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
1
vote
1answer
26 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
40 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
43 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
43 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}...
-4
votes
1answer
59 views

Attributes, Pros and Cons of GLM link functions [closed]

I would like some help understanding when the sqrt, 1 / mu^2, and inverse link functions would be useful. Thanks! My notes are shown below - . sqrt - mean of predicted value must be positive ...
1
vote
0answers
61 views

What is the difference between Gamma GLM on log output and Gamma GLM with log link function?

Here are two models (with R code to provide some context): Model 1: Take the log of the output variable $y$, then apply a Gamma GLM using the default identity link function: ...
8
votes
2answers
135 views

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 ...
0
votes
0answers
50 views

Which model should I use? (genomic problem)

I have problems with choosing which model / link function should I use for my analysis. My response: numbers from -100% to +500% (increase of tumor after therapy, may switch to ratios or log-ratios, ...
2
votes
0answers
23 views

In gradient boosting, what is the thing being boosted called?

Quoting from this answer that explains how to do boosting when a 'link' function is involved: "Instead, we can re-express this as a function of $L_i$, (in this case also known as the log odds) $$ \...
1
vote
0answers
28 views

Conditions for link functions in glm

While studying the glm, I found the conditions for the link function to be confusing for me. Lecture notes I'm studying with say the link function should be monotone and differentiable. I understand ...
1
vote
1answer
518 views

Gamma glm log link - what does predicted values mean

Does the predict function in R for gamma glm with log link predict the actual values or the mean value? There is a gamma glm model in R with log link. Using predict(model,data,type = 'response') to ...
0
votes
0answers
31 views

The link between logistic regression and logistic sigmoid

My professor once stated that the logistic sigmoid function is the inverse link function to logistic regression. I cannot find mathematical deductions showing this. Can anyone confirm his statement ...
1
vote
0answers
34 views

Canonical Location Parameter

What does "Canonical Location Parameter" mean? I'm looking for a general meaning of this term and then separately within the context of generalized linear models.z UPDATE Given how often this term ...
0
votes
1answer
350 views

Canonical link of Gamma Distribution [duplicate]

I wonder why my professor said that Gamma's canonical link is $\frac{1}{\mu}$. My thoughts are: EDIT: $\theta$ is the canonical parameter. Since $$\mathbb{E}_\theta(Y)=b^{'}(\theta)=-\frac{1}{\theta}...
0
votes
0answers
29 views

Set different link functions in Generalized Mixed Effects Model in R

Suppose I have a dataset of fish, some are salmon some are trout. I have a bivariate regression model specified roughly like below: prob(caught) = 0.5 + 0.5 * logit_inv(diet + fish_type) for salmon ...
1
vote
0answers
72 views

In a gamma regression, how can i interpret coefficients?

My question is pretty simple, i have done a bayesian gamma regression with an inverse link, so: $\eta_i$=$\beta_0+\beta_1x_{i1}+\dots+\beta_px_{ip}$ < using an inverse link, mu is the ...
2
votes
2answers
222 views

Beta regression - interpret coefficients using loglog link

Although a number of similar questions (some of them duplicates) have been asked around the interpretation of the coefficients from a beta regression, these seem to be focused on models that have used ...
3
votes
0answers
114 views

Use of sqrt link with negative binomial glmer

It doesn't seem to be directly possible to use a sqrt link function in lme4::glmer.nb. This is a pity because on my specific data, with the fix effect model, the sqrt link does improve the ...
5
votes
2answers
232 views

GLMM for count data using square root link in lme4

I have data from a field survey. The objective of the study is to relate number of seedling (respond variable, count data), landform (exploratory variable, categorical variable with 3 levels) and ...
3
votes
1answer
77 views

Compare link function: generalized linear mixed binomial

How does one compare the Goodness of Fit for different models of some given binomial data using Generalized Linear Mixed Models. Specifically we want to know whether a model with a logit link gives a ...
0
votes
0answers
69 views

Can I fit a GLMM to near-ceiling binary accuracy data?

tl;dr Can I draw inferences from this binary response data with a ceiling effect, or is it too skewed? How do I check if the model is acceptable? I would like to analyse some binary response ...
3
votes
0answers
35 views

Bagging of models with link functions

I'm trying to predict proportion data, and I've got a small dataset (~4000), so holding out a test and validation set isn't practical. However, bagging is practical because the cost of training isn't ...
2
votes
1answer
94 views

Why does the natural logarithm function pop up as default link function when doing Poisson regression?

What is the philosophy behind the logarithm as link function for Poisson regression? What is it about count variables that modelling them as a GLM with the natural logarithm function is appropriate? ...
1
vote
0answers
103 views

Link functions and fitting models to data with mle2 in bbmle

I'm fitting models to data with the mle2() function in the bbmle package. In an example problem (reproducible code below) I am fitting a count response variable ...
0
votes
1answer
42 views

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 ...
0
votes
1answer
248 views

For glmer, is it appropriate to use the negative binomial distribution for non-binary response variable, and if so, which link should be used?

I have a dataset where the response variable fits a negative binomial distribution much better than the normal distribution (see image below). The variable is discrete but not binary. I am hoping to ...
1
vote
0answers
146 views

Selecting error distribution and link function for GLMMs on count data

I would like to find out how to select an appropriate error distribution and link function to model count data to determine a treatment effect using a generalized linear mixed effects model. I have ...
6
votes
1answer
451 views

Is there a mathematical definition of non-collapsibility?

When teaching GLMs, it's commonly taught that the linear and log link are collapsible but that the logit is not. The log link is collapsible because the curves are proportional and the means are ...
2
votes
0answers
308 views

Alternatives to ordinal regression when proportional odds assumption not met

I'm trying to fit an ordinal logistic regression using the ordinal package but the proportional odds assumption is not met. I have read all post here on this. My specific question is that, if you ...
5
votes
1answer
167 views

Strange variance weights for Poisson GLM for square root link

Is there a reason why all the variance weights from a Poisson GLM are equal when a square root link is used? That is (on R): ...
3
votes
0answers
2k views

Family in GLM - how to choose the right one?

When modeling data sampled in the field, I often come across the problem of determining the Family of the dependent variable for GLM (or GLMM). An example: in an ecological study, I have ~ 60 patches. ...
1
vote
0answers
278 views

What is the canonical link function for a multinomial logit?

For the multinomial logit model, what is the canonical link function and how does it relate to the definition of the canonical link as defined in this answer? I note from this link on glms, Agresti ...
0
votes
1answer
378 views

Variance Of Uniform Distribution After Log Transformation

Suppose I have a random variable $X \sim Unif(0.61, 0.79)$ and now I'm interested in the mean and variance of $Y \sim \log X$. I can easily calculate the mean using the equation, $$ E(g(X)) = \int ...
1
vote
0answers
33 views

Quasi-likelihood and complementary log-log link

I need help to understand how R computes the adjusted value when I use the quasi-likelihood distribution and complementary log-log link with variance function mu(1-mu). My data are rates from ...
0
votes
1answer
58 views

Link Function Help Needed!

Help needed with link functions! I'm attempting to do some linear models examining how fork lenghts of fish are dependent upon sex (0 or 1), hatchery mark (0 or 1) and age (continuous). When I try a ...
2
votes
1answer
124 views

Why do I get such a large divergence between Gaussian and Gamma family GLMs?

From what I understand the Gamma distribution is a good choice for positive right skew data. My data is a magnitude quantity with heavy outliers as you can see here from a histogram of the pooled set: ...
1
vote
1answer
77 views

Accounting for denominator in Poisson rate regression model with identity link and categorical predictors

This is a followup to this question: Offset in Poisson regression when using an identity link function? I am using a Poisson regression model with identity link to model risk based on a couple of ...
1
vote
0answers
494 views

Interpretation of cloglog model in layman's terms

I fitted a beta regression model via MCMC with a complementary log-log link function. Is there a way to interpret it in a layman's terms? The estimates of the model are: \begin{align} \beta_0 &=...
2
votes
0answers
70 views

Ratios, differences, and link functions?

I recently learned that with Poisson regression, you can model rate difference by using an identity link function, or rate ratio by using a log link function. Does that work the same way with other ...
5
votes
1answer
544 views

Offset in Poisson regression when using an identity link function?

It appears that in Poisson regression, using an identity link function means your betas will be rate differences, and using a log link function your (exponentiated) betas will be rate ratios. You can ...
1
vote
1answer
128 views

Why is the link function a function of the mean and not the linear predictor?

Generalized linear models are formulated so that the link function $g$ of the mean $\mu$ of a random variable $Y$ is equal to the linear predictor $\eta=x'\beta$, i.e. \begin{align} g(\mu)=\eta. \end{...
1
vote
0answers
120 views

Am I doing too many likelihood ratio tests to simplify the model?

I am building a GLM model on a large data set. The main variables thought to be relevant are X_1,...,X_7. I think the interactions X_1*X_3 and X_2 *X_4 might be significant, so I'll include them ...
4
votes
0answers
264 views

How do sufficiency statistics help in the interpretation of regression results?

One of the results why canonical link functions are widely used in GLMs is the existence of sufficiency statistics for the regression parameters, which in turn allow for: ... minimal sufficient ...
2
votes
2answers
90 views

How are fitted Poisson means constrained to be positive when the identity link is used in Poisson regression?

I apologise for the imprecise notation that follows, but hopefully I have conveyed the idea sufficiently. In Poisson regression of $Y \sim \mathbf{x}$ , the canonical link function $\ln$ constrains ...
3
votes
0answers
634 views

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 ...
1
vote
0answers
211 views

glm link functions for multinomial and ordered probit regression?

Here's what I understand, could someone please tell me if I'm wrong, and how? For a categorical variable $Y$, the expected value $\text{E}(Y)=\mu=\sum_{y}i\cdot\text{P}(Y=i)$. Using the descriptions ...
6
votes
1answer
225 views

Relationship between binomial regression link function and goodness-of-fit tests [now with link to R code]

Some background: A number of papers in the literature (various ones by Hosmer and Lemeshow; Copas; le Cessie and van Houwelingen; Cressie and Read; Osius and Rojek; J. R. Dale) discuss a family of ...
2
votes
0answers
277 views

Log link vs logging response variable in GAM model

hope someone might be able to help: My aim is to build a value predictor of an individual’s pension pot using customer data (based in the UK). It is to be used for reporting purposes and ...
12
votes
1answer
3k views

Can you give a simple intuitive explanation of IRLS method to find the MLE of a GLM?

Background: I'm trying to follow Princeton's review of MLE estimation for GLM. I understand the basics of MLE estimation: likelihood, ...
1
vote
0answers
142 views

Interpetation of estimates in Gamma-Regression with reciprocal link

I´m new to CrossValidated and this is my first question here. In the case of a generalized linear regression model where I assume that my data follow a gamma distribution, I would like to know how to ...