QCA (version 1.0-5)

pof: Set-Relational Parameters of Fit

Description

This function computes three set-relational parameters of fit: inclusion, PRI and coverage scores.

Usage

pof(setms, outcome, data, neg.out = FALSE, relation = "necessity", ...)

Arguments

setms

Set membership scores, or a matrix with crisp-set representations, or a vector of line numbers

outcome

The name of the outcome set, or a vector of outcome values

data

The working dataset

neg.out

Logical, use negation of outcome set

relation

The set relation of the conditions to the outcome, either "necessity" or "sufficiency"

...

Other arguments from the generic print (not used in this function)

Details

The argument setms specifies a dataframe of set membership scores, where set refers to any kind of set, including original condition sets, conjunctive or disjunctive combinations returned by superSubset(), prime implicants returned by eqmcc() or any other compound set. It can also be a matrix with the crisp-set representation of the conditions, or even a vector of line numbers corresponding to those representations.

References

P. Emmenegger. Job Security Regulations in Western Democracies: A Fuzzy Set Analysis. European Journal of Political Research, 50(3):336-364, 2011.

M. L. Krook. Women's Representation in Parliament: A Qualitative Comparative Analysis. Political Studies, 58(5):886-908, 2010.

Examples

# csQCA using Krook (2010)
#-------------------------
data(Krook)
Krook
x <- Krook[,1:5]
 
# get necessity parameters of fit for all conditions
pof(x, outcome = "WNP", Krook)

# now for the negated outcome
pof(x, outcome = "WNP", Krook, neg.out = TRUE)

# get sufficiency parameters of fit for all original conditions
pof(x, outcome = "WNP", Krook, relation = "sufficiency") 

# now for the negated outcome
pof(x, outcome = "WNP", Krook, neg.out = TRUE, relation = "sufficiency")

# fsQCA using Emmenegger (2011)
#------------------------------
data(Emme)
Emme

# first test for necessary conditions with superSubset(), then 
# check whether the returned combinations are also necessary for 
# the negation of the outcome

EmmeNR <- superSubset(Emme, outcome = "JSR", incl.cut = 0.965, cov.cut = 0.6)
EmmeNR
pof(EmmeNR$coms, outcome = "JSR", Emme, neg.out = TRUE) 

# first derive the complex solution, then check whether the negations 
# of the prime implicants are also sufficient for the outcome 

EmmeSC <- eqmcc(Emme, outcome = "JSR", incl.cut1 = 0.9, details = TRUE)
EmmeSC
pof(1 - EmmeSC$pims$c.sol, outcome = "JSR", Emme, relation = "sufficiency")

# parameters of fit for any term, including configurations;
# use "-1" as a placeholder for a minimized condition;
# matrix representation of R*p*V and S*c*L*P*v:
#      "S"  "C"  "L"  "R"  "P"  "V"
#
#     [,1] [,2] [,3] [,4] [,5] [,6]
#[1,]   -1   -1   -1    1    0    1
#[2,]    1    0    1   -1    1    0

confs <- matrix(c(-1, -1, -1,  1, 0, 1, 
                   1,  0,  1, -1, 1, 0), nrow = 2, byrow = TRUE)
confs
pof(confs, outcome = "JSR", Emme, relation = "sufficiency")

# or even vectors of line numbers from the implicant matrix
pof(c(43, 57), "JSR", Emme, relation = "sufficiency")

# the line numbers 43 and 57 represent l*r*P and L*V:
#      "S"  "C"  "L"  "R"  "P"  "V"
#
#     [,1] [,2] [,3] [,4] [,5] [,6]
#[1,]   -1   -1    0    0    1   -1 
#[2,]   -1   -1    1   -1   -1    1  

getRow(rep(3, 6), c(43, 57)) - 1

# parameters of fit for a data frame
x <- data.frame(A = c(1,1,1,0,1), B = c(1,1,1,0,1),
                C = c(0,1,0,0,1), D = c(0,0,1,0,1),
                O = c(1,1,1,0,1))

pof(x[,-5], outcome = "O", x)

# for a single column from that data frame;
# requires special argument drop = FALSE to avoid
# dropping of dimensions and conversion to vector
pof(x[, "C", drop = FALSE], outcome = "O", x)

# for multiple columns from that data frame
pof(x[, 1:2], outcome = "O", x[, 1:5])

# inclusion and coverage of a single condition and the outcome
pof(x$D, x$O)

# inclusion of coverage of any two vectors
v1 <- c(.7, .1, .5, .3, .9, .7, .3, .3, .3, .1, .0, .9)
v2 <- c(.8, .3, .4, .4, .8, .6, .3, .2, .4, .2, .1, .9)
pof(v1, v2)