# Ordered logistic regression, adjacent model with category-specific effects

I am new in Bayesian Statistics and the “brms” package. I ran an ordinal logistic regression, family adjacent with category-specific effects to predict GPA (ordinal variable with five levels (less than 5.9, 6-6.9, 7-7.9, 8-8.9 and 9-10) using 2 precitors: Family income (ordinal variable with five levels) and Cognitive Reflection (continous variable:IRT scores).

I specified the model as following:

model <- brm(formula = GPA ~ cs(Gender) + cs(Family_Income) ,data=datos1, family = acat())

Nevertheless, I have had problems while interpreting the results. Taking into account that the 95% CI of the following exclude zero:
Family Income[1,2] & -0.78 & -1.4 & -0.12
Cognitive Reflection[4]& 0.43 & 0.2 & 0.68

-----------------------------------------------------RESULTS---------------------------------------------------------------

\begin{table}[H]
\caption{Ordinal Logistic Regression}
Variable & Estimate & l-95% CI & u-95% CI \
Family Income[1,1] & -0.26 & -1.39 & 0.87 \
Family Income[1,2] & -0.78 & -1.43 & -0.12\
Family Income[1,3] & 0.11 & -0.49 & 0.72 \
Family Income[1,4] & 0.34 & -0.31 & 0.96 \
Family Income[2,1] & -0.11 & -1.12 & 0.98 \
Family Income[2,2] & -0.25 & -0.85 & 0.34 \
Family Income[2,3] & 0.27 & -0.26 & 0.83 \
Family Income[2,4] & -0.52 & -1.11 & 0.04 \
Family Income[3,1] & 0.02 & -0.93 & 0.94 \
Family Income[3,2] & -0.05 & -0.54 & 0.46 \
Family Income[3,3] & 0.15 & -0.29 & 0.63 \
Family Income[3,4] & -0.28 & -0.77 & 0.18 \
Family Income[4,1] & -0.19 & -1.03 & 0.66 \
Family Income[4,2] & 0.17 & -0.25 & 0.61 \
Family Income[4,3] & -0.08 & -0.46 & 0.28 \
Family Income[4,4] & -0.15 & -0.53 & 0.24 \
Cognitive Reflection[1]& 0.2 & -0.45 & 0.93 \
Cognitive Reflection[2]& -0.06 & -0.38 & 0.26 \
Cognitive Reflection[3]& 0.17 & -0.1 & 0.45 \
Cognitive Reflection[4]&0.43 & 0.2 & 0.68 \

First of all, I wouldn’t engage in dichotomous thinking too much. In other words, don’t over-interpret the arbitrary threshold of 5%.

Then, you should check that you are not overfitting by using category-specific effects. I would recommend running one model with just standard effects and then compare both models using loo.

You may find some guidance in one of my papers: https://psyarxiv.com/x8swp/

Thank you for your reply. Actually, I performed a model comparison between two models: a standard effects model and a category-specific effects model, and found that the former had the lowest LOO value.

Model & LOOIC       &  SE
Model 1 (Standard effects) &  2955.92   & 37.52
Model 2 (Specific effects)   & 2976.33    &  42.02
Model 1 - Model 2 &-20.41 & 15.33


Nevertheless, I am still unsure which marginal effects plots are the correct ones to report.

1. marginal_effects(model) = When I ran this, a warning appeared: Warning messages:
1: Predictions are treated as continuous variables in ‘marginal_effects’ by default, which is likely invalid for ordinal families. Please set ‘categorical’ to TRUE.
2. marginal_effects(model, categorical =TRUE) =
3. marginal_effects(model, ordinal = TRUE) =
(The last two show the change in probability to answer certain category option, and it is clear that the change in probability is more evident in certain options (e.g. 3 and 4)). Does this finding suggest that a categoric-specific model could be more plausible?

Thanks

The results may indicate that you are (slightly) overfitting when using category-specific effects in all of your predictiors. That doesn’t mean they don’t capure something relevant between 3 and 4.

How does marginal_effects(model, categorical =TRUE) look like for the standard model?

marginal_effects(model, categorical =TRUE) looks like this. Where the impact of the predictor, is more clear in some response categories.

Is this the plot for that standard model? If yes, it looks pretty similar to the one from the category-specific model, doesn’t it?

Actually, they are very similar. The plot marginal_effects (specificeffects_model, categorical =TRUE) is shown below.
In conclusion, Should I select a standard effect model, although the graph is showing an effect in certain response categories?
If yes, how should I report this finding?
Thanks

I think reporting the results of the model comparison via loo, and then the coefficients of the standard model would be a reasonable choice. You may report the results of the category-specific model, as well, but state that this model is probably overfitting the data.

Thanks!