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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27 views

What assumptions are made about the link function in GLM's?

There are posts in similar vein about this topic, but what I want to know exactly is whether there is a list of properties/assumptions about link functions in generalized linear models, or if the link ...
2
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3answers
73 views

How does the logit link handle binomial (1/0) data?

I have a data set that contains a continuous explanatory variable and a set of responses as binary success and failures. For example, ...
4
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2answers
83 views

Log vs square root link for Poisson data in R

I am currently working to model deaths from AIDS over time using a GLM in R. I know that there are two possible options for the link function for Poisson data, log and square root. I know that square ...
0
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0answers
5 views

link fx and distribution in GEE model

I am working on my dissertation using a GEE approach. The reason is that my outcome is nonnormal, nonlinear, heteroscedastic, and clustered. Additionally, it is also truncated (a cutoff score) and ...
6
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1answer
61 views

Closed form function relating $\mu$ to the natural parameter for the logarithmic series distribution?

While answering another question here, I mentioned the logarithmic series distribution as a possible model for species per genus. In the course of looking at the pmf while answering that I realized ...
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1answer
45 views

Can we write the likelihood of a GLM in generality?

So I know we can explicitly write down the likelihood of any specified GLM model, for example the likelihood for the logistic regression model would be ...
0
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0answers
64 views

interpretation of coefficients from glm model, normal family with log link vs. linear model with logged outcome

I was fitting a linear model where the outcome was log transformed. The outcome is overdispersed and skewed and logging dramatically improved model fit. For reasons that relate to the software ...
1
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0answers
21 views

Slope testing for regression lines between non-normal explanatory and response variables

I would like to estimate a regression line between my explanatory and response variables. The explanatory and the response variables are (paired) instrumental measures of the same thing under ...
1
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0answers
58 views

What is the difference between lm(log(y) ~ x) and glm(y ~ x, family = gaussian(link = “log”))? [duplicate]

Is all in the title. I would like to know if there is any difference in terms of coefficients, residuals, p-values, but also conceptually.
2
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0answers
51 views

Why are the fixed effects of a panel probit regression inconsistent?

I was taught that a probit with fixed effects would not be consistent because the estimates of a non-linear model with a link function other than the canonical (in this case the logit) are not ...
11
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2answers
454 views

GLM: verifying a choice of distribution and link function

I have a generalized linear model that adopts a Gaussian distribution and log link function. After fitting the model, I check the residuals: QQ plot, residuals vs predicted values, histogram of ...
0
votes
0answers
13 views

Relationship among parameters from models with different link function and scaled response variable

Given the model, $\log(A_i) = \alpha + \beta \, covar_i$, with $i=1,\dots,1000$, $\alpha=4$, $\beta=0.2$, and covariate $covar \sim U(-1,1)$, I derived $\log(A)$ values (in $\texttt{R}$) as: ...
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1answer
84 views

Adding a square root link function to an overdispersed negative binomial GLM

I'm analyzing nematode count data (80 data points) from a randomized block design in which I have two factors with both four levels (Plant and Inoc). The data show heavy overdispersion when analyzed ...
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1answer
172 views

R binomial family with identity link

I want to fit a linear model by R with family=binomial(link="identity"), however, binomial family do not have identity link. What should I do?
3
votes
1answer
115 views

Exponential distribution: How to avoid negative predictor of $\lambda$?

I have a joint distribution $P(X, Y_{1}, Y_{2}, ....)$ which contains one univariate exponential distribution ($X$) and several univariate gaussian distributions ($Y_{1}, ...$). For details regarding ...
0
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0answers
20 views

algorithms for color image edge enhancement using potential function

I want to use the method based on the use of weighting function also known as Parzen Kernels and form estimation of the probality density function (pdf) based on ...
2
votes
2answers
104 views

Is it possible to model the conditional expectation of a binary outcome using an additively-separable link function?

Logit and probit link functions aren't additively separable. So, fitting a model using these link functions implies that the effect of one predictor in determining the outcome is not independent of ...
4
votes
1answer
157 views

simulate GLM with square root link in R

I'm trying to simulate a fitted GLM using basic functions, not using the simulate() and predict() functions that are widely questioned and answered. I get different results when I compare my math ...
1
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1answer
41 views

quantile regression with e.g. gamma distribution and log link

I have a basic question about quantile regression (I'm new to it): Why doesn't it seem possible to do a quantile regression with a specified family (e.g. gamma) and link function (e.g. log), as in a ...
10
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1answer
712 views

Nonlinear vs. generalized linear model: How do you refer to logistic, Poisson, etc. regression?

I have a question about semantics that I would like fellow statisticians' opinions on. We know models such as logistic, Poisson, etc. fall under the umbrella of generalized linear models. The model ...
1
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1answer
136 views

GLM link function for bimodal probit fitting?

I am trying to model a set of data I have physical reason to believe can be represented by a bimodal normal cumulative distribution function (Technically it is a bimodal log-normal CDF, but I think I ...
0
votes
0answers
221 views

selecting a link function for GLM's

If you don't care about using GLM model parameters to predict anything, but simply want to select the best-fitting model for your data, is it necessary to get into the theoretical debate as to which ...
1
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1answer
106 views

How to customize a link function to perform a logistic regression?

My data was collected using Randomized Response Technique. So I have additional variability into the data. I have a binary response variable. Should I customize a logit link function to incorporate ...
2
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2answers
145 views

Sine link with binary regression

I have used the SIN link to estimate probabilities, mostly with Program MARK. However, I am not sure how the SIN link works. I know the SIN link enables parameter ...
2
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0answers
122 views

What GLM family and link function for “proportion of time”?

A simple question to which I don't seem to find the answer anywhere. I have a response variable duration of time spent doing A of individuals tested for ...
2
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1answer
264 views

Generalized linear model: link function Power(-1)

During study our of statistics in my psychology coursework, we had to teach ourselves how to use generalized linear models in SPSS (only basic knowledge). For an exam we may also use generalized ...
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1answer
47 views

Regression and link function

Suppose we have $E (\log (Y)) = a+bx $ vs $\log (E (Y)) = a+bx $. Can $\exp (b) $ in both cases be interpreted as a geometric mean?
0
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0answers
19 views

What makes the canonical link function special in GLMs? [duplicate]

Why is the canonical link function used so frequently with GLMs? What makes it "natural"? Is there any reason to think that, $Q(\theta _i)$ (where $Q$ is the canonical link function, and $\theta _i$ ...
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0answers
82 views

Estimating a single proportion from a marginal or conditional model

I had a single sample of a binary outcomes (success / failure), and I wanted to estimate the population proportion with a point estimate and a confidence interval. The problem was that some subjects ...
1
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1answer
190 views

Link function for log-logistic shared gamma frailty model

I've been asked to replicate a study that models an accelerated failure time survival model with a log-logistic distribution and gamma distributed frailty (a 'log-logistic shared gamma frailty model') ...
3
votes
3answers
287 views

Problem understanding the logistic regression link function

I am trying to learn the logistic regression model. I came to know that there is no linear relationship between predictor variables and response variables since response variables are binary ...
1
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0answers
94 views

Meaning of link functions (GLM) [duplicate]

I am performing ordinal regression on several datasets, I have 5 ordered response categories and only one explanatory variable X. For each dataset I run the analysis 3 times, each time using a ...
4
votes
1answer
238 views

Fitting a Generalized Linear Model (GLM) in R

I am learning about Generalized Linear Models and the use of the R statistical package, but, unfortunately, I am unable to understand some fundamental concepts. I am trying to develop a GLM - Poisson ...
0
votes
1answer
199 views

When to take logarithms of a variable such as the Herfindahl Index?

Currently I am skimming through a couple of papers in well established journals! I became curious when I found papers with linear regression models using the Herfindahl index as the dependent ...
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0answers
179 views

Alternatives to the multinomial logit model

I am trying to estimate a model of occupational choice with three choices. Are there any alternatives to using the multinomial logistic regression when handling such unordered categorical outcomes? ...
8
votes
5answers
606 views

Do statisticians assume one can't over-water a plant, or am I just using the wrong search terms for curvilinear regression?

Almost everything I read about linear regression and GLM boils down to this: $y = f(x,\beta)$ where $f(x,\beta)$ is a non-increasing or non-decreasing function of $x$ and $\beta$ is the parameter you ...
2
votes
3answers
809 views

GAM log link does not work without starting values

I am trying to estimate a GAM regression model using the implementation of gam from the mgcv package. I have a working Gaussian ...
0
votes
1answer
215 views

Equation for a logit link function for a series of events

I have modeled some data using generalized linear modeling with a binomial distribution and logit link function. However, my data is not dichotomous, it is actually a series of events. I have fixed ...
3
votes
2answers
316 views

Asymmetric S-shaped function mapping interval $[0, 1]$ to interval $[0, 1]$

In the literature, is there any asymmetric $S$-shaped function that maps the interval $[0, 1]$ to interval $[0, 1]$? Unfortunately I can't post figure so I just describe what I mean in text. The ...
8
votes
2answers
6k views

Purpose of the link function in generalized linear model

What is the purpose of the link function as a component of the generalized linear model? Why do we need it? Wikipedia states: It can be convenient to match the domain of the link function to the ...
11
votes
4answers
2k views

Is the logit function always the best for regression modeling of binary data?

I've been thinking about this problem. The usual logistic function for modeling binary data is: $$ \log\left(\frac{p}{1-p}\right)=\beta_0+\beta_1X_1+\beta_2X_2+\ldots $$ However is the logit ...
0
votes
0answers
159 views

GLM multinomial proportional odd — what's the canonical link function?

i am kind of sure my professor is going to ask me this question on the next exam, but there is nothing about this on his notes. All i know is that this link function is different from the Multinomial ...
11
votes
2answers
1k views

Problem with comparing GLM models having a different link function

Given the same set of covariates and distribution family, how can I compare models having different link functions? I think the correct answer here is "AIC/BIC", but I am not 100% sure. Is it ...
29
votes
3answers
11k views

Choosing between LM and GLM for a log-transformed response variable

I'm trying to understand the philosophy behind using a Generalized Linear Model (GLM) vs a Linear Model (LM). I've created an example data set below where: $$\log(y) = x + \varepsilon $$ The ...
21
votes
2answers
8k views

Difference between 'link function' and 'canonical link function' for GLM

What's the difference between terms 'link function' and 'canonical link function'? Also, are there any (theoretical) advantages of using one over the other? e.g. A binary response variable can be ...
6
votes
0answers
418 views

Selecting link function in GEE with binary dependent variable

In my experiment participants had to make a binary (yes-no) decision about various stimuli. I have two categorical (stimulus characteristics coded as -1 0 and 1 and treatment group coded as 0 1) and ...
133
votes
7answers
114k views

Difference between logit and probit models

What is the difference between Logit and Probit model? I'm more interested here in knowing when to use logistic regression, and when to use Probit. If there is any literature which defines it using ...
8
votes
1answer
2k views

Calculation of canonical link function in GLM

I thought that the canonical link function $g(\cdot)$ comes from the natural parameter of exponential family. Say, consider the family $$ ...
5
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1answer
339 views

Distribution family for a ratio dependent variable in a generalized estimating equation

I have several dependent variables that are measures of racial disproportionality; I've calculated them as: % of events caused by racial minority group / % of events caused by racial majority group ...
4
votes
1answer
480 views

Undefined link function in gamma distribution

The nonlinear model I am fitting gamma distribution with inverse or log is not converging. There is one observation having zero value in the response variable. Does this zero affects to model the ...