conCovOpt {cnaOpt}

Find consistency and coverage optima for configurational data

Description

conCovOpt issues pairs of optimal consistency and coverage scores that atomic solution formulas (asf) of an outcome inferred from configurational data can possibly reach (cf. Baumgartner and Ambuehl 2021).

Usage

conCovOpt(x, outcome = NULL, ..., rm.dup.factors = FALSE, rm.const.factors = FALSE,
          maxCombs = 1e+07, approx = FALSE, allConCov)
## S3 method for class 'conCovOpt'
print(x, ...)
## S3 method for class 'conCovOpt'
plot(x, con = 1, cov = 1, ...)

Arguments

x

In conCovOpt: a data.frame or configTable. In the print- and plot-method: an output of conCovOpt.

outcome

A character vector of one or several factor values in x.

...

In conCovOpt: arguments passed to configTable, e.g. case.cutoff. The ‘...’ are currently not used in plot.conCovOpt.

rm.dup.factors

Logical; defaults to FALSE (which is different from configTable). If TRUE, all but the first of a set of factors with identical values in x are removed.

rm.const.factors

Logical; defaults to FALSE (which is different from configTable). If TRUE, factors with constant values in x are removed.

maxCombs

Maximal number of combinations that will be tested for optimality. If the number of necessary iterations exceeds maxCombs, conCovOpt will stop executing and return an error message stating the necessary number of iterations. Early termination can then be avoided by increasing maxCombs accordingly.

approx

Logical; if TRUE, an exhaustive search is only approximated; if FALSE, an exhaustive search is conducted.

allConCov

Defunct argument (as of package version 0.5.0). See the remark in ?multipleMax.

con, cov

Numeric scalars between 0 and 1 indicating consistency and coverage thresholds marking the area of "good" models in a square drawn in the plot. Points within the square correspond to models reaching these thresholds.

Details

conCovOpt implements a procedure introduced in Baumgartner and Ambuehl (2021). It calculates consistency and coverage optima for models (i.e. atomic solution formulas, asf) of an outcome inferred from data x prior to actual CNA or QCA analyses.

An ordered pair (con, cov) of consistency and coverage scores is a con-cov optimum for outcome Y=k in data x iff it is not excluded (based e.g. on the data structure) for an asf of Y=k inferred from x to reach (con, cov) but excluded to score better on one element of the pair and at least as well on the other.

conCovOpt calculates con-cov optima by executing the following steps:

1. if x is a data frame, aggregate x in a configTable,

2. build exo-groups with constant values in all factors other than the outcome,

3. assign output values to each exo-group that reproduce the behavior of outcome as closely as possible,

4. calculate con-cov scores for each assignment resulting in step 3,

5. eliminate all non-optimal scores.

The implementation of step 4 calculates con-cov scores of about 10 million output value assignments in reasonable time, but step 3 may result in considerably more assignments. In such cases, the argument approx may be set to its non-default value "TRUE", which determines that step 4 is only executed for those assignments closest to the outcome's median value. This is an efficient approach for finding many, but possibly not all, con-cov optima.

In case of crisp-set and multi-value data, at least one actual model (asf) inferrable from x and reaching an optimum's consistency and coverage scores is guaranteed to exist for every con-cov optimum. The function DNFbuild can be used to build these optimal models. The same does not hold for fuzzy-set data. In fuzzy-set data it merely holds that the existence of a model reaching an optimum's consistency and coverage scores cannot be excluded prior to an actual application of cna.

Value

An object of class 'conCovOpt'. The exo-groups resulting from step 2 are stored as attribute "exoGroups", the lists of output values resulting from step 3 are stored as attribute "reprodList" (reproduction list).

References

Baumgartner, Michael and Mathias Ambuehl. 2021. “Optimizing Consistency and Coverage in Configurational Causal Modeling.” Sociological Methods & Research.
doi:10.1177/0049124121995554.

See Also

configTable, selectMax, DNFbuild

Examples

(cco.irrigate <- conCovOpt(d.irrigate))
conCovOpt(d.irrigate, outcome = c("R","W"))
# Plot method.
plot(cco.irrigate)
plot(cco.irrigate, con = .8, cov = .8)

dat1 <- d.autonomy[15:30, c("EM","SP","CO","AU")]
(cco1 <- conCovOpt(dat1, outcome = "AU"))

print(cco1, digits = 3, row.names = TRUE)
plot(cco1)

# Exo-groups (configurations with constant values in all factors other than the outcome).
attr(cco1$A, "exoGroups")

# Rep-list (list of values optimally reproducing the outcome).
attr(cco1$A, "reprodList")

dat2 <- d.pacts
# Maximal number of combinations exceeds maxCombs.
(cco2 <- conCovOpt(dat2, outcome = "PACT")) # Generates a warning
# Increase maxCombs.
(cco2_full <- try(conCovOpt(dat2, outcome = "PACT", 
  maxCombs=1e+08))) # Takes a long time to terminate
# Approximate an exhaustive search.
(cco2_approx1 <- conCovOpt(dat2, outcome = "PACT", approx = TRUE))
selectMax(cco2_approx1)
# The search space can also be reduced by means of a case cutoff.
(cco2_approx2 <- conCovOpt(dat2, outcome = "PACT", case.cutoff=2))
selectMax(cco2_approx2)