# 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

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QCAcluster documentation built on Oct. 26, 2021, 5:06 p.m.