# Help to interpret coefficient estimate of a ordered model with category-specific effects

Hi all,
I ran an ordinal model with category-specific effects to predict the grade of gravity of Gastro-intestinal advers effects (vcograde, an ordinal variable with 4 levels) in dogs with lymphoma treat with two different chemoterapic (DOX vs EPI)

this the model:

model ← brm(formula = VCograde~ 1+cs(treatment) ,data=mydata, family = acat(“probit”))

I have some difficlt to interpret the results. I followed the example in seminal paper of Paul Buerkner, but it is very far from my field of interest and it is not easy to transfer that example to my results.

this is the coefficient:

``````             Estimate       Est.Error       l-95% CI      u-95% CI
Intercept[1]        0.69      0.13            0.44           0.95
Intercept[2]        0.05      0.18           -0.30          0.42
Intercept[3]        0.69      0.24            0.22          1.18
treatmentDOX[1]     0.61      0.22            0.19          1.04
treatmentDOX[2]    -0.53      0.29            -1.10         0.03
treatmentDOX[3]    -0.76      0.60            -2.02         0.35

``````

I understand that category 4 of VCograde is the category reference for Y variable and EPI is the reference level of tratment factor , what mean 0.61 for treatmentDOX[1] …

this is the marginal effect

looking at this plot i see that dogs treat with EPI have higher probability to be in the first grade of Vcograde rating, for the second grade the situation is the reverse : dogs treat with EPI have lower probability to be in the second VCograde rating, quite similar fot the third grade , finally dogs treat with EPI have a little more probability to be in the max grade of gravity in Vcograde rating.

But how can support this impression using the coefficient of the model…
COnsidering that the model it is a probit model, i know that coefficient 0.61 it means that on the latent scale Y dogs treat with dox have 0.69 deviation standard more… what?
Please can you help me to interpret this results?

Thank you very much for your attention and patience
Massimo

• Operating System: Windows 11
• brms Version:2.20.1
1 Like

Rather than looking at the model parameters directly, it may be easier to compare DOX and EPI with marginaleffects::avg_comparisons:

``````marginaleffects::avg_comparisons(fit, variables = "treatment", type = "response")
#> Group      Term  Contrast Estimate  2.5 %  97.5 %
#>     1 treatment DOX - EPI   0.2168  0.143  0.2899
#>     2 treatment DOX - EPI  -0.0514 -0.132  0.0251
#>     3 treatment DOX - EPI  -0.0954 -0.156 -0.0399
#>     4 treatment DOX - EPI  -0.0698 -0.122 -0.0184
``````

Each contrast is a comparison of the form: Pr(VCograde = 1 | treatment = DOX) - Pr(VCograde = 1 | treatment = EPI). Note: The numbers don’t match the `conditional_effects` plot because I fitted the model on fake data.

Great. Thank you very much.
Massimo