# Effect sizes for categorical variable in brm cumulative logit model

Hi,

I haven’t been able to find the answer to this anywhere, but it should be simple:

I’m running an ordinal regression model in brms using cumulative(“logit”).

I am using a categorical variable which I have set with ‘factor’.

I would like to know what the effect size would be for the reference value for this variable.

Regards,
Gareth

Can you please be more specific on what you are trying to achieve for instance by showing use the code you are using?

# ‘Ratings’ is collected on a 7-point Likert scale

Data\$Height <- 1/2*scale(Data\$Height)
Data\$Chord <- factor(Data\$Chord)
Data\$Number <- factor(Data\$Number)

mdlchord <- brm(Ratings ~ 1 + Height + I(Height^2) + Chord + (1 |Number),
prior = c(set_prior (“student_t(3,0,2.5)”, class = “b”)),
data = Data, family = cumulative(“logit”), save_all_pars = TRUE,
warmup = 1000, iter = 4000, init = 0, cores = 4)

For the population level effects I get

Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
Intercept[1] -2.49 0.18 -2.85 -2.12 166 1.03
Intercept[2] -1.06 0.18 -1.42 -0.70 164 1.03
Intercept[3] 0.01 0.18 -0.35 0.37 166 1.03
Intercept[4] 0.70 0.18 0.34 1.06 167 1.03
Intercept[5] 1.86 0.18 1.50 2.23 166 1.03
Intercept[6] 3.19 0.18 2.83 3.56 166 1.03
Height -0.06 1.96 -3.84 3.94 4000 1.00
IHeightE2 -0.07 1.94 -3.99 3.82 4000 1.00
Chord2 -1.18 0.30 -1.77 -0.58 4000 1.01
Chord3 -0.29 0.28 -0.83 0.27 437 1.01
Chord4 -0.46 0.28 -1.01 0.07 475 1.01
Chord5 -0.02 0.27 -0.55 0.50 413 1.01
Chord6 -0.24 0.29 -0.82 0.32 384 1.01
Chord7 -0.04 0.28 -0.57 0.50 551 1.01
Chord8 0.39 0.28 -0.13 0.94 4000 1.01
Chord9 0.55 0.30 -0.02 1.13 4000 1.01
Chord10 -0.52 0.29 -1.07 0.06 589 1.01

I’m looking for the effect sizes of the chords after taking account of Height.
What is my effect size for Chord1?

Thanks

It seems to me that the effect sizes for the other chords are shown relative to Chord1? In which case I can assign it 0. I only am not sure of that because I would have expected a rather different result for where Chord1 fits amongst the others.

The regression coefficients of the chords are indeed relative for Chord1, as by default R using dummy coding for factors.

Ok, thanks.

I should have immediately accepted this most simple answer, but needed to confirm because of the unexpected result it gave.