# 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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### 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 ...
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### Goodness of fit and which model to choose linear regression or Poisson

I need some advice regarding two main dilemmas in my research, which is a case study of 3 big pharmaceuticals and innovation. Number of patents per year is the dependent variable. My questions are ...
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### How do you deal with "nested" variables in a regression model?

Consider a statistical problem where you have a response variable that you want to describe conditional on an explanatory ...
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### Simulation of logistic regression power analysis - designed experiments

This question is in response to an answer given by @Greg Snow in regards to a question I asked concerning power analysis with logistic regression and SAS ...
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### Regression for an outcome (ratio or fraction) between 0 and 1

I am thinking of building a model predicting a ratio $a/b$, where $a \le b$ and $a > 0$ and $b > 0$. So, the ratio would be between $0$ and $1$. I could use linear regression, although it doesn'...
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### Why do my p-values differ between logistic regression output, chi-squared test, and the confidence interval for the OR?

I have built a logistic regression where the outcome variable is being cured after receiving treatment (Cure vs. No Cure). All ...
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### Diagnostic plots for count regression

What diagnostic plots (and perhaps formal tests) do you find most informative for regressions where the outcome is a count variable? I'm especially interested in Poisson and negative binomial models, ...
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### 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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### Bayesian logit model - intuitive explanation?

I must confess that I previously haven't heard of that term in any of my classes, undergrad or grad. What does it mean for a logistic regression to be Bayesian? I'm looking for an explanation with a ...
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### Difference between generalized linear models & generalized linear mixed models

I am wondering what the differences are between mixed and unmixed GLMs. For instance, in SPSS the drop down menu allows users to fit either: ...
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### How to simulate artificial data for logistic regression?

I know I'm missing something in my understanding of logistic regression, and would really appreciate any help. As far as I understand it, the logistic regression assumes that the probability of a '1' ...
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### Interpretation of Fixed Effects from Mixed Effect Logistic Regression

I am confused by statements at a UCLA webpage about mixed effects logistic regression. They show a table of fixed effects coefficients from fitting such a model and the first paragraph belows seems to ...
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### Can you give a simple intuitive explanation of IRLS method to find the MLE of a GLM?

Background: I'm trying to follow Princeton's review of MLE estimation for GLM. I understand the basics of MLE estimation: likelihood, ...
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### How to derive the least square estimator for multiple linear regression?

In the simple linear regression case $y=\beta_0+\beta_1x$, you can derive the least square estimator $\hat\beta_1=\frac{\sum(x_i-\bar x)(y_i-\bar y)}{\sum(x_i-\bar x)^2}$ such that you don't have to ...
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### Interpretation of plot (glm.model)

Can anyone tell me how to interpret the 'residuals vs fitted', 'normal q-q', 'scale-location', and 'residuals vs leverage' plots? I am fitting a binomial GLM, saving it and then plotting it.
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### What is the difference between logistic regression and Fractional response regression?

As far as I know, the difference between logistic model and fractional response model (frm) is that the dependent variable (Y) in which frm is [0,1], but logistic is {0, 1}. Further, frm uses the ...
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### What is the difference between a "link function" and a "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? For example, a binary response variable ...
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### Linear model with log-transformed response vs. generalized linear model with log link

In this paper titled "CHOOSING AMONG GENERALIZED LINEAR MODELS APPLIED TO MEDICAL DATA" the authors write: In a generalized linear model, the mean is transformed, by the link function, instead of ...
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### Interpreting plot of residuals vs. fitted values from Poisson regression

I am trying to fit data with a GLM (poisson regression) in R. When I plotted the residuals vs the fitted values, the plot created multiple (almost linear with a slight concave curve) "lines". What ...
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### What are modern, easily used alternatives to stepwise regression?

I have a dataset with around 30 independent variables and would like to construct a generalized linear model (GLM) to explore the relationship between them and the dependent variable. I am aware that ...
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### How are regression, the t-test, and the ANOVA all versions of the general linear model?

How are they all versions of the same basic statistical method?
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### When to use gamma GLMs?

The gamma distribution can take on a pretty wide range of shapes, and given the link between the mean and the variance through its two parameters, it seems suited to dealing with heteroskedasticity in ...
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### How to interpret coefficients in a Poisson regression?

How can I interpret the main effects (coefficients for dummy-coded factor) in a Poisson regression? Assume the following example: ...
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### How to decide which glm family to use?

I have fish density data that I am trying to compare between several different collection techniques, the data has lots of zeros, and the histogram looks vaugley appropriate for a poisson distribution ...
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### Interpreting residual diagnostic plots for glm models?

I am looking for guidelines on how to interpret residual plots of glm models. Especially poisson, negative binomial, binomial models. What can we expect from these plots when the models are "correct"...
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### Why is the square root transformation recommended for count data?

It is often recommended to take the square root when you have count data. (For some examples on CV, see @HarveyMotulsky's answer here, or @whuber's answer here.) On the other hand, when fitting a ...
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### When is logistic regression solved in closed form?

Take $x \in \{0,1\}^d$ and $y \in \{0,1\}$ and suppose we model the task of predicting y given x using logistic regression. When can logistic regression coefficients be written in closed form? One ...
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### Family of GLM represents the distribution of the response variable or residuals?

I have been discussing with several lab members about this one, and we have gone to several sources but still don't quite have the answer: When we say a GLM has a family of poisson let's say are we ...
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### Interaction in generalized linear model

I have 2 continuous variables as my predictors and the interaction between them, so 3 effects all together (when I center my predictors only the interaction is significant). I am using a binary logit ...
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### What is the difference between generalized estimating equations and GLMM?

I'm running a GEE on 3-level unbalanced data, using a logit link. How does this differ (in terms of the conclusions I can draw and the meaning of the coefficients) from a GLM with mixed effects (GLMM)...
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### Properties of logistic regressions

We're working with some logistic regressions and we have realized that the average estimated probability always equals the proportion of ones in the sample; that is, the average of fitted values ...
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