Hello,

I am fitting a model in brms. My independent variable is a categorical (employee satisfaction category) and my dependent variable is ordinal (workload on 5 point scale). I expect the relationship to be quadratic (too low and too high workload is bad for satisfaction). However I dont understand how to add a quadratic effect effect with ordinal data. I first tried to make the values nummeric and than do a transformation:

fit_workload_l_quad ← brm(

formula = category ~ poly(as.numeric(workload), 2) +

(1 + poly(as.numeric(workload), 2, raw = TRUE) || em_ID + yearperiod),

data = data_workload,

family = cumulative(“logit”),

iter = 2000,

chains = 2,

warmup = 500,

cores = parallel::detectCores()

)

However it is hard to interpretate the results and the estimation of the effect are high. However if I tread the predictor as ordinal the estimation also include higher polynomial terms:

Code:

data_workload$workload ← factor(data_workload$workload, ordered = TRUE)

fit_workload_q ← brm(

formula = category ~ workload + (1 + workload || technische_sleutel + yearperiod),

data = data_workload,

family = cumulative(“logit”),

iter = 2000,

chains = 2,

warmup = 500,

cores = parallel::detectCores()

)

Output:

Regression Coefficients:

Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS

Intercept[1] -1.64 0.07 -1.79 -1.50 1.00 1435 1188

Intercept[2] 0.70 0.07 0.56 0.84 1.00 1431 1752

workload.L -0.82 0.21 -1.22 -0.41 1.00 1167 1241

workload.Q -1.00 0.17 -1.35 -0.65 1.00 958 1152

workload.C -0.09 0.13 -0.35 0.16 1.00 962 1426

workloadE4 0.48 0.07 0.33 0.62 1.00 1258 1421

Can somebody help me with building the model and writing the formula? So I need a model were I can include only the linear and quadratic effect but for ordinal predictor.

Thanks a lot!!!