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 $(-\infty, +\infty)$.
0
votes
1answer
82 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
107 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 ...
3
votes
2answers
165 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 ...
5
votes
4answers
306 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:
$$
\log\left(\frac{p}{1-p}\right)=\beta_0+\beta_1X_1+\beta_2X_2+....
$$
However is the logit function, ...
0
votes
0answers
81 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 ...
9
votes
2answers
235 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 ...
9
votes
2answers
696 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 ...
7
votes
2answers
621 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 ...
5
votes
0answers
149 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 ...
37
votes
5answers
13k views
Difference between logit and probit models
Can anybody please tell me 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 ...
6
votes
1answer
634 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
votes
1answer
216 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
339 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 ...
3
votes
1answer
273 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 ...
2
votes
1answer
398 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 ...
3
votes
2answers
432 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 ...
