Using a generalized linear model vs generalized mixed effect linear model

Question

I conducted a study with 28 subjects to measure the effect of an intervention. Thus, I have 3 data points from each subject: pre-treatment, treatment, and post-treatment.

I tried running a generalized mixed-effect linear model, since my data is binomial and non-independent. In this model, I included subject as a random effect (together with three fixed effects I wanted to look at). My problem is that the model would not converge. So I was wondering whether using a generalized linear model instead would be a good alternative, as this one does converge. I know it is not the best solution, but my knowledge of statistics is pretty limited and I cannot think of a better alternative. Even though I would not be able to account for those random effects, would this model still give me some useful information/results?

Note: I tried using different optimizers and none of them worked, since I still got convergence warnings.

More information about my study:

It's a teaching-intervention study. I looked at whether explicit instruction during a language class led to better use of two particular linguistic structures. I also had two groups (corresponding to 2 different classes: intermediate learners and advanced learners).

My code:

lm_general = lme4::glmer(TARGET~CONSTRUCTION*PHASE*TYPE_OF_SPEAKER + (1|SUBJECT) + (1|ITEM), data = my_df, family = "binomial")

My results (for fixed effects):

                         Estimate Std. Error z value Pr(>|z|)    
(Intercept)              1.0461     0.3352   3.120  0.00181 ** 
CONSTRUCTIONpassives    -2.8949     0.2050 -14.121  < 2e-16 ***
PHASEpretreatment       -0.1810     0.2321  -0.780  0.43548    
PHASEposttreatment      -0.3527     0.2300  -1.534  0.12504    
TYPE_OF_SPEAKERintermediate -2.3805     0.3903  -6.099 1.07e-09 ***
CONSTRUCTIONpassives:PHASEpretreatment  -18.0473  1319.5225  -0.014  0.98909    
CONSTRUCTIONpassives:PHASEposttreatment  -17.8300  1302.0983  -0.014  0.98907    
CONSTRUCTIONpassives:TYPE_OF_SPEAKERintermediate 2.6915     0.2687  10.018  < 2e-16 ***
PHASEpretreatment:TYPE_OF_SPEAKERintermediate -0.9765     0.3584  -2.725  0.00643 ** 
PHASEposttreatment:TYPE_OF_SPEAKERintermediate 0.6715     0.3100   2.166  0.03028 *  
CONSTRUCTIONpassives:PHASEpretreatment:TYPE_OF_SPEAKERintermediate 0.4458  1744.3590   0.000  0.99980    
CONSTRUCTIONpassives:PHASEposttreatment:TYPE_OF_SPEAKERintermediate -1.2249  1729.7634  -0.001  0.99943    

My warning: "Model failed to converge: degenerate Hessian with 1 negative eigenvalues"

Answer 1

You have huge standard errors in these interaction groups:

                                      Estimate Std. Error z value Pr(>|z|)    
CONSTRUCTIONpassives:PHASEpretreatment  -18.0473  1319.5225  -0.014  0.98909    
CONSTRUCTIONpassives:PHASEposttreatment  -17.8300  1302.0983  -0.014  0.98907    

This usually happens when there is not at least one positive outcome and one negative outcome in each group (passives + pretreatment observations, and passives + posttreatment observations). It is called separation and prevents the model from converging.

One way to fix this is just to take that interaction out. You can also use something like Firth logistic regression, which will converge even when there is separation.