On Oct 5, 2010, at 15:36 , Ravi Varadhan wrote: > Likelihood is a function of the parameters, conditioned upon the data. It is > not the same as a probability density function. Terms or factors which do > not involve parameters can be omitted from the likelihood function. For > continuous random variables, the density function can be in (0, Inf). > Therefore, the likelihood function can assume any value between 0 and Inf. > Hence the log-likelihood can be in (-Inf, Inf). > > When the random variable is discrete, the density or probability mass > function cannot be greater than 1. Hence the likelihood cannot be greater > than 1, in which case, the log-likelihood cannot be positive.
...unless one of the above mentioned terms that do not involve parameters is omitted. E.g. the Poisson likelihood is x log lambda - lambda - log(x!) and the sum of the first two terms can easily be positive. > > Ravi. > ____________________________________________________________________ > > Ravi Varadhan, Ph.D. > Assistant Professor, > Division of Geriatric Medicine and Gerontology > School of Medicine > Johns Hopkins University > > Ph. (410) 502-2619 > email: rvarad...@jhmi.edu > > > ----- Original Message ----- > From: Daniel Haugstvedt <daniel.haugstv...@gmail.com> > Date: Tuesday, October 5, 2010 9:16 am > Subject: [R] subject: Log likelihood above 0 > To: r-help@r-project.org > > >> Hi - >> >> In an effort to learn some basic arima modeling in R i went through >> the tutorial found at >> >> >> One of the examples gave me a log likelihood of 77. Now I am simply >> wondering if this is the expected behavior? Looking in my text book >> this should not be possible. I have actually spent some time on this >> but neither the documentation ?arima or google gave me a satisfying >> answer. >> >> >> >> Data and code: >> >> gTemp.raw = c(-0.11, -0.13, -0.01, -0.04, -0.42, -0.23, -0.25, -0.45, >> -0.23, 0.04, -0.22, -0.55 >> , -0.40, -0.39, -0.32, -0.32, -0.27, -0.15, -0.21, -0.25, -0.05, >> -0.05, -0.30, -0.35 >> , -0.42, -0.25, -0.15, -0.41, -0.30, -0.31, -0.21, -0.25, -0.33, >> -0.28, -0.02, 0.06 >> , -0.20, -0.46, -0.33, -0.09, -0.15, -0.04, -0.09, -0.16, -0.11, >> -0.15, 0.04, -0.05 >> , 0.01, -0.22, -0.03, 0.03, 0.04, -0.11, 0.05, -0.08, 0.01, >> 0.12, 0.15, -0.02 >> , 0.14, 0.11, 0.10, 0.06, 0.10, -0.01, 0.01, 0.12, -0.03, >> -0.09, -0.17, -0.02 >> , 0.03, 0.12, -0.09, -0.09, -0.18, 0.08, 0.10, 0.05, -0.02, >> 0.10, 0.05, 0.03 >> , -0.25, -0.15, -0.07, -0.02, -0.09, 0.00, 0.04, -0.10, -0.05, >> 0.18, -0.06, -0.02 >> , -0.21, 0.16, 0.07, 0.13, 0.27, 0.40, 0.10, 0.34, 0.16, >> 0.13, 0.19, 0.35 >> , 0.42, 0.28, 0.49, 0.44, 0.16, 0.18, 0.31, 0.47, 0.36, >> 0.40, 0.71, 0.43 >> , 0.41, 0.56, 0.70, 0.66, 0.60) >> >> gTemp.ts = ts(gTemp.raw, start=1880, freq=1) >> >> gTemp.model = arima(diff(gTemp.ts), order=c(1,0,1)) >> >> >> >> Results: >> >>> gTemp.model >> >> Call: >> arima(x = diff(gTemp.ts), order = c(1, 0, 1)) >> >> Coefficients: >> ar1 ma1 intercept >> 0.2695 -0.8180 0.0061 >> s.e. 0.1122 0.0624 0.0030 >> >> sigma^2 estimated as 0.01680: log likelihood = 77.05, aic = -146.11 >> >> ______________________________________________ >> R-help@r-project.org mailing list >> >> PLEASE do read the posting guide >> and provide commented, minimal, self-contained, reproducible code. > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. -- Peter Dalgaard Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
