# Differences between cumulative link models (ordinal) and multinom (nnet) for fitting multinomial data

I'm trying to understand cumulative link models and how they differ from multinom models in R. Here's a simple example of a multinom model and plot output using the nnet package:

library(ordinal)
library(nnet)
library(sjPlot)

hous1.mu <- nnet::multinom(Sat ~ Freq,data = housing)
plot_model(hous1.mu, type="pred", ci.lvl = 0.95)


The 'ordinal' package in R states on page 17:

It is possible to fit multinomial models (i.e. with nominal effects) as the following example shows:

But, when I use the example code, the plot fits look wildly different than the multinom output:

hous1.clm <- clm(Sat ~ Freq, data = housing)
plot_model(hous1.clm, type="pred", ci.lvl = 0.95)


Even though the likelihood between the two models is the same:

all.equal(logLik(hous1.mu), logLik(hous1.clm))


Can anyone point me in the right direction as to what clm models are doing in this instance?

My reading of the ordinal package is that I can use clm with a nominal variable, but this gives a different plot fit.

Ultimately I would like to use clmm to model a nominal variable with random effects as: i) there's no straightforward way of doing this other than MCMCglmm, and ii) ordinal plays nicely with sjPlot, but... I'd first like to understand why clmm differs from multinom.