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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41 views

### Different results with different link functions

I have used the R package eventglm to construct pseudo observations, and want to estimate the relative risk and the risk difference for exposure with age adjustment....
76 views

On pg. 125 in Agresti's Categorical Data Analysis, it's suggested by a plot of the dependent variable (a count) vs an independent variable (categorized version of continuous width variable) that the ...
95 views

### Purpose for the conditions of Link Function

I am studying GLM at the moment and have a few questions regarding link functions. Why are the conditions of the link function to be smooth monotonic function? What properties are preserved by having ...
21 views

### Split linear predictors with link function

Is it possible to split linear predictors contribution up when talking glm of non-normal distributions? If: $$µ_i = g^{-1}(η_i)$$ and $$µ_i = g^{-1}(β_0 + β_1X_{i1} + β_2X_{i2} +···+β_kX_{ik})$$ Is it ...
44 views

### GLM with Gamma distribution: Choosing between two link functions

I need to perform a GLM based analysis on a purely positive, continuous, and highliy right skewed (inflated around low values) outcome variable. I tested several combinations of distributions and link ...
89 views

### Back transform predict.gam() from nb link log model run?

I have model with 1 covariate. I would like to run y values from gam in another model. I used nb(log=link) in gam model. Because I used nb and link log in gam, do I need to back transform to use ...
43 views

### Back transforming standard errors in a GLMM with a log-link

I'm using lme4 and have a GLMM with a log link and gaussian variance structure. I would like to report my fixed effect estimates with their standard errors, as well as the standard deviation of my ...
31 views

### Deriving initial weights for IRLS in DESeq2's GLM model

DeSEQ2 is a frequently-used R package for researchers studying differential gene expression via changes in molecular markers such as Poly(A) RNA. Understanding how ...
278 views

### Which link function in binomial regression is better?

Concerning the choice of the link function in binomial regression (e.g. logit versus probit or cauchit), I wonder what the recommended comparison criterion might be. Note that I am not interested in ...
15 views

### 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 ...
1 vote
83 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 ...
110 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 $i=0,1,2$) ...
88 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 ...
43 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 ...
75 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 ...
799 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 ...
1 vote
35 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 ...
74 views

1 vote
1k 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 ...
1 vote
428 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 ...
546 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 ...
57 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
396 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
51 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....
287 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). ...
600 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 ...
278 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
50 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 ...
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 ...