rdata {pricelevels}

Simulate random price and quantity data

Description

Simulate random price and quantity data for a specified number of regions (r=1,\ldots,R), product groups (b=1,\ldots,B), and individual products (n=1,\ldots,N_{b}) using function rdata().

The sampling of prices relies on the NLCPD model (see nlcpd()), while expenditure weights for product groups are sampled using function rweights(). Purchased quantities are assigned to individual products. Moreover, random sales and gaps (using function rgaps()) can be introduced in the sampled data.

Usage

rgaps(r, n, amount=0, prob=NULL, pairs=FALSE, exclude=NULL)

rweights(r, b, type=~1)

rdata(R, B, N, gaps=0, weights=~b+r, sales=0, settings=list())

Arguments

r, n, b

A character vector or factor of regional entities r, individual products n, and product groups (or basic headings) b, respectively.

R, B, N

A single integer specifying the number of regions R and product groups B, respectively, and a vector of length B specifying the number of individual products N in each product group.

weights, type

A formula specifying the sampling of expenditure weights for product groups. If type=~1, product groups receive identical weights, while weights are product group specific for type=~b. If weights should vary among product groups and regions, use type=~b+r. As long as there are no data gaps, the weights add up to 1 for each region.

gaps, sales, amount

Percentage amount of gaps and sales (between 0 and 1), respectively, to be introduced in the data.

prob

A vector of probability weights, see also sample(). Either NULL or the same length as r and n. Larger values make gaps occur more likely at this position.

pairs

A logical indicating if gaps should be introduced such that there are always at least two observations per product available (pairs=TRUE). Only in this case, all products provide valuable information for a spatial price comparison. Otherwise, if pairs=FALSE, there can be products with only one observation. See also the Details section.

exclude

Data.frame of two (character) variables r and n, specifying regions and products to be excluded from introducing gaps. Default is NULL, meaning that gaps are allowed to occur in all regions and products present in the data. Missing values (NA) are translated into no gaps for the corresponding product or region, e.g. data.frame(r="r1", n=NA) means that there will be no gaps in region r1.

settings

A list of control settings to be used. The following settings are supported:

• gaps.prob : See argument prob.

• gaps.pairs : See argument pairs.

• gaps.exclude : See argument exclude.

• sales.max.rebate : Maximum allowed percentage price rebate for a sale (between 0 and 1). Default is 1/4.

• sales.max.qi : Maximum allowed percentage quantity decrease for a sale (between 0 and 1). Default is 2.

• par.sd : named vector specifying the standard deviations used for sampling true parameters and errors. Default is c(lnP=0.1, pi=exp(1), delta=0.5, error=0.01).

• par.add : logical, specifying if the parameters underlying the data generating process should be added the function output. This is particularly useful if rdata() is applied in simulations. Default is FALSE.

• round : logical, specifying if prices should be rounded to two decimals or not. While prices usually have two decimal places in reality, this rounding can cause small differences between estimated and true parameter values. For simulation purposes, it is therefore recommended to use unrounded prices by setting round=FALSE.

Details

Function rgaps() ensures that gaps do not lead to non-connected price data (see is.connected()). Therefore, it could happen that the amount of gaps specified in rgaps() is only approximate, in particular, in cases where certain regions and/or products should additionally be excluded from exhibiting gaps by exclude.

If rgaps(pairs=FALSE), the minimum number of observations for a connected data set is R+N-1. Otherwise, for rgaps(pairs=TRUE), this number is defined by 2N+\text{max}(0, R-N-1).

Note that setting sales>0 in function rdata() distorts the initial price generating process. Consequently, parameter estimates may deviate stronger from their true values. Note also that the sampled expenditure weights weight represent the relevance of product groups as (often) derived from national accounts and other data sources. Therefore, they cannot be derived from the sampled prices and quantities in the data, which would represent the expenditure shares of available products.

Value

Function rgaps() returns a logical vector of the same length as r where TRUEs indicate gaps and FALSEs no gaps.

Function rweights() returns a numeric vector of (non-negative) expenditure share weights of the same length as r.

Function rdata() returns a data.table with the following variables:

group		product group identifier (factor)
weight		expenditure weight of product groups (numeric)
region		region identifier (factor)
product		product identifier (factor)
sale		are prices and quantities affected by sales (logical)
price		sampled price (numeric)
quantity		consumed quantity (numeric)
share		expenditure share weights (numeric)

or a list with the sampled data and its underlying parameter values, if settings=list(par.add=TRUE).

Author(s)

Sebastian Weinand

Examples

# sample price data for ten regions and five product groups
# containing three individual products each:
set.seed(1)
dt <- rdata(R=10, B=5, N=3)
boxplot(price~paste(group, product, sep=":"), data=dt)

# sample price data for ten regions and five product groups
# containing one to five individual products:
set.seed(1)
dt <- rdata(R=10, B=5, N=c(1,2,3,4,5))
boxplot(price~paste(group, product, sep=":"), data=dt)

# sample price data for three product groups (with one product each) in four regions:
dt <- rdata(R=4, B=3, N=1)

# add expenditure share weights:
dt[, "w1" := rweights(r=region, b=group, type=~1)] # constant
dt[, "w2" := rweights(r=region, b=group, type=~b)] # product-specific
dt[, "w3" := rweights(r=region, b=group, type=~b+r)] # product-region-specific

# weights add up to 1:
dt[, list("w1"=sum(w1),"w2"=sum(w2),"w3"=sum(w3)), by="region"]

# introduce 25% random gaps:
dt.gaps <- dt[!rgaps(r=region, n=product, amount=0.25), ]

# weights no longer add up to 1 in each region:
dt.gaps[, list("w1"=sum(w1),"w2"=sum(w2),"w3"=sum(w3)), by="region"]

# approx. 25% random gaps, but keep observation for product "n2"
# in region "r1" and all observations in region "r2":
no_gaps <- data.frame(r=c("r1","r2"), n=c("n2",NA))

# apply to data:
dt[!rgaps(r=region, n=product, amount=0.25, exclude=no_gaps), ]

# or, directly, in one step:
dt <- rdata(R=4, B=3, N=1, gaps=0.25, settings=list("gaps.exclude"=no_gaps))

# introduce systematic gaps:
dt <- rdata(R=15, B=1, N=10)
dt[, "prob" := data.table::rleidv(product)] # probability for gaps increases per product
dt.gaps <- dt[!rgaps(r=region, n=product, amount=0.25, prob=prob), ]
plot(table(dt.gaps$product), type="l")