omitting an intercept

[Tim Lyons]

Are there any papers or informal resources discussing dropping an intercept in a hierarchical model to achieve convergence or improve model fit? I've seen a few examples now,  ranging from log-link abundance, log-link detection (distance sampling), and logit-link detection.

Is it generally acceptable and just uncommon?

[Denis Valle]

We talk about dropping the intercept when covariates sum to a constant (e.g., land-use land-cover proportions) in the article below:

Valle, D.; Mintz, J.; Brack, I. V. 2024. Estimation and interpretation problems and solutions when using proportion covariates in linear regression models. Ecology e4256.

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[Matthijs Hollanders]

Dropping an intercept to achieve convergence is generally a red flag. For proportions or otherwise categorical data, you have to either set a reference category or use sum-to-zero constraints. For example, let's say you have a categorical predictor with three levels. There are three (maybe more) options:

1. Set one level as reference (intercept) and estimate the "offsets" from this reference for the remaining two categories.
2. Drop the intercept and estimate the effect of each level. Note that essentially, you're just fitting three intercepts here, one for each level.
3. Keep the intercept but impose a sum-to-zero constraint on the level effects. This is nice, especially when your model has an arbitrary number of categorical predictors with arbitrary levels. The intercept is interpreted as the average across your levels, and the sum-to-zero constraint on the categorical effects ensures the model is fully identified.

What is your model exactly? I'm guessing you have a redundancy that makes your model not identified. 

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[Tim Lyons]

Thanks all!

Its a project I'm providing feedback on, in this case it's dropping an intercept on the detection function in distance sampling because they had random effects that weren't working with the intercept included. In another instance, they had a zero-inflated abundance model and dropped the intercept on the linear model for abundance. The covariates have always been continuous.

My impression was that when the folks I work with were doing this, it was because they over-parameterized a model and/or had too sparse of data for the model they wanted to fit. I just was looking to make sure it's not a practice I'm just ignorant of.