# Interpretion of Monotonic Effects

Please also provide the following information in addition to your question:

• Operating System: Windows 10 Enterprise
• brms Version: brms_2.6.0

Hello

I ran the following the bernoulli Modell with brms

`mo5 <- brm(mensa ~ age + gender + member + mo(Natt_1) + mo(Natt_6) + mo(Natt_9) +mo(Natt_10) + mo(tho_1) + mo(tho_5) + mo(meat) , data=df_R, family="bernoulli")`

where mensa is a 0/1 Variable indicating if a person went to canteen for her/his lunch or if she/he brought her/his own food.

All variables with mo() are ordinal variables (see Bürkner, P. C., & Charpentier, E. (2018). Monotonic Effects: A Principled Approach for Including Ordinal Predictors in Regression Models.).

This are my results of the regression:

Family: bernoulli
Links: mu = logit
Formula: mensa ~ age + gender + member + mo(att_1) + mo(att_6) + mo(att_9) + mo(att_10) + mo(tho_1) + mo(tho_5) + mo(meat)
Data: df_R (Number of observations: 393)
Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 4000

Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
Intercept -0.86 1.25 -3.38 1.58 2556 1.00
age 0.10 0.03 0.03 0.17 3509 1.00
genderMann 0.46 0.28 -0.09 1.01 4243 1.00
memberMitarbeiterDin 0.72 0.56 -0.34 1.86 3176 1.00
memberAndere -2.01 1.04 -4.15 -0.00 3860 1.00
moatt_1 -1.55 0.50 -2.58 -0.62 2594 1.00
moatt_6 -0.82 0.53 -1.86 0.23 2457 1.00
moatt_9 -1.98 0.50 -3.04 -1.09 3225 1.00
moatt_10 2.53 0.59 1.45 3.72 2826 1.00
motho_1 -0.12 0.56 -1.25 1.02 3008 1.00
motho_5 -0.61 0.68 -2.11 0.57 2367 1.00
momeat 1.18 0.63 -0.06 2.50 2599 1.00

Simplex Parameters:
Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
moatt_11[1] 0.24 0.16 0.01 0.58 3546 1.00
moatt_11[2] 0.20 0.14 0.01 0.55 4682 1.00
moatt_11[3] 0.56 0.17 0.22 0.88 3891 1.00
moatt_61[1] 0.20 0.18 0.01 0.68 3371 1.00
moatt_61[2] 0.38 0.23 0.02 0.85 4597 1.00
moatt_61[3] 0.41 0.24 0.03 0.88 4364 1.00
moatt_91[1] 0.26 0.16 0.02 0.60 3575 1.00
moatt_91[2] 0.50 0.18 0.16 0.84 4492 1.00
moatt_91[3] 0.25 0.14 0.02 0.54 3727 1.00
moatt_101[1] 0.29 0.13 0.04 0.55 2472 1.00
moatt_101[2] 0.30 0.14 0.06 0.60 3477 1.00
moatt_101[3] 0.42 0.14 0.13 0.68 3096 1.00
motho_11[1] 0.37 0.25 0.01 0.87 4392 1.00
motho_11[2] 0.33 0.23 0.01 0.83 5029 1.00
motho_11[3] 0.30 0.22 0.01 0.80 4592 1.00
motho_51[1] 0.38 0.24 0.02 0.86 2990 1.00
motho_51[2] 0.38 0.24 0.02 0.87 3275 1.00
motho_51[3] 0.25 0.20 0.01 0.75 3350 1.00
momeat1[1] 0.18 0.14 0.01 0.50 4876 1.00
momeat1[2] 0.15 0.12 0.00 0.46 5877 1.00
momeat1[3] 0.17 0.13 0.01 0.48 4451 1.00
momeat1[4] 0.16 0.13 0.01 0.47 5069 1.00
momeat1[5] 0.21 0.15 0.01 0.55 3955 1.00
momeat1[6] 0.13 0.11 0.00 0.42 4883 1.00

Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
is a crude measure of effective sample size, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I am now not sure how to interpret the monotonic effects. Do I just add the Simplex Parameters?
For example for people who are in category [3] for “meat” the Estimator is 0 1.18+0.18+0.15+0.17? And what do I do with the Confidential Interval? Also just sum up?

And for negative Estimator I do the same? For example for People who are in category [1] in the ordinal variable “att_1” the estimator is = -1.55-0.24 and the 95% CI is= lowerbound -2.58 - 0.1 - 0.1 uperbound -0.62 -0.58 - 0.55?

Thank you in advance.

First of all, all your parameters are on the logit scale in default bernoulli models, which adds another layer of complexity.

Apart from that, what exactly are you trying to understand that is not explained in detail in the paper you are citing?

If you want to get estimates for certain values of your predictors, use `fitted` with new data. Don’t try to work that out using the results in the summary output, in particular not for CIs.

Thank you for your answer

Read first (and second and third) and than ask… I think I misunderstood the interpretation of b and an additional parameter vector.

Excuse the effort.