# Questions tagged [generalized-linear-model]

A generalization of linear regression allowing for nonlinear relationships via a "link function" and for the variance of the response to depend on the predicted value. (Not to be confused with "general linear model" which extends the ordinary linear model to general covariance structure and multivariate response.)

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94 views

### What is the “direct likelihood” point of view in statistics?

I am reading a Springer title from 1997 called Applied Generalized Linear Models by James K. Lindsey. In the preface, Lindsey writes For this text, the reader is assumed to have knowledge of basic ...
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### Correlation between two binary variables within one categorical variable

The Problem: I have measured two binary variables within 1 categorical variable with 5 levels. Initially, I thought I'd be able to use Fisher's Exact test or some N x M x K version of it. However I ...
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### Comparing models using the deviance and log-likelihood ratio tests

This is an update to a previous question that I have posted. I am looking for clarification on comparing glm models using deviance and log-likelihood ratio tests (I have updated my question to make it ...
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### Comparing two multinomial distributions

Background: Imagine a pizza cut into 8 slices. [ On each straight edge of the slice, I insert a magnet with opposite polarities facing outwards. If I separate these components, prevent flipping and ...
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### How do sufficiency statistics help in the interpretation of regression results?

One of the results why canonical link functions are widely used in GLMs is the existence of sufficiency statistics for the regression parameters, which in turn allow for: ... minimal sufficient ...
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### Robust Gamma Regression

I am modeling some spectroscopic data where the response of the instrument to the size of the input is strictly positive and non-linear. Gamma regression seems like a good choice to explain the data, ...
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### “weight” input in glm.nb function in R. How exactly does the weight affect the likelihood?

I would like to understand how the weight argument of glm.nb is affecting the likelihood function. I understand that glm.nb find the MLE in an alternating iteration process where for a given theta the ...
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### Alternatives to Cohen's d for non-Gaussian models

Cohen's d (or Hedges' g) are often used to compute effect size. They rely on the assumption of homogeneity of variance across samples however. Because of the pooling of variance that they do, I'm also ...
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### Analysis of survival data using binomial GLM with offset

We are interested in determining whether there's an association between frequency of screening visits and cancer outcomes and whether that differs by race. We have Medicare data to analyze this. ...
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### Should I use a linear mixed model or a generalized mixed model?

I have a test dataset with repeated measures, different individuals sampled at different time points, here measured in days. I want to know if I should use a GLMM or a LMM to see how well, if at all, ...
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### Time series models (e.g. ARMA) a type or extension of GLM? Particular/stipulated forms of dependence in time series models

I am trying to understand the relationship between ARMA Time Series models and the GLM (Generalized Linear Model) family of models. As far I know, all GLMs have the following 3 components: 1) random ...
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### Which approach can be used to regress sleep time on brain mass, in this data set?

I was reading this blog post: https://htmlpreview.github.io/?https://raw.githubusercontent.com/avehtari/BDA_R_demos/master/demos_rstan/sleep.html the author describes a model to predict how many ...
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### Why is the $\chi^{2}$ approximation for deviance GLM $\sim \operatorname{Binomial}(n_{i},\pi_{i})$ not valid when $n_{i} = 1$?

I know from McCullagh & Nelder's text (p.118) that the $\chi^{2}$ approximation for deviance for the binomial family is based on a limiting operation in which $n$, the number of observations, is ...
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### Bradley-Terry model for unequal team comparisons

I'm trying to predict the outcome of a sports match between two teams. I have data on wins and losses for all teams in the league. I intend to use a Bradley-Terry model to find the relative rankings ...
178 views

### Adding a magnitude penalty to a GAM

This is a follow-up to a previous question of mine, explaining the problem in more detail in the hopes of getting more precise advice. Consider the following structured additive regression model or ...
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### Is this degrees of freedom calculation from McCullagh and Nelder wrong?

This is a question regarding the Generalized Linear Models book of Mccullough and Nelder. It's available here. Starting on page 204 there is an example regarding shipping incidents; one of the ...
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### Dispersion parameters in GLM

I'm trying to find the motivation behind the extended form of the exponential family of distributions in the fundamental paper on GLM by Nelder and Wedderburn (Generalized Linear Models, J. R. Statist....
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### creating contrast matrix (limma) for two factorial in R

I am attempting to construct a contrast matrix that I can run in R, using the limma bioconductor package, but I am not sure that I have coded the contrast matrix correctly. A previous post and the ...
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### Examples of spatial generalized linear models

I've been reading some materials on Spatial data analysis, and I've a good background in GLMs. Right now I'm looking to find an example in spatial generalized linear models, but so far I've not found ...
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### Nonnegative identity-link Poisson regression with ridge or fused ridge penalty

I would like to fit nonnegative identity-link Poisson regression models with a ridge or fused ridge penalty, i.e. with nonnegativity constraints on the fitted coefficients, Poisson error noise & a ...
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### How to estimate confidence intervals for LC50

This is my first question, so I hope the question is properly done (my apologies if it's not...) I am using a binomial GLM model (logit) for some toxicology data investigating the effects of a ...
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### using lmer to fit the linear mixed effects models

Edit: I know some people vote this question is off-topic since it is more like a Cross Validated question. However, I am not here to ask about the coding thing (but I might word in the wrong way). I ...
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### binomial glm where number of trials is also a predictor

I am modeling the probability of success $p_i$ under a binomial framework. In fact I am actually modeling $x_i \sim Bin\left( n_i, p_i\right)$ being the number of trial varying along each observation. ...
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### Is the use of loglik or AIC to compare logit/probit/cloglog models valid?

I would like to know whether I can use AIC, or if the models have the same number of predictors, the log-likelihood, to compare logit vs probit vs cloglog models (fitted for instance with glmer or ...
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### How are distributions and regression models related?

This is likely a very simple question for many of you but is something that has been poorly covered in the statistics courses I've taken to date. We have talked extensively about distributions (normal,...
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### IRLS for truncated normal GLM

I have data for which responses fall in $y \in [0,\infty)$ for which, it seems, the standard GLMs based on, say, gamma or inverse-Gaussian fail since they don't allow responses with values equal to 0. ...
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### Different goodness-of-fit statistics for same model fit as GLM and linear mixed model - why?

When I fit a simple linear model such as y ~ 1 + x1 + x2 in MATLAB R2018a or R2017a, the fitglm() and ...
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### Prediction interval for function of binary outcomes in GLM

I have a large data set with binary outcomes $\vec{y} = (y_1,\dots,y_n)$ with $y_i\in\{0,1\}$ and covariates $\mathbf{X} = (\vec{x}_1, \dots ,\vec{x}_n)^\top$. One of the goals of the model I am ...
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### Modelling % cover that do not add up to 100% : GLM distribution families

I have an experimental set-up that consists in studying the impact of diversity of plant mixtures on the development of invasive species. On each plot, we recorded the % cover of each species which ...
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### Why using offset for a Gamma (link=log) glm doesn't yield the same predicted average response as the average observed?

One of my analyst asked me why his Gamma/link=log glm with offsets was always overstating his observed data points. I was able to reproduce the behavior in R with intercept only glm using offsets. ...
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### GAMs vs GLMs with feature engineering - is there a practical difference?

I recently came across this tutorial on General Additive Models (GAMs). Quoting the article: The principle behind GAMs is similar to that of regression, except that instead of summing effects of ...
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### Multiple imputation of glm binomial size parameter

Suppose we have a generalized linear model with a binomial response $y_i\sim \mathrm{bin}(n_i,p_i)$ where $p_i$ is determined by the linear predictor in the usual way via some link function. Is there ...
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### Standard error of the coefficient in GLM

I'm trying to learn about Wald test. I know, that its test statistics is $$t = \frac{\beta_i}{se\left( \beta_i \right)}$$ But, how is standard error $se$ computed in GLM? I've found only the ...
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### Can I get away with using GLM models on “pseudo-panel” big N small time=T data?

Suppose I have a kind of panel data set, where we track the investment totals of a great many customers, which may be highly variable, and is measured on a monthly basis over the course of 7-10 years. ...
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### GLMM for binomially distributed outcome, testing differential hypothesis

I am trying to find a way, to investigate differences between conditions in an experiment. The design is as follows: Depended Variable: Logical (answer is correct [correct accepted or correct ...
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### all regressions: coefficients interpretation

good morning to all, I open this topic with the intention of being useful to me but also to many in my situational. I would like to clarify the "interpretation" of the coefficients in the regression. ...
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### Connecting Poisson and multinomial models

Let's say we have multinomial counts $y_{jp}$ (corresponding to observations $j$ over categories $p=1,...P$) that are arranged in a table of $n$ rows and $P$ columns. Then say we have the log-linear ...
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### What does one do when the coefficient for the log of the rate estimator for a poisson rate model is very different from 1?

Let's say we have "number of accidents" as the response in a poisson regression model. One of the predictors is "number of days." Naturally, we expect more accidents to occur over more days, so it ...
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### Random or fixed effects? GLM or GLMM?

I am interested in the behavioral response of floral visitors to a treatment, applied in a paired fashion within plants. That is, one stem on each plant receives the treatment, and another stem serves ...
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### Post-Production Model Monitoring?

I am interested in model monitoring techniques. To be clear, for production of a statistical model, let's say GLM, with a set of covariates (continuous). The model will go into production (live ...
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### How to fit a regression for log-normal with gamlss

Since my original question was to R-code-specific I'm trying to rewrite it: I want to make a regression where my dependent variable y should follow a log-normal-...
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### Spatial Autoregressive Poisson model in R

I am estimating a gravity model of migration on cross-sectional data. The Moran I statistic indicates a positive and significant spatial autocorrelation in the residuals of the non-spatial model, and ...
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### How a tweedie glm handles an offset?

I am trying to fit a model with a glm using a tweedie family. I use a index parameter p between 1 and 2 to get a compound Poisson Gamma distribution to fit my data. But I want to use an offset only on ...
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### How can I evaluate spatial autocorrelation in a binomial GLMM?

Following Dormann et al 2007 Ecography, I have employed a GLMM approach in R to account for spatial autocorrelation in a binomial regression model (logistic regression) that does not have random terms....
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### Paper showing that logistic regression intercept biased in rare events

I'm studying the logistic regression for estimate the Probability of Default of SME's. Fortunately the event (firm's default) is a rare event. King and Zeng tell us that "logistic regression can ...
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### compare quasi poisson models

I have two models: ...
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### Data analysis : replication, pseudoreplication and mixed models

I have several questions concerning analysis of data, especially when there are replications and/or pseudoreplications. First, I read an example in « pseudoreplication is a pseudoproblem » where we ...
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### Why do my boostrapped CI's (using boot.ci in R) not include the point estimate?

I'm interested in estimating an average treatment effect $$\operatorname{ATE}\left(A', A''\right) = \mathbb{E}\left( Y\ |\ A'' \right) - \mathbb{E}\left( Y\ |\ A' \right)$$ with a generalized ...
I have time-series count data $N_{i,j}$ (population sizes in site $i$ and year $j$) and I want to correlate year-to-year changes with the environmental conditions $x_{i,j}$. For this, I want to fit ...