Hi,

I tried to model the same question with two different models for an ordinal outcome and ordinal predictor:

fit1: crated 3 dummy variables for an 4 levels ordinal variable and each level was always compared to basic level as 0.

fit 2: Used the ordinal variable in the model but use mo()

Below are the results for fit 1 and 2 and loo_comparison.

And marginal graphs for mo.

It seems fit 1 is better if i am right, but how come these two estimates are too different in fit1 and fit2.

Fit 1 estimates is more similar to frequentist ordinal regression model!!!

```
fit1:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept[1] 0.43 0.36 -0.27 1.14 1.00 914 843
Intercept[2] 1.59 0.35 0.93 2.34 1.00 882 812
Intercept[3] 2.63 0.35 2.00 3.33 1.00 850 811
Intercept[4] 3.46 0.35 2.80 4.20 1.00 813 867
Intercept[5] 4.23 0.36 3.54 4.95 1.00 802 811
Intercept[6] 5.01 0.36 4.33 5.75 1.00 804 872
Intercept[7] 5.69 0.37 5.00 6.43 1.00 809 802
Intercept[8] 6.42 0.38 5.73 7.20 1.00 781 842
Intercept[9] 7.24 0.39 6.49 8.01 1.00 851 807
Intercept[10] 8.03 0.40 7.28 8.86 1.00 831 727
Intercept[11] 9.18 0.44 8.36 10.07 1.00 783 892
hearing2cat1 1.35 0.14 1.07 1.61 1.00 904 743
hearing3cat1 1.28 0.24 0.81 1.72 1.00 1272 849
hearing4cat1 1.33 0.30 0.75 1.91 1.00 1113 704
age10int1 0.66 0.05 0.57 0.75 1.00 785 763
sex1 0.30 0.10 0.10 0.48 1.00 1366 912
yrs2 0.04 0.04 -0.03 0.11 1.00 1044 906
fit2:
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept[1] -0.04 0.42 -0.84 0.81 1.00 3046 3209
Intercept[2] 1.17 0.42 0.38 2.03 1.00 3051 2904
Intercept[3] 2.27 0.43 1.48 3.15 1.00 3160 2665
Intercept[4] 3.13 0.43 2.33 4.00 1.00 3096 2837
Intercept[5] 3.91 0.43 3.09 4.78 1.00 3075 2849
Intercept[6] 4.68 0.44 3.85 5.56 1.00 3095 2681
Intercept[7] 5.36 0.44 4.52 6.25 1.00 3110 2781
Intercept[8] 6.08 0.45 5.23 6.99 1.00 3132 2639
Intercept[9] 6.88 0.45 6.03 7.78 1.00 3131 2701
Intercept[10] 7.66 0.46 6.81 8.60 1.00 3167 2741
Intercept[11] 8.79 0.49 7.84 9.80 1.00 3408 2846
sex1 0.31 0.10 0.11 0.51 1.00 7074 3825
yrs2 0.04 0.04 -0.03 0.12 1.00 4747 3722
morec_sevhearing1 0.56 0.07 0.45 0.70 1.00 4011 3279
moage10int1 0.63 0.07 0.51 0.77 1.00 2465 2756
Simplex Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
morec_sevhearing11[1] 0.73 0.08 0.56 0.89 1.00 3585
morec_sevhearing11[2] 0.12 0.06 0.02 0.26 1.00 6196
morec_sevhearing11[3] 0.15 0.08 0.03 0.33 1.00 3997
moage10int11[1] 0.13 0.06 0.02 0.26 1.00 3198
moage10int11[2] 0.10 0.05 0.03 0.20 1.00 5083
moage10int11[3] 0.32 0.05 0.22 0.43 1.00 3751
moage10int11[4] 0.16 0.04 0.09 0.24 1.00 4982
moage10int11[5] 0.11 0.03 0.05 0.18 1.00 5265
moage10int11[6] 0.06 0.03 0.01 0.12 1.00 6426
moage10int11[7] 0.11 0.05 0.02 0.22 1.00 2997
LOO fit 1
Computed from 1000 by 1320 log-likelihood matrix
Estimate SE
elpd_loo -2832.5 22.8
p_loo 16.4 0.4
looic 5665.0 45.7
------
Monte Carlo SE of elpd_loo is 0.1.
All Pareto k estimates are good (k < 0.5).
See help('pareto-k-diagnostic') for details.
loo fit2
Estimate SE
elpd_loo -2819.9 23.0
p_loo 19.3 0.5
looic 5639.7 46.1
------
Monte Carlo SE of elpd_loo is 0.1.
All Pareto k estimates are good (k < 0.5).
See help('pareto-k-diagnostic') for details.
loo_compare(fit1,fit2)
loo_compare(fit1,fit2)
elpd_diff se_diff
fit2 0.0 0.0
fit1 -12.6 5.6
the marginal graph for fit2 is attached!
Another question is about yrs(figure is also attached), with a wide variation! Do I need to transform this variable?
Thanks for your inputs, it will help me move forward! ![hearing1|575x324](upload://kOmTf2SEEPZ2YpGaP3AyRGEaBqY.png) ![time2_bodn2|575x324](upload://kIwkwZkJuKXgpLObhsH3gAaenPq.png)
```