> On Jan 23, 2016, at 5:24 AM, mara.pfleide...@uni-ulm.de wrote: > > Hi David, > > I'm sorry. I'm not familiar with posting problems on helppages. > As the data I deal with is confidential I can't provide all details, > but I will try to be as precise as possible about my problem: > > As I said I'm working on a Poisson regression model with a linear > predictor and the identity as link function.
Then that is not what most people would call a "Poisson regression model". In particular: I have data which consists of observations of two random variables X and Y over the period of about 3 months. I have clustered this data into hours, so I received 2088 observations of those variables and each observation represents the values of the variables in one hour. Now I assume Y to be Poisson distributed (Y_i~Poi(lambda_i)) and that the values of Y come from two different impacts, so I split Y_i into two Poisson-distributed variables Y_i1 and Y_i2. I assume that the values of X have a long-term effect (of at least one day) on the part Y_i1 and I have estimators for the parameters lambda_i2, but I have no exact values of the variables of Y_i1 and Y_i2 but only of Y_i as a whole. > So my model looks as follows: > fml=Y_i1 ~ b_1*X_i+....+b_n*X_(i-n+1) - lambda_i2 -1 with n>=24 > That means that the last 24 (or more) values of X influence the value of Y_i1 > in an additive way and I have no intercept(b_0=0). > Now I made a matrix whose rows represent Y_i, all of its 24 (or more) > regressors for each observation of Y_i and the corresponding estimator > lambda_i2. > Then I used glm(fml, family=poisson(link="identity"), data=matrix) and tried > it for different values of n (=24,48,36,...). I worry that might not construct the model you described above. The use of `poisson` constructs Poisson distributed _errors_ with an additive link, and to my understanding does _not_ assume Poisson distributed Y values. > But always some of the coefficients received negative values which doesnt't > make sense in interpretation. (The values of X represent certain events which > can only have a positive or none effect on the value of Y.) > > Now I want to use the constraint b_i >=0 in my model, but I don't know how I > can do this. > > I also thought of analyzing this model in a Bayesian way, but yet I haven't > found a Bayesian version of glm() for the Poisson distribution such that I > can specify the prior for the b_i on my own. (Then I could include the > positivity in the prior.) Do you have a hint for me? The R blogoshere has been heralding the arrival of the `rstanarm` package which provides a glm-like interface to an MCMC (Bayesian) estimation engine. Version 2.90 is on CRAN. The list of authors in the description file is impressive: Authors@R: c(person("Jonah", "Gabry", email = "jsg2...@columbia.edu", role = "aut"), person("Trustees of", "Columbia University", role = "cph"), person("R Core", "Deveopment Team", role = "cph", comment = "R/pp_data.R, R/stan_aov.R"), person("Douglas", "Bates", role = "cph", comment = "R/pp_data.R"), person("Martin", "Maechler", role = "cph", comment = "R/pp_data.R"), person("Ben", "Bolker", role = "cph", comment = "R/pp_data.R"), person("Steve", "Walker", role = "cph", comment = "R/pp_data.R"), person("Brian", "Ripley", role = "cph", comment = "R/stan_aov.R, R/stan_polr.R"), person("William", "Venables", role = "cph", comment = "R/stan_polr.R"), person("Ben", "Goodrich", email = "benjamin.goodr...@columbia.edu", role = c("cre", "aut"))) > > I'm sorry if I went too much into detail now... > I hope you understand my point now and have some answers for me! > > Best, > Mara > > > Zitat von David Winsemius <dwinsem...@comcast.net>: > >> >>> On Jan 22, 2016, at 7:01 AM, mara.pfleide...@uni-ulm.de wrote: >>> >>> Hi all, >>> >>> I am dealing with a problem about my linear Poisson regression model >>> (link function=identity). >>> >>> I am using the glm()-function which results in negative coefficients, but >>> a negative influence of the regressors wouldn't make sense. >> >> Negative coefficients merely indicate a lower relative rate. You need to >> be more specific about the exactly data and model output before you can >> raise our concern to a level where further comment can be made. >> >> >>> >>> (i) Is there a possibility to set constraints on the regression >>> parameters in glm() such that all coefficients are positive? Or is there >>> another function in R for which this is possible? >>> >>> (ii) Is there a Bayesian version of the glm()-function where I can >>> specify the prior distribution for my regression parameters? (e.g. a >>> Dirichlet prior s.t. the parameters are positive) >>> >>> All this with respect to the linear Poisson model... >> >> As I implied above, the word "linear" means something different than >> "additive" when the link is log(). >> >> -- >> >> David Winsemius >> Alameda, CA, USA >> David Winsemius Alameda, CA, USA ______________________________________________ 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.