add 'loss' to the list of brms data sets

R/brm.R

@@ -326,16 +326,21 @@
 #' summary(fit4)
 #'
 #'
-#' # Simple non-linear gaussian model
-#' x <- rnorm(100)
-#' y <- rnorm(100, mean = 2 - 1.5^x, sd = 1)
-#' data5 <- data.frame(x, y)
-#' prior5 <- prior(normal(0, 2), nlpar = a1) +
-#'   prior(normal(0, 2), nlpar = a2)
-#' fit5 <- brm(bf(y ~ a1 - a2^x, a1 + a2 ~ 1, nl = TRUE),
-#'             data = data5, prior = prior5)
+#' # Non-linear Gaussian model
+#' fit5 <- brm(
+#'   bf(cum ~ ult * (1 - exp(-(dev/theta)^omega)),
+#'      ult ~ 1 + (1|AY), omega ~ 1, theta ~ 1, 
+#'      nl = TRUE),
+#'   data = loss, family = gaussian(),
+#'   prior = c(
+#'     prior(normal(5000, 1000), nlpar = "ult"),
+#'     prior(normal(1, 2), nlpar = "omega"),
+#'     prior(normal(45, 10), nlpar = "theta")
+#'   ),
+#'   control = list(adapt_delta = 0.9)
+#' )
 #' summary(fit5)
-#' plot(conditional_effects(fit5), ask = FALSE)
+#' conditional_effects(fit5)
 #'
 #'
 #' # Normal model with heterogeneous variances

R/datasets.R

@@ -24,6 +24,10 @@
 #'    and \code{PKD} specifying the type of disease}
 #' }
 #' 
+#' @source McGilchrist, C. A., & Aisbett, C. W. (1991). 
+#'   Regression with frailty in survival analysis. 
+#'   \emph{Biometrics}, 47(2), 461-466.
+#' 
 #' @examples 
 #' \dontrun{
 #' ## performing surivival analysis using the "weibull" family
@@ -40,9 +44,6 @@
 #' plot(fit2)         
 #' }
 #' 
-#' @source McGilchrist, C. A., & Aisbett, C. W. (1991). 
-#'   Regression with frailty in survival analysis. 
-#'   \emph{Biometrics, 47(2)}, 461-466.
 "kidney"
 
 
@@ -66,6 +67,10 @@
 #'  \item{carry}{A contrast to indicate possible carry over effects}
 #' } 
 #' 
+#' @source Ezzet, F., & Whitehead, J. (1991). 
+#'   A random effects model for ordinal responses from a crossover trial. 
+#'   \emph{Statistics in Medicine}, 10(6), 901-907.
+#'   
 #' @examples
 #' \dontrun{
 #' ## ordinal regression with family "sratio"
@@ -84,9 +89,6 @@
 #' plot(fit2)
 #' }
 #' 
-#' @source Ezzet, F., & Whitehead, J. (1991). 
-#'   A random effects model for ordinal responses from a crossover trial. 
-#'   \emph{Statistics in Medicine, 10(6)}, 901-907.
 "inhaler"
 
 
@@ -114,7 +116,15 @@
 #'  \item{zAge}{Standardized \code{Age}}
 #'  \item{zBase}{Standardized \code{Base}}
 #' } 
-#' 
+#'  
+#' @source Thall, P. F., & Vail, S. C. (1990). 
+#'  Some covariance models for longitudinal count data with overdispersion. 
+#'  \emph{Biometrics, 46(2)}, 657-671. \cr
+#'    
+#' Breslow, N. E., & Clayton, D. G. (1993). 
+#'  Approximate inference in generalized linear mixed models. 
+#'  \emph{Journal of the American Statistical Association}, 88(421), 9-25.
+#'  
 #' @examples
 #' \dontrun{
 #' ## poisson regression without random effects. 
@@ -131,12 +141,54 @@
 #' summary(fit2) 
 #' plot(fit2)
 #' }
-#'  
-#' @source Thall, P. F., & Vail, S. C. (1990). 
-#'  Some covariance models for longitudinal count data with overdispersion. 
-#'  \emph{Biometrics, 46(2)}, 657-671. \cr
-#'    
-#' Breslow, N. E., & Clayton, D. G. (1993). 
-#'  Approximate inference in generalized linear mixed models. 
-#'  \emph{Journal of the American Statistical Association, 88(421)}, 9-25.
-"epilepsy"
+#' 
+"epilepsy"
+
+#' Cumulative Insurance Loss Payments
+#' 
+#' @description This dataset, discussed in Gesmann & Morris (2020), contains
+#'   cumulative insurance loss payments over the course of ten years.
+#' 
+#' @format A data frame of 55 observations containing information 
+#'   on the following 4 variables. 
+#' \describe{
+#'  \item{AY}{Origin year of the insurance (1991 to 2000)}
+#'  \item{dev}{Deviation from the origin year in months}
+#'  \item{cum}{Cumulative loss payments} 
+#'  \item{premimum}{Achieved premiums for the given origin year}
+#' } 
+#' 
+#' @source Gesmann M. & Morris J. (2020). Hierarchical Compartmental Reserving 
+#'   Models. \emph{CAS Research Papers}.
+#' 
+#' @examples 
+#' \dontrun{
+#' # non-linear model to predict cumulative loss payments
+#' fit_loss <- brm(
+#'   bf(cum ~ ult * (1 - exp(-(dev/theta)^omega)),
+#'      ult ~ 1 + (1|AY), omega ~ 1, theta ~ 1, 
+#'      nl = TRUE),
+#'   data = loss, family = gaussian(),
+#'   prior = c(
+#'     prior(normal(5000, 1000), nlpar = "ult"),
+#'     prior(normal(1, 2), nlpar = "omega"),
+#'     prior(normal(45, 10), nlpar = "theta")
+#'   ),
+#'   control = list(adapt_delta = 0.9)
+#' )
+#' 
+#' # basic summaries
+#' summary(fit_loss)
+#' conditional_effects(fit_loss)
+#' 
+#' # plot predictions per origin year
+#' conditions <- data.frame(AY = unique(loss$AY))
+#' rownames(conditions) <- unique(loss$AY)
+#' me_loss <- conditional_effects(
+#'   fit_loss, conditions = conditions, 
+#'   re_formula = NULL, method = "predict"
+#' )
+#' plot(me_loss, ncol = 5, points = TRUE)
+#' }
+#' 
+"loss"

doc/brms_nonlinear.R

@@ -50,7 +50,7 @@ pp_check(fit2)
 loo(fit1, fit2)
 
 ## ---------------------------------------------------------------------------------------
-loss <- read.csv("https://paul-buerkner.github.io/data/loss.csv")
+data(loss)
 head(loss)
 
 ## ---- results='hide'--------------------------------------------------------------------

doc/brms_nonlinear.Rmd

@@ -100,15 +100,15 @@ formula should be treated as non-linear.
 
 In contrast to generalized linear models, priors on population-level parameters
 (i.e., 'fixed effects') are often mandatory to identify a non-linear model.
-Thus, **brms** requires the user to explicitely specify these priors. In the
+Thus, **brms** requires the user to explicitly specify these priors. In the
 present example, we used a `normal(1, 2)` prior on (the population-level
 intercept of) `b1`, while we used a `normal(0, 2)` prior on (the
 population-level intercept of) `b2`. Setting priors is a non-trivial task in all
 kinds of models, especially in non-linear models, so you should always invest
 some time to think of appropriate priors. Quite often, you may be forced to
 change your priors after fitting a non-linear model for the first time, when you
 observe different MCMC chains converging to different posterior regions. This is
-a clear sign of an idenfication problem and one solution is to set stronger
+a clear sign of an identification problem and one solution is to set stronger
 (i.e., more narrow) priors.
 
 To obtain summaries of the fitted model, we apply
@@ -151,13 +151,13 @@ loo(fit1, fit2)
 
 Since smaller `LOOIC` values indicate better model fit, it is immediately
 evident that the non-linear model fits the data better, which is of course not
-too surpirsing since we simulated the data from exactly that model.
+too surprising since we simulated the data from exactly that model.
 
 ## A Real-World Non-Linear model
 
 On his blog, Markus Gesmann predicts the growth of cumulative insurance loss
 payments over time, originated from different origin years (see
-http://www.magesblog.com/post/2015/11/loss-developments-via-growth-curves-and.html).
+https://www.magesblog.com/post/2015-11-03-loss-developments-via-growth-curves-and/).
 We will use a slightly simplified version of his model for demonstration
 purposes here. It looks as follows:
 
@@ -169,10 +169,10 @@ dependency using the variable $dev$. Further, $ult_{AY}$ is the (to be
 estimated) ultimate loss of accident each year. It constitutes a non-linear
 parameter in our framework along with the parameters $\theta$ and $\omega$,
 which are responsible for the growth of the cumulative loss and are assumed to
-be the same across years. We load the data
+be the same across years. The data is already shipped with brms.
 
 ```{r}
-loss <- read.csv("https://paul-buerkner.github.io/data/loss.csv")
+data(loss)
 head(loss)
 ```
 
@@ -221,7 +221,8 @@ plot(me_loss, ncol = 5, points = TRUE)
 It is evident that there is some variation in cumulative loss across accident
 years, for instance due to natural disasters happening only in certain years.
 Further, we see that the uncertainty in the predicted cumulative loss is larger
-for later years with fewer available data points.
+for later years with fewer available data points. For a more detailed discussion
+of this data set, see Section 4.5 in Gesmann & Morris (2020).
 
 ## Advanced Item-Response Models
 
@@ -323,3 +324,8 @@ that accounting for item and person variability (e.g., using a multilevel model
 with varying intercepts) becomes necessary as we have multiple observations per
 item and person. Luckily, this can all be done within the non-linear framework
 of **brms** and I hope that this vignette serves as a good starting point.
+
+## References 
+
+Gesmann M. & Morris J. (2020). Hierarchical Compartmental Reserving Models.
+*CAS Research Papers*.