Hello Christofer,
That’s good information. Thanks for the precision.
Think I can use this now to work on a script:
Based on what you provided:
1. Two distinct sets of coefficients, β¹ and β², each associated with the
logits for:
• P(Y≤1)P(Y ≤ 1)P(Y≤1)
• P(Y≤2)P(Y ≤ 2)P(Y≤2)
2. Separate sum co
Hi Gregg,
Below I try to address
1) The sum constraint would apply for each set β¹ and β² i.e. sum(β¹)
= sum(β²) = 1.60
2) Just like 1) the lower and upper bounds will be applied for
individual set i.e. individual elements of β¹ are subject to lower =
c(1, -1, 0) and upper = c(2, 1, 1) and ind
Hello again Christofer,
This clarification changes the model structure somewhat significantly -it
shifts us from a standard cumulative logit model with proportional odds to a
non-parallel cumulative logit model, where each threshold has its own set of β
coefficients. At least, that is now my un
Christofer,
That was a detailed follow-up — you clarified the requirements precisely enough
providing a position to proceed from...
To implement this, a constrained optimization procedure to estimate an ordinal
logistic regression model is needed (cumulative logit), based on:
1. Estimated Cut
Hi Gregg,
Many thanks for your detail feedback, those are really super helpful.
I have ordered a copy of Agresti from our local library, however it
appears that I would need to wait for a few days.
Regrading my queries, it would be super helpful if we can build a
optimization algo based on below
Hello again Christofer,
Thanks for your thoughtful note — I’m glad the outline was helpful. Apologies
for the long delay getting back to you. Had to do a small bit of research…
Recommended Text on Ordinal Log-Likelihoods:
You're right that most online sources jump straight to code or canned
func
Logarithms are being referred to in two contexts here... log of likelihood, and
log of domain variables. I just wanted to highlight that the latter has a
surprisingly simple theoretical basis in optimization.
If you have a function that you want to find an optimum of, but an input
variable need
Section 2 of the vignette for the ordinal package:
https://cran.r-project.org/web/packages/ordinal/vignettes/clm_article.pdf
gives a reasonably complete, if short, definition/discussion of the
log-likelihood framework for ordinal models. It's probably also
discussed in Venables and Ripley
Hi Gregg,
I am sincerely thankful for this workout.
Could you please suggest any text book on how to create log-likelihood
for an ordinal model like this? Most of my online search point me
directly to some R function etc, but a theoretical discussion on this
subject would be really helpful to con
Christofer,
Given the constraints you mentioned—bounded parameters, no intercept, and a sum
constraint—you're outside the capabilities of most off-the-shelf ordinal
logistic regression functions in R like vglm or polr.
The most flexible recommendation at this point is to implement custom
likel
It may be overkill, but package nlsr has function nlxb() that can handle
various models and bound the parameters. Note that bounds can sometimes give
weird results if the bounds and initial parameter guesses are such that the
minimization of the sum of squares gets "stuck".
JN
On 2025-04-21 09:
Hi Gregg,
I thank you for for information about the function vglm()
However it appears that my constraints are a little different.
My parameters have lower and upper bounds and also sum of the
estimated coefficients should be equal to some predefined value.
Other than that, there is no Intercep
there are ways to implement constraints on parameter estimates in ordinal
logistic regression in R. Here are a few approaches:
The rms package (Regression Modeling Strategies) by Frank Harrell offers the
lrm function which can handle constraints through its penalty parameter, though
it's primar
13 matches
Mail list logo
