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. 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.
