BuSuCo: Business Survey Sample Coordination

Core Coordination Algorithms

The package implements four different business sample coordination algorithms:

• Dutch.BSC(): Modified Dutch Business Sample Coordination Algorithm (Smeets & Boonstra, 2018)
• French.BSC(): Modified French Business Sample Coordination Algorithm (Guggemos & Sautory, 2012; Gros, 2015)
• Norwegian.BSC(): Modified Norwegian Business Sample Coordination Algorithm (Zhang, 2009)
• Swiss.BSC(): Modified Swiss Business Sample Coordination Algorithm (Qualité, 2009)

Each algorithm has its own approach to handling response burden, rotation schemes, and simultaneous samples for different surveys. Small modifications have been made to each of them by Straubinger (2025).

Data Generation

• Gen.Data(): Generate synthetic business data with Pareto-distributed variables, allowing for population dynamics such as births, deaths, and stratum/domain jumpers.

Supporting Functions

• Survey.relevance(): Creates an array indicating survey relevance for each element
• Stratify(): Creates an array indicating stratum membership of each element
• uneq.sample(): Draws samples with unequal probabilities (with/without replacement)
• target.corr.sort(): Rearranges data to achieve a targetted correlation between variables
• nearest.neighbour(): Finds the nearest neighbours of elements
• random.order(): Randomly reorders elements of a dataset
• is.in.interval(): Checks whether a number is within a given interval

Step 1: Generate or Load Data

library(BuSuCo)

# Generate synthetic business data
DATA <- Gen.Data(
  N = 1000,
  periods = 5,
  D = 2,
  D.probs = c(0.8, 0.2),
  H = 3,
  borders = c(100, 500),
  corr.B.U = 0.75
)

Step 2: Define Survey Relevance

# Define which enterprises are relevant for each survey
Sur_rel <- Survey.relevance(
  DATA,
  periods = 5,
  years = c(1, 2),
  domains.survey = list(1:2, 1),
  ge.or.less = c("ge", "l"),
  TO.or.EM = c("TO", "EM"),
  size.class = c(0, 5)
)

Step 3: Create Strata

# Stratify the population
strat <- Stratify(
  DATA,
  Survey.relevant = Sur_rel,
  periods = 5,
  years = c(1, 2),
  TO.or.EM = c("TO", "EM"),
  strata.TO = c(500),
  strata.EM = c(10)
)

Step 4: Draw Coordinated Samples

# Apply Dutch BSC algorithm for period 1
result <- Dutch.BSC(
  DATA = DATA,
  period = 1,
  sf = c(0.2, 0.5),        # Sampling fractions
  rf = c(0.5, 1),          # Rotation fractions
  years = c(1, 2),         # Survey periodicity
  chi_S = c(0.5, 2),       # Response burden in hours
  survey.prio = 1:2,       # Survey priority order
  burden.periods = 5,
  seed = 123,
  Survey.relevant = Sur_rel,
  stratification = strat
)

# Use updated DATA for next period
DATA <- result$DATA
in_sample <- result$in.sample

Dutch Algorithm

The Modified Dutch Business Sample Coordination Algorithm achieves coordination via ordering the data according to the values of a customisable burden indicator.

French Algorithm

The Modified French Business Sample Coordination Algorithm uses a theoretical sample inclusion indicator which is determined through a beta-distribution.

Norwegian Algorithm

The Modified Norwegian Business Sample Coordination Algorithm achieves coordination by using two separate burden indicators, one based on the total number of draws, the other one based on the number of consecutive inclusion or pause periods.

Swiss Algorithm

The Modified Swiss Business Sample Coordination Algorithm supports interval-based coordination across periods for sophisticated longitudinal sample coordination.

Burden Weights

Some of the abovementioned algorithms contain a burden score which can be customised. For this purpose, the following parameters are available (see Straubinger, 2025, pp.48ff. for details): - Stratum size weight (alpha) - Enterprise size weight (vita) - Pause duration weight (ggamma)