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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44 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 ...
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2answers
84 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
29 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
75 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
37 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?
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0answers
14 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
37 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 ...
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0answers
53 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') ...
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3answers
183 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 ...
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0answers
77 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 ...
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1answer
186 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 ...
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1answer
116 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
128 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? ...
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5answers
386 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 ...
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3answers
395 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 ...
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1answer
149 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
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2answers
266 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 ...
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2answers
1k 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 ...
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4answers
873 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 ...
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0answers
133 views

GLM multinomial proportional hazard — 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 ...
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2answers
843 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 ...
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2answers
4k 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 + \epsilon $. The example ...
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2answers
4k 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 ...
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0answers
285 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 ...
86
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5answers
54k views

Difference between logit and probit models

What is the difference between the logit and the probit model? I'm more interested here in knowing when to use logistic regression, and when to use probit. If there's any literature which define it ...
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1answer
1k 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 $$ ...
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1answer
296 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 ...
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1answer
418 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 ...
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1answer
354 views

Appropriate link function for 2AFC data?

Contrary to some here, others (e.g. Brian Ripley, the authors of sensR, and the authors of psyphy) appear to think that using a standard binomial link function when analyzing two alternative forced ...
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1answer
519 views

Mixed regression models and custom link functions in R?

It seems like the current revision of lmer does not allow for custom link functions. If one needs to fit a logistic linear mixed effect model with a custom link function what options are available ...
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2answers
568 views

Consequences of an improper link function in N alternative forced choice procedures (e.g. 2AFC)?

Background: In some cognitive psychology research areas N-alternative forced choice tasks are common. The most common of these is a two alternative forced choice (2AFC). This usually takes the form ...