This is the main function which will call scfa() und mcfa() as required to handle the simple and the multiple cfa.
cfa(cfg, cnts=NA, sorton="chisq", sort.descending=TRUE, format.labels=TRUE,
casewise.delete.empty=TRUE,
binom.test=FALSE, exact.binom.test=FALSE, exact.binom.limit=10,
perli.correct=FALSE, lehmacher=FALSE, lehmacher.corr=TRUE,
alpha=0.05, bonferroni=TRUE)Some of these elements will only be returned when the corresponding argument in the function call has been set. The relation is obvious due to corresponding names.
The cfa output table
Label for the given configuration
Observed n for this configuration
Expected n for this configuration
Coefficient of pronouncedness (varies between 0 and 1)
Chi squared for the given configuration
p for the chi squared test
Is it significant (will Bonferroni-adjust if argument bonferroni
is set)
z-approximation for chi squared
p of z-test
Is it significant (will Bonferroni-adjust if argument bonferroni
is set)?
Statistic for Perli's test
Is it significant (this is designed as a multiple test)?
z for Lehmacher's test
Is it significant (this is designed as a multiple test)?
z for Lehmacher's test (with continuity correction)
Is it significant (this is designed as a multiple test)?
p for exact binomial test
Summary stats for entire table
Total chi squared
Degrees of freedom
p for the chi squared test
Sum of all counts
Levels for each configuration. Should all be 2 for the bivariate case
Contains the configurations. This can be a dataframe or a matrix. The dataframe can contain numbers, characters, factors, or booleans. The matrix can consist of numbers, characters, or booleans (factors are implicitely re-converted to numerical levels). There must be >=3 columns.
Contains the counts for the configuration. If it is set to NA, a count of one is assumed for every
row. This allows untabulated data to be processed. cnts can be a vector or a matrix/dataframe with >=2 columns.
Determines the sorting order of the output table. Can be set to chisq, n, or label.
Sort in descending order
Format the labels of the configuration. This makes to output wider but it will increase the readability.
If set to TRUE all configurations containing a NA in any column will be deleted. Otherwise NA is handled as the string "NA" and will appear as a valid configuration.
Use z approximation for binomial test.
Do an exact binomial test.
Maximum n for which an exact binomial test is performed (n >10 causes p to become inexact).
Use Perli's correction for multiple test.
Use Lehmacher's correction for multiple test.
Use a continuity correction for Lehmacher's correction.
Alpha level
Do Bonferroni adjustment for multiple test (irrelevant for Perli's and Lehmacher's test).
Stefan Funke <s.funke@t-online.de>
Note than spurious "significant" configurations are likely to appear in very large tables.
The results should therefore be replicated before they are accepted as real. boot.cfa can be helpful to check
the results.
The cfa is used to sift large tables of nominal data. Usually it is used for dichotomous
variables but can be extended to three or more possible values. There should be at least three configuration variables
in cfg - otherwise a simple contigency table would do.
All tests of significance are two-sided: They test for both types or antitypes, i.e. if n is significantly larger or
smaller than the expected value.
The usual caveats for testing contigency tables apply. If a configuration has a n <5 an exact test
should be used. As an alternative the least interesting configuration variable can be left out (if
it is not essential) which will automatically increase the n for the remaining configurations.
Krauth J., Lienert G. A. (1973, Reprint 1995) Die Konfigurationsfrequenzanalyse (KFA) und ihre Anwendung in Psychologie und Medizin. Beltz Psychologie Verlagsunion
Lautsch, E., von Weber S. (1995) Methoden und Anwendungen der Konfigurationsfrequenzanalyse in Psychologie und Medizin. Beltz Psychologie Verlagsunion
Eye, A. von (1990) Introduction to configural frequency analysis. The search for types and anti-types in cross-classification. Cambride 1990
scfa, mcfa
# library(cfa) if not yet loaded
# Some random configurations:
configs<-cbind(c("A","B")[rbinom(250,1,0.3)+1],c("C","D")[rbinom(250,1,0.1)+1],
c("E","F")[rbinom(250,1,0.3)+1],c("G","H")[rbinom(250,1,0.1)+1])
counts<-trunc(runif(250)*10)
cfa(configs,counts)
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