Drop a single coefficient (one level from categorical variable) from formula/modelmatrix for Likelihood ratio test

[MaximilianNuber]

Dear all,

I am fitting MixedModels for large single cell datasets. One approach to test for covariates is to drop a single coefficient from the modelmatrix, which belongs to one level of a categorical variable. I have not been able to find this possibility in Julia.

As an example, let me use the iris dataset. It may not be a mixed model, but in principle it is the same.

We have the full model: full = lm(@formula(SepalLength ~ Species), iris) with results

SepalLength ~ 1 + Species

Coefficients:
─────────────────────────────────────────────────────────────────────────────
                     Coef.  Std. Error      t  Pr(>|t|)  Lower 95%  Upper 95%
─────────────────────────────────────────────────────────────────────────────
(Intercept)          5.936   0.0728022  81.54    <1e-99   5.79213    6.07987
Species: setosa     -0.93    0.102958   -9.03    <1e-15  -1.13347   -0.726531
Species: virginica   0.652   0.102958    6.33    <1e-08   0.448531   0.855469
─────────────────────────────────────────────────────────────────────────────

My goal would be, to drop Species: setosa in the formula or model matrix for another linear model. This nested model would be compared to the full model by likelihood ratio test.

Everything I found so far would be dropping the Species variable entirely, but it is not what I want.

I have played around with contrasts, where in the example the modelmatrix column for Species: setosa would be all zeros, but got the warning that the model is not full rank.

Is there any solution to this, or possibly a workaround?

Thank you for any help, Max