# Function called by optim to calculate the log likelihood from the probabilities and hence perform the fitting of regression models to the binary data. Fits specified regression models to the data. ```r LL.Regression.Counts(parameter, model.type, model.name, link, list.data, covariates.matrix.mean, covariates.matrix.scalef, offset.mean, offset.scalef, ltvalue, utvalue, fixed.b, weights, grad.method) ``` ## Arguments - `parameter`: A vector of the parameters of the model which is set to initial estimates on function call. - `model.type`: Takes one of two values i.e. 'mean only' or 'mean and scale-factor'. The 'mean only' value fits a linear predictor function to the parameter 'a' in equation (3) of of Faddy and Smith (2011). If the model type being fitted is Poisson modeling 'a' is the same as modeling the mean. The 'mean and scale-factor' value fits linear predictor functions to both the mean and the scale-factor. - `model.name`: If model.type is 'mean only' the model being fitted is one of the three 'Poisson', 'negative binomial', 'Faddy distribution'. If model.type is 'mean and scale-factor' the model being fitted is either 'general' i.e. as equations (4) and (6) of Faddy and Smith (2011), or 'limiting' i.e. as equations (9) and (10) of of Faddy and Smith (2011). - `link`: Takes one of one values i.e., 'log'. The default is 'log'. - `list.data`: A list of vectors of the counts as grouped data i.e. number of observations for each possible count value. - `covariates.matrix.mean`: A matrix of covariates for the mean where rows are the number of values in list.counts and columns the covariates. This matrix is extracted from the formulae in function CountsEPPM. However, in the accompanying example it is shown how it can be constructed independently of function CountsEPPM. - `covariates.matrix.scalef`: A matrix of covariates for the scale-factor where rows are the number of values in list.counts and columns the covariates. The default is a vector of ones. This matrix is extracted from the formulae in function CountsEPPM. However, in the accompanying example it is shown how it can be constructed independently of function CountsEPPM. - `offset.mean`: An offset vector for the mean. The default is a vector of ones. - `offset.scalef`: An offset vector for the scale-factor. The default is a vector of ones. - `ltvalue`: Lower truncation value. - `utvalue`: Upper truncation value. - `fixed.b`: Set to the value of the parameter b if a fixed.b model is being used. - `weights`: A vector or list of weights for the modeling of probability of success. The default is a vector of ones. - `grad.method`: Set to the method to be used to calculate the gradients either "simple" or "Richardson". ## Returns The log likelihood with an attribute of the gradients produced by the function grad from the package numDerive is returned. ## Author(s) David M. Smith ## References Faddy M, Smith D. (2011). Analysis of count data with covariate dependence in both mean and scale-factor. **Journal of Applied Statistics**, 38 , 2683-2694. tools:::Rd_expr_doi("10.1002/bimj.201100214") . ## Examples ```r all.counts=c(rep(0,5),352,479,530,291,101,17) nmax1 <- length(all.counts) nmax <- nmax1 - 1 cnum <- 0:nmax ncount <- sum(all.counts) all.mean <- sum(cnum*all.counts)/ncount all.scalef <- ((sum(cnum*cnum*all.counts) - ncount*all.mean*all.mean) / (ncount - 1)) / all.mean alldata <- data.frame(all.mean, all.scalef) mf <- model.frame(formula = all.mean~1, data = alldata) covariates.matrix.mean <- model.matrix(attr(mf, "terms"), data = mf) mf <- model.frame(formula=all.scalef~1, data=alldata) covariates.matrix.scalef <- model.matrix(attr(mf, "terms"), data=mf) list.data <- list(all.counts) parameter <- c(1.8388023, 0.6009881) names(parameter) <- c("beta0 log(mean)", "beta0 log(scale-factor)") offset.mean <- matrix(c(rep(0,nrow(covariates.matrix.mean))), ncol=1) offset.scalef <- matrix(c(rep(0,nrow(covariates.matrix.scalef))), ncol=1) link <- "log" attr(link, which="mean") <- make.link(link) output <- LL.Regression.Counts(parameter, model.type = "mean and scale-factor", model.name = "limiting", link, list.data, covariates.matrix.mean, covariates.matrix.scalef, offset.mean, offset.scalef, ltvalue=4, utvalue=11, fixed.b=NA, weights = NULL, grad.method = "simple") print(output) ```

LL.Regression.Counts function