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I´d like to know the difference between these parameters when I am using GLM/GLMM/GAMLSS/BETAREG. I have observed a lot of published studies using offset, weights and covariates, however I am not sure about the use of these parameters in models.

Could someone explain to me when should I use each one parameters (offset and weights) and/or if should I use it as covariate?

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    $\begingroup$ Weights are strange, and depend on what program you are using, and even what function within the program. Have you tried the documentation for your program - if so, can you be a bit more specific about what you need to know. $\endgroup$
    – Jeremy Miles
    Commented Nov 16, 2016 at 20:54
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    $\begingroup$ An offset is a covariate but with a fixed coefficient, not an estimated one. $\endgroup$
    – mdewey
    Commented Nov 16, 2016 at 22:00

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Offset and weights are very different things. Offset is really a covariable included in a model with a fixed coefficient of $1$, which is not estimated. They are mostly used with poisson models to represent exposure, see Should I use an offset for my Poisson GLM? , When to use an offset in a Poisson regression? and search this site, there are many posts. For example of use with logistic regression, see Using offset in binomial model to account for increased numbers of patients

Weights are used to modify the estimation algorithm, by giving some observation more importance ("weight") than others. Their use varies by model type and software implementation, so you really have to read the docs!

See also Can Weights and Offset lead to similar results in poisson regression?

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