Weight of partitions"
In QCAcluster: Tools for the Analysis of Clustered Data in QCA

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(QCAcluster)
library(knitr) # nicer html tables

Conservative and parsimonious solution

We use the data from Thiem (2011) for illustrating how the function wop() calculates the weights of partitions. The weight of a partition is defined on the level of individual models and can be calculated for the consistency and coverage value of a model that has been derived from the pooled data. The weight of a partition for the consistency value of the pooled solution is calculated by applying the consistency formula only to the cases that belong to a partition. The weight of partition is calculated in absolute terms by calculating separately its contribution to the numerator and denominator of the formula. When one divides the partition-specific absolute contribution to the numerator by the contribution to the denominator, then one receives the partition-specific consistency or coverage score (depending on the type of formula).

The arguments of the functions are:

n_cut: Frequency threshold for pooled data
incl_cut: Inclusion threshold (a.k.a. consistency threshold) for pooled data
solution: Either C for conservative solution (a.k.a. complex solution) or P for parsimonious solution
amb_selector: Numerical value for selecting a single model in the presence of model ambiguity. Models are numbered according to their order produced by minimize by the QCA package.

# load data (see data description for details)
data("Thiem2011")
# calculate weight of partitions
wop_pars <- wop(
  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",
  amb_selector = 1)
kable(wop_pars)

When one aggregates the partition-specific absolute weights for the between-dimension or within-dimension, one gets the absolute value for the pooled solution. We illustrate this with the following chunk

# sum over all cross-sections for consistency denominator
sum(wop_pars[wop_pars$type == "between", ]$denom_cons)
# sum over all time series for coverage  numerator
sum(wop_pars[wop_pars$type == "within", ]$num_cov)

On the basis of the absolute weights, one can calculate the relative weight of a partition by dividing its absolute contribution by the corresponding value for the pooled solution.

# relative contribution of cross sections to denominator for consistency
wop_between  <- wop_pars[wop_pars$type == "between", ]
wop_between$rel_denom_cons <- round(wop_between$denom_cons / 
  sum(wop_between$denom_cons), digits = 2)
kable(wop_between)

Intermediate solution

The weight of partitions for intermediate solutions is produced with wop_inter(). We use data from Schwarz 2016 to illustrate the function.

# load data (see data description for details)
data("Schwarz2016")
# calculating weight of partitions
Schwarz_wop_inter <- partition_min_inter(
  Schwarz2016,
  units = "country", time = "year",
  cond = c("poltrans", "ecotrans", "reform", "conflict", "attention"),
  out = "enlarge",
  n_cut = 1, incl_cut = 0.8,
  intermediate = c("1", "1", "1", "1", "1"))
kable(Schwarz_wop_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