topic Re: Does JMP's loglikelihood value include a constant? in Discussions

Does JMP's loglikelihood value include a constant?

etmsni — Sun, 11 Jun 2023 11:09:41 GMT

When JMP shows the loglikelihood value, does it set the constant to 0 or some number? Thanks!

Re: Does JMP's loglikelihood value include a constant?

peng_liu — Fri, 08 Jan 2021 15:40:33 GMT

It depends on where you see the loglikelihood. For Normal distribution related loglikelihood, the constant is a function of pi and sample size; for Lognormal distribution related loglikelihood, the constant adds a function of data as well. Including constant will increase complexity and time consumption in calculation. So the strategy is NOT to include the constant, unless we have to. E.g. in Life Distribution, constants are included, because there is a need to compare different distributions like between Normal and Lognormal, where the constants matters.

Re: Does JMP's loglikelihood value include a constant?

etmsni — Fri, 08 Jan 2021 16:33:48 GMT

For the single Weibull fitting and competing two Weibull risk mixture, what would the constants be? Thanks!

Re: Does JMP's loglikelihood value include a constant?

peng_liu — Fri, 08 Jan 2021 18:35:18 GMT

Seems you are talking about loglikelihood in Life Distribution. Then the answer is about another "depends". If the data have failure observations, then the constant is the function of those failure time, just like the constant of a Lognormal distribution. If there are not failure observations, then there are no separable constant. For mixture, either regular mixture or competing risk mixture, I don't believe there are separable constants, at least in general. In Life Distribution, the loglikelihood is "full", so it does not deliberately differentiate a constant part and a non-constant part.

Re: Does JMP's loglikelihood value include a constant?

etmsni — Fri, 08 Jan 2021 20:48:55 GMT

For censored data, the likelihood function is:

So isn't the constant set beforehand, and not a function of data? Thanks!

Ref: https://www.itl.nist.gov/div898/handbook/apr/section4/apr412.htm

Re: Does JMP's loglikelihood value include a constant?

peng_liu — Fri, 08 Jan 2021 21:05:42 GMT

C can be different things for different distributions, depending on what is f.

For example, when fitting a Weibull likelihood, if f and F are density and distribution functions of Weibull, then there is not separable constant at all.

However, the likelihood is equivalent to a form, in which there is a constant C, and f and F are density and distribution functions of Smallest Extreme Value (SEV) distribution. I guess that is what the NIST formula is depicting.

Re: Does JMP's loglikelihood value include a constant?

etmsni — Sat, 09 Jan 2021 20:48:18 GMT

Since JMP is giving the loglikelihood value, then when taking the log form of the formula, doesn't the C constant become separate? That's why I'm confused, because I thought that the constant could be set this way.

Re: Does JMP's loglikelihood value include a constant?

peng_liu — Mon, 11 Jan 2021 20:45:39 GMT

In this context, the constant C is not a known quantity before seeing the data. In general, when one says the loglikelihood does not include a constant, that usually means that MLE is not affected by subtracting the constant from the loglikelihood. The constant can be anything that does not involve parameters. E.g. constant can be a function of data, a function of sample size, etc.