Re: [R] Theta from negative binomial regression and power_NegativeBinomiial from PASSED
Yes, theta is the 'size' or overdispersion parameter. Sometimes also denoted as k. Wikipedia discusses this parameterization in the paragraph starting "In negative binomial regression ..." (but they call this parameter r rather than theta or k). You can also see this in MASS on google books: https://www.google.ca/books/edition/Modern_Applied_Statistics_with_S/CzwmBQAAQBAJ?hl=en=1=venables+ripley+negative+binomial=PA206=frontcover This parameterization was added to R in version 1.3.0 ... On 2023-09-15 2:27 a.m., Ivan Krylov wrote: On Fri, 15 Sep 2023 01:51:27 + "Sorkin, John" wrote: What is theta, and how does it relate to the parameters of the negative binomial distribution? Plugging the p (the success probability) and the r (the number of successes until the experiment is stopped) from the Wikipedia article (where they are defined in terms of mean mu and variance sigma^2) together with the variance from ?MASS::rnegbin (where it's defined as mu + mu^2/theta) into Maxima and then solving for theta, I get: solve( [ p = mu / sigma^2, r = mu^2/(sigma^2-mu), sigma^2 = mu + mu^2/theta ], [mu, sigma, theta] ); [ mu = ((1-p)*r)/p, sigma = sqrt(r-p*r)/p, theta = r ] That is, the theta from MASS seems to be equivalent to the number of successes from the formulation in the Wikipedia article. -- Dr. Benjamin Bolker Professor, Mathematics & Statistics and Biology, McMaster University Director, School of Computational Science and Engineering (Acting) Graduate chair, Mathematics & Statistics > E-mail is sent at my convenience; I don't expect replies outside of working hours. __ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
Re: [R] Theta from negative binomial regression and power_NegativeBinomiial from PASSED
On Fri, 15 Sep 2023 01:51:27 + "Sorkin, John" wrote: > What is theta, and how does it relate to the parameters of the > negative binomial distribution? Plugging the p (the success probability) and the r (the number of successes until the experiment is stopped) from the Wikipedia article (where they are defined in terms of mean mu and variance sigma^2) together with the variance from ?MASS::rnegbin (where it's defined as mu + mu^2/theta) into Maxima and then solving for theta, I get: solve( [ p = mu / sigma^2, r = mu^2/(sigma^2-mu), sigma^2 = mu + mu^2/theta ], [mu, sigma, theta] ); [ mu = ((1-p)*r)/p, sigma = sqrt(r-p*r)/p, theta = r ] That is, the theta from MASS seems to be equivalent to the number of successes from the formulation in the Wikipedia article. -- Best regards, Ivan __ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
[R] Theta from negative binomial regression and power_NegativeBinomiial from PASSED
Colleagues, I want to use the power_NetativeBinomial function from the PASSED library. The function requires a value for a parameter theta. The meaning of theta is not given in the documentation (at least I can�t find it) of the function. Further the descriptions of the negative binomial distribution that I am familiar with do not mention theta as being a parameter of the distribution. I noticed that when one runs the glm.nb function to perform a negative binomial regression one obtains a value for theta. This leads to two questions 1. Is the theta required by the power_NetativeBinomial function the theta that is produced by the glm.nb function 2. What is theta, and how does it relate to the parameters of the negative binomial distribution? Thank you, John [[alternative HTML version deleted]] __ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
