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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17 views

Log binomial regression with a case-control sample

It is my understanding that log binomial regression involves a direct comparison of prevalence ratios ("% cases among the exposed" vs. "% cases among the unexposed"), rather than using prevalence odds ...
2
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2answers
58 views

What are the error distribution and link functions of a model family in R?

When building models with the glm function in R, one needs to specify the family. A family specifies an error distribution (or variance) function and a link ...
5
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1answer
74 views

Robustness of GLM to link function

When I first learned about GLMs I was taught that the link function wasn't that important so long as the domain and codomain match up. For instance, in a logistic regression we certainly need $g: ...
0
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0answers
24 views

GLM model specification in distribution and link function for fractional (percentage) response data

I have some aggregated data. Indep. Dep. N 1.3 78% 23 1.2 67% 20 Note that both the independent and dependent variables are aggregated by ...
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0answers
8 views

How to understand is additional variance additive or multiplicative

I have 100 data samples of $10^6$ ordered points. Each point with number $i$ in sample $v$ assumed to be generated from model 1: $x_{iv} = NB(r,p) + \epsilon_v$ or model 2: $x_{iv} = NB(r,p) \cdot ...
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0answers
15 views

Same Estimate and Confidence Intervals with Logistic and Link Functions

I fit a logistic regression and calculated the expected difference in probabilities of my outcome between two treatment levels holding all other variables constant. I obtained confidence intervals ...
3
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2answers
43 views

Sigmoid type functions for logistic regression

I am trying to find sigmoid function alternatives for logistic regression. I am curious that if any cumulative distribution function can be replaced with sigmoid function and what will be the best?
8
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1answer
103 views

Pros and Cons of Log Link Versus Identity Link for Poisson Regression

I am carrying out a Poisson regression with the end goal of comparing (and taking the difference of) the predicted mean counts between two factor levels in my model: $\hat{\mu}_1-\hat{\mu}_2$, while ...
3
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1answer
45 views

Link function in a Gamma-distribution GLM

In a GLM, if the response variable has a Gamma distribution, why is the inverse used as the link function, i.e.: $\mu = -(X\beta)^{-1}$? In particular, why is the inverse the canonical link? Does it ...
2
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1answer
38 views

What type of Generalized Linear Model can handle high-to-low-variance heteroscedasticity?

I am trying to model the relationship between a continuous response variable (sample-corrected species-diversity estimates) and a continuous predictor variable (geographic spread). I have ...
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0answers
33 views

Selecting Link Function for Negative Binomial GLM

I'm trying to model insect abundance data with a variety of vegetation/site related covariates. Because it is count data that is over-dispersed, I've decided to use the negative binomial distribution. ...
0
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0answers
16 views

Is it possible to convert a Gaussian Mixture Model implementation into a Categorical Mixture Model?

I am modelling whether a customer will spend when given a voucher. I have a theory that a customer falls into one of two latent classes: call them spendthrift and miser. So I would like to fit a ...
3
votes
1answer
54 views

Are there any reasons to use the identity link in logistic regression (or any other glm)?

From this answer, the following statement is posed: 'Though not "wrong", you'd want a good reason for using an identity link to model a Bernoulli probability.' I would like to know what good reasons ...
0
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0answers
20 views

Inverse Gaussian with MCMCglmm in R

I am trying to specify a mixed model using the MCMCglmm package/function in R. My data follow an inverse gaussian distribution, so I want to use MCMCglmm as an alternative to using an inverse ...
0
votes
1answer
38 views

modeling probability with the multinomial logit link

I am attempting to model probabilities using the multinomial logit link and I am confused about how the link works. To study the link function I have been attempting to use a deterministic system. ...
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0answers
25 views

Canonical Link Function in Zero-Inflated Poisson Model

For a zero-inflated Poisson model, I understand that the Poisson Model uses the canonical link of log(mu). For the logistic portion of the model, I usually see the equation written as logit(phi), and ...
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1answer
61 views

Interpreting GLM regression analysis result

I'm using the following code in R to predict votes (e.g. non-negative integer count data). ...
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0answers
25 views

Selecting an appropriate link function for zero inflated negative binomial regression

I have count data distributed according to zero-inflated negative binomial RV. I have been able to find good sources for a lot of model diagnostic steps, but there are a few things that are eluding ...
1
vote
1answer
56 views

In a GLM, does the link transform the estimated mean, or is the mean estimated from the transformed RHS?

Is a GLM with a log link function the same as estimating: $$y_i = \exp(\beta_0 + \beta_1 x_i)\ ?$$ A GLM is the following: $$g(\mu_i) = \eta_i = b_0 + b_1 X_i$$ where $g(x)$ is the link function. ...
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1answer
62 views

GLM vs least squares with Gamma errors

To illustrate the usefulness of GLMs in comparison to the least square method I did a simple program in which I add random noise to a straight line (Y=m*x + b; red line in the attached plot). The ...
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0answers
130 views

Square root link function

I'm running a glm that estimates gaussian variable of production in kilogrames using different independent variables. i found a problem of heteroskedasticity so i tried different transfromations of my ...
2
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3answers
134 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
votes
2answers
474 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
11 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
87 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
59 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 ...
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0answers
31 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 ...
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0answers
64 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
233 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
1k 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 ...
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vote
1answer
156 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 ...
3
votes
1answer
1k 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
237 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 ...
2
votes
2answers
204 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
328 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 ...
2
votes
1answer
62 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 ...
14
votes
1answer
2k 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
vote
1answer
280 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
547 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
vote
1answer
129 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
votes
2answers
187 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
votes
0answers
193 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
votes
1answer
434 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 ...
2
votes
1answer
55 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
votes
0answers
22 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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vote
0answers
122 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
vote
1answer
274 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
387 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
vote
0answers
102 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
276 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 ...