Minimization of partitions

Conservative and parsimonious solution

We first illustrate the parsimonious solution with dataset from Thiem (2011).

# load data (see data description for details)
data(Thiem2011)
# partition data into time series (within-unit) and cross sections (between-unit)
Thiem_pars <- partition_min(
  dataset = Thiem2011,
  units = "country", time = "year",
  cond = c("fedismfs", "homogtyfs", "powdifffs", "comptvnsfs", 
           "pubsupfs", "ecodpcefs"),
  out = "memberfs",
  n_cut = 6, incl_cut = 0.8,
  solution = "P", # parsimonious solution
  BE_cons = c(0.9, 0.8, 0.7, 0.8, 0.85, 0.8, 0.8, 0.8, 0.8, 0.8, 0.8),
  BE_ncut = rep(1, 11),
  WI_cons = c(0.75, 0.8, 0.9, 0.8, 0.85, rep(0.75, 10)),
  WI_ncut = rep(1, 15))
kable(Thiem_pars)

The output of partition_min() is a dataframe summarizing the solutions for the pooled data and the partitions and the consistency and coverage values for the solution. The column model shows whether model ambiguity is given for the pooled data or individual partitions if one can derive any model from the data in the first place.

There are different reasons why one might not be able to derive a partition-specific solution:

• All rows could be consistent
• All rows could be inconsistent
• There is no variation across cases of a partition and all cases belong to the same truth table row.

When one the reason applies, it is listed in the column solution.

Intermediate solution

The intermediate solution is derived with partition_min_inter(). The only command that is new compared to partition_min() is intermediate that is available for specifying the directional expectations. The data structure for Schwarz 2016 is an unbalanced panel with eight countries, ten years and 74 observations in total. We assume that one is only interested in the between-unit dimension and wants to derive one solution per cross section. For this reason, the argument for the within-unit dimension (unit) is not specified.

# load data (see data description for details)
data(Schwarz2016)
# partition data into cross sections
Schwarz_inter <- partition_min_inter(
  Schwarz2016, 
  time = "year", 
  cond = c("poltrans", "ecotrans", "reform", "conflict", "attention"), 
  out = "enlarge", 
  n_cut = 1, incl_cut = 0.8, 
  WI_cons = rep(0.8, 8), BE_cons = c(0.75, 0.75, 0.75, 0.75, 0.75,
                                     0.8, 0.8, 0.8, 0.8, 0.8),
  WI_ncut = rep(1, 8), BE_ncut = rep(1, 10),
  intermediate = c("1", "1", "1", "1", "1"))
kable(Schwarz_inter)

Other packages used in this vignette

Yihui Xie (2021): knitr: A General-Purpose Package for Dynamic Report Generation in R. R package version 1.33.

Yihui Xie (2015): Dynamic Documents with R and knitr. 2nd edition. Chapman and Hall/CRC. ISBN 978-1498716963

Yihui Xie (2014): knitr: A Comprehensive Tool for Reproducible Research in R. In Victoria Stodden, Friedrich Leisch and Roger D. Peng, editors, Implementing Reproducible Computational Research. Chapman and Hall/CRC. ISBN 978-1466561595