# Effect of factor level order in cumulative link model

I ran the below CLM (from the clm() function in the R package "ordinal"), my dependant categorical variable is agg_full and I have two categorical variables, treatment and region. The variable region has two levels, AR and OZ.

In a first version of the model, AR is the reference level for region. In a second model, I used aggression_full$region <- factor(aggression_full$region,levels=c("OZ","AR"),ordered=T) to set OZ as the reference level instead (AR is then coded as L in the second model summary).

My question is why are the levels of significance different in the two versions for the effect of the treatments low_sugar and OA_low_sugar? Looking at the standard errors, they are higher in the first version of the model which explains why the levels of significance are lower. The AIC are the same, so I assume that the models are identical, but the interpretation is quite different between the two versions. The first model tells me that low_sugar and OA_low_sugar treatments effects are marginally significant, and that's the same in OZ (not such a powerful statement) while the second one indicates that the effect of these two treatments is highly significant in OZ, as in AR (cf non significant interaction terms).

Also, that may be related to my question, all the estimates are quite close from one model to another, but the regionOZ term in the first model and the region.L in the second model are not matching. Any thoughts?

Version with AR as the reference level:

formula: as.factor(aggression_full$agg_full) ~ treatment * region data: aggression_full link threshold nobs logLik AIC niter max.grad cond.H logit equidistant 6002 -8978.41 17974.81 5(0) 1.75e-12 5.7e+02 Coefficients: Estimate Std. Error z value Pr(>|z|) treatmentlow_sugar -0.18561 0.09754 -1.903 0.0571 . treatmentOA 0.11062 0.09726 1.137 0.2554 treatmentOA_low_sugar 0.18436 0.09715 1.898 0.0577 . regionOZ 0.23744 0.09844 2.412 0.0159 * treatmentlow_sugar:regionOZ 0.01611 0.13536 0.119 0.9053 treatmentOA:regionOZ 0.02906 0.13440 0.216 0.8288 treatmentOA_low_sugar:regionOZ -0.01839 0.13591 -0.135 0.8924 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Threshold coefficients: Estimate Std. Error z value threshold.1 -0.32498 0.07080 -4.59 spacing 0.78295 0.01254 62.45  Version with OZ as the reference level: formula: as.factor(aggression_full$agg_full) ~ treatment * region
data:    aggression_full

logit equidistant 6002 -8978.41 17974.81 5(0)  4.55e-12 2.1e+02

Coefficients:
Estimate Std. Error z value Pr(>|z|)
treatmentlow_sugar             -0.17756    0.06770  -2.623  0.00872 **
treatmentOA                     0.12515    0.06721   1.862  0.06260 .
treatmentOA_low_sugar           0.17517    0.06798   2.577  0.00997 **
region.L                       -0.16790    0.06961  -2.412  0.01586 *
treatmentlow_sugar:region.L    -0.01139    0.09571  -0.119  0.90527
treatmentOA:region.L           -0.02055    0.09504  -0.216  0.82882
treatmentOA_low_sugar:region.L  0.01300    0.09610   0.135  0.89238
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Threshold coefficients:
Estimate Std. Error z value
threshold.1 -0.44370    0.05088   -8.72
spacing      0.78295    0.01254   62.45