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#' @templateVar name_model_full Pareto/NBD
#' @template template_class_clvmodelnocov
#'
#' @keywords internal
#' @seealso Other clv model classes \linkS4class{clv.model}, \linkS4class{clv.model.pnbd.static.cov}, \linkS4class{clv.model.pnbd.dynamic.cov}
#' @seealso Classes using its instance: \linkS4class{clv.fitted}
#' @include all_generics.R class_clv_model_withcorrelation.R
#' @importFrom methods setClass
setClass(Class = "clv.model.pnbd.no.cov", contains = "clv.model.with.correlation")
#' @importFrom methods new
clv.model.pnbd.no.cov <- function(){
return(new("clv.model.pnbd.no.cov",
name.model = "Pareto/NBD Standard",
names.original.params.model = c(r="r", alpha="alpha", s="s", beta="beta"),
names.prefixed.params.model = c("log.r","log.alpha", "log.s", "log.beta"),
start.params.model = c(r=1, alpha=1, s=1, beta=1),
optimx.defaults = list(method = "L-BFGS-B",
# lower = c(log(1*10^(-5)),log(1*10^(-5)),log(1*10^(-5)),log(1*10^(-5))),
# upper = c(log(300),log(2000),log(300),log(2000)),
itnmax = 3000,
control = list(
kkt = TRUE,
save.failures = TRUE,
# Do not perform starttests because it checks the scales with max(logpar)-min(logpar)
# but all standard start parameters are <= 0, hence there are no logpars what
# produces a warning
starttests = FALSE))))
}
# Methods --------------------------------------------------------------------------------------------------------------------------------
# .clv.model.check.input.args -----------------------------------------------------------------------------------------------------------
setMethod(f = "clv.model.check.input.args", signature = signature(clv.model="clv.model.pnbd.no.cov"), definition = function(clv.model, clv.fitted, start.params.model, optimx.args, verbose, use.cor, start.param.cor, ...){
err.msg <- c()
# Have to be > 0 as will be logged
if(any(start.params.model <= 0))
err.msg <- c(err.msg, "Please provide only model start parameters greater than 0 as they will be log()-ed for the optimization!")
err.msg <- c(err.msg, .check_user_data_single_boolean(b=use.cor, var.name ="use.cor"))
err.msg <- c(err.msg, check_user_data_startparamcorm(start.param.cor=start.param.cor, use.cor=use.cor))
check_err_msg(err.msg)
})
# .clv.model.put.estimation.input --------------------------------------------------------------------------------------------------------
# Nothing required, use clv.model.with.correlation
# .clv.model.transform.start.params.model --------------------------------------------------------------------------------------------------------
#' @importFrom stats setNames
setMethod("clv.model.transform.start.params.model", signature = signature(clv.model="clv.model.pnbd.no.cov"), definition = function(clv.model, original.start.params.model){
# Log all user given or default start params
return(setNames(log(original.start.params.model[clv.model@names.original.params.model]),
clv.model@names.prefixed.params.model))
})
# .clv.model.backtransform.estimated.params.model --------------------------------------------------------------------------------------------------------
setMethod("clv.model.backtransform.estimated.params.model", signature = signature(clv.model="clv.model.pnbd.no.cov"), definition = function(clv.model, prefixed.params.model){
# exp all prefixed params
return(exp(prefixed.params.model[clv.model@names.prefixed.params.model]))
})
# .clv.model.prepare.optimx.args --------------------------------------------------------------------------------------------------------
#' @importFrom utils modifyList
setMethod(f = "clv.model.prepare.optimx.args", signature = signature(clv.model="clv.model.pnbd.no.cov"), definition = function(clv.model, clv.fitted, prepared.optimx.args){
# Only add LL function args, everything else is prepared already, incl. start parameters
optimx.args <- modifyList(prepared.optimx.args,
list(LL.function.sum = pnbd_nocov_LL_sum,
LL.function.ind = pnbd_nocov_LL_ind, # if doing correlation
obj = clv.fitted,
vX = clv.fitted@cbs$x,
vT_x = clv.fitted@cbs$t.x,
vT_cal = clv.fitted@cbs$T.cal,
# parameter ordering for the callLL interlayer
LL.params.names.ordered = c(log.r="log.r", log.alpha="log.alpha",
log.s="log.s", log.beta="log.beta")),
keep.null = TRUE)
return(optimx.args)
})
# . clv.model.process.post.estimation -----------------------------------------------------------------------------------------
setMethod("clv.model.process.post.estimation", signature = signature(clv.model="clv.model.pnbd.no.cov"), definition = function(clv.model, clv.fitted, res.optimx){
# No additional step needed (ie store model specific stuff, extra process)
return(clv.fitted)
})
# .clv.model.cor.to.m --------------------------------------------------------------------------------------------------------
setMethod(f="clv.model.cor.to.m", signature = signature(clv.model="clv.model.pnbd.no.cov"), definition = function(clv.model, prefixed.params.model, param.cor){
.cor.part <- function(params){
r <- exp(params[["log.r"]])
alpha <- exp(params[["log.alpha"]])
s <- exp(params[["log.s"]])
beta <- exp(params[["log.beta"]])
fct.part <- function(param.ab, param.rs){
return( (sqrt(param.rs) / (1+param.ab)) * ((param.ab / (1+param.ab))^param.rs))
}
return(fct.part(param.ab = alpha, param.rs = r) * fct.part(param.ab = beta, param.rs = s))
}
res.m <- param.cor / .cor.part(params=prefixed.params.model)
# return unnamed as otherwise still called "cor"
return(unname(res.m))
})
setMethod(f="clv.model.m.to.cor", signature = signature(clv.model="clv.model.pnbd.no.cov"), definition = function(clv.model, prefixed.params.model, param.m){
.cor.part <- function(params){
r <- exp(params[["log.r"]])
alpha <- exp(params[["log.alpha"]])
s <- exp(params[["log.s"]])
beta <- exp(params[["log.beta"]])
fct.part <- function(param.ab, param.rs){
return( (sqrt(param.rs) / (1+param.ab)) * ((param.ab / (1+param.ab))^param.rs) )
}
return(fct.part(param.ab = alpha, param.rs = r) * fct.part(param.ab = beta, param.rs = s))
}
res.cor <- param.m * .cor.part(params=prefixed.params.model)
# return unnamed as otherwise still called "m"
return(unname(res.cor))
})
# .clv.model.vcov.jacobi.diag --------------------------------------------------------------------------------------------------------
setMethod(f = "clv.model.vcov.jacobi.diag", signature = signature(clv.model="clv.model.pnbd.no.cov"), definition = function(clv.model, clv.fitted, prefixed.params){
# Jeff:
# Delta method:
# h=(log(t),log(t),log(t),log(t),t,t,t)
# g=h^-1=(exp(t),exp(t),exp(t),exp(t),t,t,t)
# Deltaexp = g' = (exp(t),exp(t),exp(t),exp(t),1,1,1)
# Create matrix with the full required size
m.diag <- diag(x = 0, ncol = length(prefixed.params), nrow=length(prefixed.params))
rownames(m.diag) <- colnames(m.diag) <- names(prefixed.params)
# Add the transformations for the model to the matrix
# All model params need to be exp()
m.diag[clv.model@names.prefixed.params.model,
clv.model@names.prefixed.params.model] <- diag(x = exp(prefixed.params[clv.model@names.prefixed.params.model]),
nrow = length(clv.model@names.prefixed.params.model),
ncol = length(clv.model@names.prefixed.params.model))
# If correlation, add the transformations for each parameter vs correlation param.m
if(clv.model@estimation.used.correlation){
# This is same as m.to.cor
cor.phi <- function(param.m, a, r, s, b){
return(param.m * (sqrt(r)/(1+a)) * (a/(1+a))^r * (sqrt(s)/(1+b)) * (b/(1+b))^s)
}
a <- exp(prefixed.params["log.alpha"])
r <- exp(prefixed.params["log.r"])
b <- exp(prefixed.params["log.beta"])
s <- exp(prefixed.params["log.s"])
param.m <- prefixed.params[clv.model@name.prefixed.cor.param.m]
# eq 2
phi_dloga <- cor.phi(param.m=param.m, a=a, r=r, b=b, s=s) * (r - ((a*(1+r))/(1+a)))
# eq 3
phi_dlogb <- cor.phi(param.m=param.m, a=a, r=r, b=b, s=s) * (s - ((b*(1+s))/(1+b)))
# eq 4
phi_dlogr <- cor.phi(param.m=param.m, a=a, r=r, b=b, s=s) * (0.5 - r*log(1+a) + r*log(a))
# eq 5
phi_dlogs <- cor.phi(param.m=param.m, a=a, r=r, b=b, s=s) * (0.5 - s*log(1+b) + s*log(b))
# eq 6
phi_dlogm <- (sqrt(r)/(1+a)) * (a/(1+a))^r * (sqrt(s)/(1+b)) * (b/(1+b))^s
# Add to transformation matrix on last line only! (not aswell on the last column)
m.diag[clv.model@name.prefixed.cor.param.m, "log.alpha"] <- phi_dloga
m.diag[clv.model@name.prefixed.cor.param.m, "log.r"] <- phi_dlogr
m.diag[clv.model@name.prefixed.cor.param.m, "log.beta"] <- phi_dlogb
m.diag[clv.model@name.prefixed.cor.param.m, "log.s"] <- phi_dlogs
m.diag[clv.model@name.prefixed.cor.param.m,
clv.model@name.prefixed.cor.param.m] <- phi_dlogm
}
return(m.diag)
})
# clv.model.process.newdata --------------------------------------------------------------------------------------------------------
setMethod(f = "clv.model.process.newdata", signature = signature(clv.model = "clv.model.pnbd.no.cov"), definition = function(clv.model, clv.fitted, verbose){
# clv.data in clv.fitted is already replaced with newdata here
# Only need to redo cbs if new data is given
clv.fitted@cbs <- pnbd_cbs(clv.data = clv.fitted@clv.data)
return(clv.fitted)
})
# clv.model.predict --------------------------------------------------------------------------------------------------------
setMethod("clv.model.predict", signature(clv.model="clv.model.pnbd.no.cov"), definition = function(clv.model, clv.fitted, dt.predictions, verbose, continuous.discount.factor, ...){
period.length <- Id <- x <- t.x <- T.cal <- PAlive <- i.PAlive <- CET <- i.CET <- DERT <- i.DERT <- NULL # cran silence
predict.number.of.periods <- dt.predictions[1, period.length]
# To ensure sorting, do everything in a single table
dt.result <- copy(clv.fitted@cbs[, c("Id", "x", "t.x", "T.cal")])
# Add CET
dt.result[, CET := pnbd_nocov_CET(r = clv.fitted@prediction.params.model[["r"]],
alpha_0 = clv.fitted@prediction.params.model[["alpha"]],
s = clv.fitted@prediction.params.model[["s"]],
beta_0 = clv.fitted@prediction.params.model[["beta"]],
dPeriods = predict.number.of.periods,
vX = x,
vT_x = t.x,
vT_cal = T.cal)]
# Add PAlive
dt.result[, PAlive := pnbd_nocov_PAlive(r = clv.fitted@prediction.params.model[["r"]],
alpha_0 = clv.fitted@prediction.params.model[["alpha"]],
s = clv.fitted@prediction.params.model[["s"]],
beta_0 = clv.fitted@prediction.params.model[["beta"]],
vX = x,
vT_x = t.x,
vT_cal = T.cal)]
# Add DERT
dt.result[, DERT := pnbd_nocov_DERT(r = clv.fitted@prediction.params.model[["r"]],
alpha_0 = clv.fitted@prediction.params.model[["alpha"]],
s = clv.fitted@prediction.params.model[["s"]],
beta_0 = clv.fitted@prediction.params.model[["beta"]],
continuous_discount_factor = continuous.discount.factor,
vX = x,
vT_x = t.x,
vT_cal = T.cal)]
# Add results to prediction table, by matching Id
dt.predictions[dt.result, CET := i.CET, on = "Id"]
dt.predictions[dt.result, PAlive := i.PAlive, on = "Id"]
dt.predictions[dt.result, DERT := i.DERT, on = "Id"]
return(dt.predictions)
})
# . clv.model.expectation --------------------------------------------------------------------------------------------------------
setMethod("clv.model.expectation", signature(clv.model="clv.model.pnbd.no.cov"), function(clv.model, clv.fitted, dt.expectation.seq, verbose){
r <- s <- alpha_i <- beta_i <- date.first.actual.trans <- T.cal <- t_i <- NULL
params_i <- clv.fitted@cbs[, c("Id", "T.cal", "date.first.actual.trans")]
fct.expectation <- function(params_i.t) {return(pnbd_nocov_expectation(r = clv.fitted@prediction.params.model[["r"]],
s = clv.fitted@prediction.params.model[["s"]],
alpha_0 = clv.fitted@prediction.params.model[["alpha"]],
beta_0 = clv.fitted@prediction.params.model[["beta"]],
vT_i = params_i.t$t_i))}
return(DoExpectation(dt.expectation.seq = dt.expectation.seq, params_i = params_i,
fct.expectation = fct.expectation, clv.time = clv.fitted@clv.data@clv.time))
})
# . clv.model.pmf --------------------------------------------------------------------------------------------------------
setMethod("clv.model.pmf", signature=(clv.model="clv.model.pnbd.no.cov"), function(clv.model, clv.fitted, x){
Id <- T.cal <- pmf.x <- NULL
dt.res <- clv.fitted@cbs[, list(Id, T.cal)]
dt.res[, pmf.x := pnbd_nocov_PMF(r = clv.fitted@prediction.params.model[["r"]],
alpha_0 = clv.fitted@prediction.params.model[["alpha"]],
s = clv.fitted@prediction.params.model[["s"]],
beta_0 = clv.fitted@prediction.params.model[["beta"]],
vT_i = T.cal,
x = x)]
dt.res <- dt.res[, list(Id, pmf.x)]
setnames(dt.res, "pmf.x", paste0("pmf.x.", x))
return(dt.res)
})
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