi)\bigg)$, then $\theta$ is called the canonical parameter. I'm told we can get a link function $...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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....
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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). ...
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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 ...
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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'...
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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 ...
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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 ...
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Poisson regression with custom offset and link

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 ...
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How to run a quadratic model with plateau with binary outcome?

I'm trying to build a generalised linear model in which the predicted probability of y follows a quadratic curve but hits a plateau at its maximum. I have found some solutions for a linear model ...