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 $(-\infty, +\infty)$.

Filter by
Sorted by
Tagged with
7
votes
1answer
101 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 ...
1
vote
1answer
26 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 ...
0
votes
0answers
29 views

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 ...
0
votes
0answers
5 views

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 ...
0
votes
0answers
11 views

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: ...
0
votes
1answer
132 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 ...
0
votes
0answers
18 views

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 ...
0
votes
2answers
53 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?
0
votes
0answers
14 views

In GLIM, how do I understand “the link maps mu to the entire real line, from −∞ to +∞”?

I always read in generalised linear model that the link function has to have a 1-1 correspondence from the range of mu to (-infinity, infinity). But, when we look at log link, for instance, it is not ...
1
vote
1answer
35 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 ...
0
votes
0answers
17 views

Explaining the link-function in regression

I am writing a medical paper, which provides a methodological strategy for analysing non-transformed, non-normal (zero-inflated, extremely positively skewed) outcome variables. As I am not a ...
1
vote
0answers
34 views

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 ...
0
votes
0answers
8 views

Interpretetion of linear predictor of a random variable that follows a gamma distribution

Assuming that: $0 < \nu, \alpha, y < \infty$ $$f_Y(y; \nu, \alpha) = \frac{y^{\nu-1}{\alpha}^{\nu}e^{-y\alpha}}{\Gamma (\nu)} \mathbb{1}_{Y \in (0, \infty)}$$ $$ = \exp \{ -y\alpha + \nu \log \...
0
votes
0answers
116 views

Expected Fisher Information Matrix for Gamma Distribution using canonical link

How to find the fisher information matrix for a random variable $Y \sim $ Gamma$(\nu,\alpha)$? $0 < \nu, \alpha, y < \infty$ I have written: $$f_Y(y; \nu, \alpha) = \frac{y^{\nu-1}{\alpha}^{\nu}...
3
votes
1answer
79 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 ...
1
vote
2answers
27 views

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 ...
0
votes
0answers
19 views

SAS proc genmod regression equation

I am using proc genmod with tweedie distribution and log link to analyze positively skewed outcome. Trying to figure out the actual regression equation to include ...
3
votes
1answer
71 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? ...
2
votes
1answer
236 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 ...
3
votes
1answer
122 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 ...
1
vote
1answer
39 views

GLM: effect of link function on choice of transformation of covariate

It struck me that if I have data of the form below, ...
0
votes
1answer
43 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?
1
vote
2answers
128 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 ...
0
votes
0answers
48 views

When AIC and pseudo-R2 give opposite conclusions in beta regression models

I conducted an experiment to quantify the effect of two factors on a response variable: the response variable (Y) is a proportion (percentage cover) factor A is represented by the continuous ...
3
votes
2answers
699 views

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 ...
2
votes
1answer
99 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 ...
2
votes
0answers
32 views

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 ...
2
votes
0answers
31 views

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 $...
1
vote
0answers
274 views

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 ...
0
votes
0answers
62 views

Poisson/NegBinom model with identity or logarithmic link

I am wondering about the implications of using (1) a logarithmic, and (2) an identity link within a Poisson model for count data. I have read through related posts here on CV: Pros and Cons of Log ...
0
votes
0answers
26 views

is there a difference in fitted values $\mu_i$ depending on the link function chosen for a poisson GLM

I'm new to stats/R, and have just started learning about generalized linear models and am a little lost. Does choice of link function (in this case identity link vs log link) affect the fitted values $...
0
votes
0answers
43 views

Why should link functions be differentiable?

I'm beginner in stats. I do know that link functions should be continuous, but I do not understand that why should they be differentiable.
1
vote
1answer
84 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 ...
12
votes
2answers
294 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 ...
4
votes
0answers
44 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 ...
1
vote
0answers
159 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 ...
1
vote
1answer
38 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....
3
votes
1answer
59 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). ...
2
votes
1answer
286 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 ...
6
votes
2answers
150 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'...
1
vote
0answers
23 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 ...
6
votes
2answers
768 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 ...
1
vote
0answers
30 views

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 ...
1
vote
0answers
58 views

Interprete GLMM Estimates with log link

i am relatively new to this field and this is my first time using Generalized Linear Mixed-Effects Model. my response variable is Reaction Time (RT) and i have two fixed effects: prime and type. both ...
3
votes
1answer
43 views

Model/link function to deal with dependent variable in range [-1,1]?

My dependent variable, $Y$, contains values anywhere from -1 to 1 (i.e. it is bounded continuously on the range $[-1,1]$). I know that a regular OLS regression on such a variable would sometimes ...
3
votes
1answer
76 views

Do you specify priors according to the link function's transformed space?

Suppose I'm developing a model where the response variable is weight measured in pounds and is Gamma distributed. I would like to specify a prior on my intercept coefficient using other information ...
1
vote
0answers
64 views

Trying to slightly alter logistic GLM - Link function seems unstable [closed]

So the data I have is whether a subject has performed a test correctly, or incorrectly. They have to match choose which of a pair of stimuli matches one they have memorized, and this gets harder and ...
0
votes
0answers
37 views

GLM: Empirical cloglog transformation for exploratory data analysis

Prior to fitting a GLM to an ordered categorical response $Y$ (6 levels), I would like to check the linearity assumption between the one (and only) continuous covariate $x$ in my linear predictor and ...
0
votes
0answers
103 views

What kind of regression to use with heavily skewed data?

I have data with an explanatory variable $X$ (I think I can treat this as continuous, as scores 1-100 on a certain test) and a response variable $Y$ (continuous variable, never lower than 0). Both ...
3
votes
1answer
155 views

Is this GLM for the Poisson distribution correct?

I'm currently taking a machine learning class, and one of the problem set questions is to construct a GLM that models the Poisson distribution, defined as $$P(y;\lambda) = e^{-\lambda}\frac{\lambda^y}...