Displaying 3 results from an estimated 3 matches for "theta_k".
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2004 Apr 02
0
Hessian in constrOptim
...rOptim there is an option to get an approximation
to the hessian of the surrogate function R at MLE by declaring
hessian=TRUE in the calls to the function optim. I would like to ask
if it is advisable to get an approximate hessian for the funcrion f as
follows:
f''(theta)=R''(theta|theta_k)-B''(theta)
where B''(theta)=mu*sum((g(theta_k)/g(theta)^2)u_i*u_i^T) denotes the
second derivative of the barrier function
(following the notation given by Lange (1999)) where
R''(theta|theta_k) will be replaced by the approximate hessian at MLE
returned by optim.
Thanks...
2025 Apr 30
1
Estimating regression with constraints in model coefficients
...r now)
> > >
>
> > > Technical Approach
> > >
>
> > > ? Attempt to write a custom negative log-likelihood function using the cumulative logit formulation:
> > >
>
> > > P(Y?k?X)=11+exp?[?(?k?X?)]P(Y \leq k \mid X) = \frac{1}{1 + \exp[-(\theta_k - X\beta)]}
> > >
>
> > > and derive P(Y=k)P(Y = k) from adjacent differences of these.
> > >
>
> > > ? Cutpoints ?k\theta_k will be estimated as separate parameters, with constraints to ensure they?re strictly increasing for identifiability.
> > >...
2025 May 04
0
Estimating regression with constraints in model coefficients - Follow-up on Constrained Ordinal Model — Optimized via COBYLA
...UCLA (for now)
>
> > > > > Technical Approach
>
> > > > > ? Attempt to write a custom negative log-likelihood function using the cumulative logit formulation:
>
> > > > > P(Y?k?X)=11+exp?[?(?k?X?)]P(Y \leq k \mid X) = \frac{1}{1 + \exp[-(\theta_k - X\beta)]}
>
> > > > > and derive P(Y=k)P(Y = k) from adjacent differences of these.
>
> > > > > ? Cutpoints ?k\theta_k will be estimated as separate parameters, with constraints to ensure they?re strictly increasing for identifiability.
>
> > >...