ASM 22.2 Likelihood Ratio Algorithm

[GoBolts]

(22.2 From the 4th edition)

The question lists loglikelihoods for 1,2,3,4,5 parameter distributions. Using 95% confidence how many parameters are in the selected model.

In the solution it compares 2(1param-2param) to the value in the chi sq table, then it compares 2(1param-3param) and then 2(1param-4param). The 4 param distribution is the first which twice the difference in the loglikelihoods is greater than the value from the table. Then when you test the 5 parameter distribution the solution is comparing 2(4param-5param).

What is the process when you are moving up through adding new parameters. Is it as follows: You start off assuming the simplist 1 parameter distribution. Then you add parameters if they are deemed worth it by the test. Then once you find one that is worth it, that becomes your new starting point for comparing and adding more parameters?

[Kabaka]

Originally Posted by GoBolts

What is the process when you are moving up through adding new parameters. Is it as follows: You start off assuming the simplist 1 parameter distribution. Then you add parameters if they are deemed worth it by the test. Then once you find one that is worth it, that becomes your new starting point for comparing and adding more parameters?

That's how I understand it.

[Kazodev]

The theory is basically you have a tradeoff between fit and complexity. So if you wanted you could pick a distribution with 200 parameters and it would fit your data perfectly but is that really what you shoul do? What if you picked a distribution with 3 paramters and it fit 98% of your data? So there are different ways to penalize for adding paramters, loglikelihood is one, AIC(BIC) is another one, etc.