Yes, of course! So, the complete answer is: the log-likelihood can be in (-Inf, Inf), regardless of whether the random variable is continuous or discrete or mixed.
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: peter dalgaard <pda...@gmail.com> Date: Tuesday, October 5, 2010 9:49 am Subject: Re: [R] subject: Log likelihood above 0 To: Ravi Varadhan <rvarad...@jhmi.edu> Cc: Daniel Haugstvedt <daniel.haugstv...@gmail.com>, r-help@r-project.org > 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 > > > > PLEASE do read the posting guide > > 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.