Odds ratios for clm() and alike from package ordinal

[strengejacke]

Only the intercept (i.e. thresholds) are exponentiated and the location and scale parameters are not. I wonder whether it should be exactly the other way round?

library(ordinal)
library(parameters)

fm1 <- clm(rating ~ temp + contact + judge + temp * contact, data=wine, link="logit")
summary(fm1)

parameters::model_parameters(fm1)
parameters::model_parameters(fm1, exponentiate=TRUE)

fm2 <- clm2(rating ~ temp + contact + judge + temp * contact, data=wine, link="logistic")
summary(fm2)

parameters::model_parameters(fm2)
parameters::model_parameters(fm2, exponentiate=TRUE)

fm3 <- clm(rating ~ temp + contact + judge + temp * contact, scale=~judge, data=wine, link="logit")
summary(fm3)

parameters::model_parameters(fm3)
parameters::model_parameters(fm3, exponentiate=TRUE)

[mattansb]

The location and scale parameters should be exponentiated (to proportional odd ratio and ratios, respectively). I think an argument can also be made for the intercepts, since they are akin to the single intercept for a logistic binomial model.

[bwiernik]

I think we need to do -1 * intercepts though. Compare:

library(ordinal)
fm2 <- clm(factor(am) ~ cyl, data = mtcars)
summary(fm2)

fm3 <- glm(factor(am) ~ cyl, data = mtcars, family = "binomial")
summary(fm3)

parameters::parameters(fm3, exponentiate = TRUE)
parameters::parameters(fm2, exponentiate = TRUE)

Wdyt @mattansb ?

[bwiernik]

CLM

formula: factor(am) ~ cyl
data:    mtcars

 link  threshold nobs logLik AIC   niter max.grad cond.H 
 logit flexible  32   -16.98 37.95 4(0)  2.30e-07 5.2e+02

Coefficients:
    Estimate Std. Error z value Pr(>|z|)   
cyl  -0.6912     0.2536  -2.725  0.00642 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Threshold coefficients:
    Estimate Std. Error z value
0|1   -3.778      1.546  -2.444

Binomial model

Call:
glm(formula = factor(am) ~ cyl, family = "binomial", data = mtcars)

Coefficients:
            Estimate Std. Error z value Pr(>|z|)   
(Intercept)   3.7777     1.5456   2.444  0.01452 * 
cyl          -0.6912     0.2536  -2.725  0.00642 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 43.230  on 31  degrees of freedom
Residual deviance: 33.951  on 30  degrees of freedom
AIC: 37.951

Number of Fisher Scoring iterations: 4

[mattansb]

Yes, in ordinal models the intercepts are actually thresholds. But that might be confusing to the user?

[strengejacke]

I think we need to do -1 * intercepts though. Compare:

Isn't this depending on whether you look at: Intercept is event to reference (glm), or threshold from reference to next higher category (clm)? Thus, the different sign makes sense?

[strengejacke]

Keeping this as discussion.