Calculate parameters of fit
These functions returns inclusion (consistency) and coverage, plus PRI for sufficiency
and RoN for necessity. The function pofind() is a stripped down version
of the pof() function, to calculate parameters of fit for single conditions.
pof(setms, outcome, data, relation = "necessity", inf.test = "",
incl.cut = c(0.75, 0.5), add, ...)
pofind(data, outcome, conditions, relation = "necessity", ...)setms |
A data frame or a single vector of (calibrated) set memberships, or an expression written in sum of products form. |
outcome |
The name of the outcome column from a calibrated data frame, or the actual numerical column from the data frame, representing the outcome. |
data |
A calibrated data frame. |
conditions |
A single string containing the conditions' (columns) names separated by commas, or a character vector of conditions' names. |
relation |
The set relation to |
inf.test |
Specifies the statistical inference test to be performed (currently
only |
incl.cut |
The inclusion cutoff(s): either a single value for the presence of the
output, or a vector of length 2, the second for the absence of the output. Used
only in conjunction with the argument |
add |
A function, or a list containing functions, to add more parameters of fit. |
... |
Other arguments to be passed to the main function. |
The function pof() is one of the most flexible functions in the
QCA package. Depending on particular situations, its arguments can be provided
in various formats which are automatically recognized and treated accordingly.
When specified as a data frame, the argument setms contains any kind
of set membership scores:
- calibrated causal conditions from the original data,
- membership scores from the resulting combinations (component coms)
of function superSubset(),
- prime implicant membership scores (component pims) from function
minimize(),
- any other, custom created combinations of set memberships.
When specified as a matrix, setms contains the crisp causal combinations
similar to those found in the truth table. The number of columns in the matrix should be
equal to the number of causal conditions in the original data. If some of
them are minimized, they can be replaced by the numerical value -1 (see
examples section).
More generally, setms can be a numerical vector of line numbers from the
implicant matrix (see function createMatrix()), which are automatically
transformed into their corresponding set membership scores.
The argument setms can also be a string expression, written in SOP - sum of
products form.
For all other situations when setms is something else than a data frame, it
requires the original data to generate the set memberships.
If character, the argument outcome is the name of the column from the
original data, to be explained (it is a good practice advice to specify
it using upper case letters, although it will nevertheless be converted to upper case,
by default).
If the outcome column is multi-value, the argument outcome should use
the standard curly-bracket notation X{value}. Multiple values are
allowed, separated by a comma (for example X{1,2}). Negation of the
outcome can also be performed using the tilde ~ operator, for example
~X{1,2}, which is interpreted as: "all values in X except 1 and 2" and
it becomes the new outcome to be explained.
The argument outcome can also be a numerical vector of set membership
values, either directly from the original data frame, or a recoded version (if
originally multi-value).
The argument inf.test provides the possibility to perform statistical
inference tests, comparing the calculated inclusion score with a pair of thresholds
(ic1 and ic0) specified in the argument incl.cut.
Currently, it can only perform binomial tests ("binom"), which means that
data should only be provided as binary crisp (not multivalue, not fuzzy).
If the critical significance level is not provided, the default level of 0.05
is taken.
The resulting object will contain the calculated p-values (pval1 and pval0) from two
separate, one-tailed tests with the alternative hypothesis that the true inclusion
score is:
- greater than ic1 (the inclusion cut-off for an output value of 1)
- greater than ic0 (the inclusion cut-off for an output value of 0)
It should be noted that statistical tests are performing well only when the number of cases is large, otherwise they are usually not significant.
For the necessity relation, the standard measures of inclusion and coverage are
supplemented with the RoN (Relevance of Necessity) measure, as suggested by
Schneider & Wagemann's (2012).
The negation of both setms and outcome is accepted and
recognized using the Boolean subtraction from 1. If the names of the conditions are
provided via an optional (undocumented) argument conditions, the
column names of the setms object are negated using the function
negate().
The logical argument neg.out is deprecated, but backwards compatible.
neg.out = TRUE and a tilde ~ in the outcome name don't
cancel each other out, either one (or even both) signaling if the outcome
should be negated.
The arguments from function pofind() are passed to the main function
pof() to calculate parameters of fit.
Adrian Dusa
Cebotari, V.; Vink, M.P. (2013) “A Configurational Analysis of Ethnic Protest in Europe”. International Journal of Comparative Sociology vol.54, no.4, pp.298-324, doi: 10.1177/0020715213508567
Schneider, C. and Wagemann, C. (2012) Set-Theoretic Metods for the Social Sciences. A Guide to Qualitative Comparative Analysis. Cambridge: Cambridge University Press.
# -----
# Cebotari & Vink (2013) fuzzy data
conds <- CVF[, 1:5]
PROTEST <- CVF$PROTEST
# parameters of fit (default is necessity)
pof(conds, PROTEST)
# parameters of fit negating the conditions
pof(1 - conds, PROTEST)
# negating the outcome
pof(conds, 1 - PROTEST)
# parameters of fit for sufficiency
pof(conds, PROTEST, relation = "suf")
# also negating the outcome
pof(conds, 1 - PROTEST, relation = "suf")
# -----
# standard analysis of necessity
# using the "coms" component from superSubset()
nCVF <- superSubset(CVF, outcome = PROTEST, incl.cut = 0.90, cov.cut = 0.6)
# also checking their necessity inclusion score in the negated outcome
pof(nCVF$coms, 1 - PROTEST)
# -----
# standard analysis of sufficiency
# using the "pims" component from minimize()
# conservative solution
cCVF <- minimize(CVF, outcome = PROTEST, incl.cut = 0.8, details = TRUE)
# verify if their negations are also sufficient for the outcome
pof(1 - cCVF$pims, PROTEST, relation = "sufficiency")
# -----
# using a SOP expression, translated using the function translate()
pof(~NATPRIDE + GEOCON -> PROTEST, data = CVF)
# same for the negation of the outcome
pof(~NATPRIDE + GEOCON -> ~PROTEST, data = CVF)
# necessity is indicated by the reverse arrow
pof(~NATPRIDE + GEOCON <- PROTEST, data = CVF)
# -----
# more parameters of fit, for instance Haesebrouck' consistency
inclH <- function(x, y) {
sum(fuzzyand(x, y)) /
sum(fuzzyand(x, y) + sqrt(fuzzyor(x - y, 0) * x))
}
pof(~NATPRIDE + GEOCON -> ~PROTEST, data = CVF, add = inclH)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.