Test according to Lindner

Description

Performs a test of significance according to Lindner

Usage

PXisM(m,n,Nt,k)

Arguments

Value

returns p for the test according to Linder

Note

The test according to Lindner requires the packages parallel. All other parts of cfa do not.

Author(s)

J. Harloff <oachimharloff@joachimharloff.de>

References

Lindner, K.: Eine exakte Auswertungsmethode zur Konfigurationsfrequenzanalyse [An exact procedure for the configural frequency analysis]. Psycholog Beitraege 26, 393?415 (1984)

Harloff, Joachim, An efficient algorithm for Lindners test (configural frequency analysis), Qual Quant DOI 10.1007/s11135-011-9499-9

See Also

cfa

Examples

# Does not work with windows since there is no parallel for it
if (require(parallel)) {
lk<-4 # number of parameters
ln<-c(59,57,59,58) # marginal sums of the parameters realized in the configuration to be tested
lNt<-116 # sample size of configurations
lm0<-16 # observed frequency of the configuration tested


# New algorithm
starttime=proc.time()
pHXsmallerequalM0<-sum(unlist(mclapply(0:lm0,PXisM,ln,lNt,lk)))
pHXequalM0<-PXisM(lm0,ln,lNt,lk)
pHlargerequalM0<-sum(unlist(mclapply(lm0: min(ln),PXisM,ln,lNt,lk)))
stoptime<-proc.time()
list(pHXsmallerequalM0=pHXsmallerequalM0,pHXequalM0=pHXequalM0,pHlargerequalM0=pHlargerequalM0,
timed.required=stoptime-starttime)

# End of the new algorithm
}

Test according to Lindner

Description

Performs a test of significance according to Lindner - old algorithm

Usage

PXisMclassic(m,n,Nt,k)

Arguments

Value

returns p for the test according to Linder

Note

The test according to Lindner requires the packages parallel. All other parts of cfa do not.

Author(s)

J. Harloff <oachimharloff@joachimharloff.de>

References

Lindner, K.: Eine exakte Auswertungsmethode zur Konfigurationsfrequenzanalyse [An exact procedure for the configural frequency analysis]. Psycholog Beitraege 26, 393?415 (1984)

Harloff, Joachim, An efficient algorithm for Lindners test (configural frequency analysis), Qual Quant DOI 10.1007/s11135-011-9499-9

See Also

cfa

Examples

# Does not work with windows since there is no parallel for it
if (require (parallel)) {

lk<-4 # number of parameters
ln<-c(59,57,59,58) # marginal sums of the parameters realized in the configuration to be tested
lNt<-116 # sample size of configurations
lm0<-16 # observed frequency of the configuration tested


# Old algorithm
starttime=proc.time()
pHXsmallerequalM0<-sum(unlist(mclapply(0:lm0,PXisMclassic,ln,lNt,lk)))
pHXequalM0<-PXisMclassic(lm0,ln,lNt,lk)
pHlargerequalM0<-sum(unlist(mclapply(lm0: min(ln),PXisMclassic,ln,lNt,lk)))
stoptime<-proc.time()
list(pHXsmallerequalM0=pHXsmallerequalM0,pHXequalM0=pHXequalM0,pHlargerequalM0=pHlargerequalM0,
timed.required=stoptime-starttime)
# End of the old algorithm
}

Bootstrap-CFA

Description

The bootstrap-CFA tries to replicate the pattern of significant configurations by re-sampling.

Usage

bcfa(configs, cnts, runs=100, sig.item="sig.z",...)

Arguments

Details

Takes 'runs' samples and does as many CFAs while counting how many times this configuration was considered to be significant.

Repeated-measures CFAs (mcfa) are not provided.

This is a heuristic method rather than a strict test of significance since there is no adjustment for multiple testing whatsoever. The advantage is a more reliable picture compared to splitting the original data, doing a CFA, and checking if the configurations re-appear in a CFA with the other half of the data.

Value

Note

bcfa() performs many CFAs which are by themselves slow, so the execution can be very time-consuming, especially if a sufficiently high value for runs was selected

Author(s)

Stefan Funke <s.funke@t-online.de>

References

Lautsch, E., von Weber S. (1995) Methoden und Anwendungen der Konfigurationsfrequenzanalyse Psychologie und Medizin, Beltz Psychologie Verlagsunion

See Also

cfa, scfa

Examples

# 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)
bcfa(configs,counts,runs=25) 

Analysis of configuration frequencies

Description

This is the main function which will call scfa() und mcfa() as required to handle the simple and the multiple cfa.

Usage

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)

Arguments

Details

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.

Value

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.

WARNING

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.

Note

There are no hard-coded limits in the program so even large tables can be processed. The output table can be very wide if the levels of factors variables are long strings so ‘options(width=..)’ may need to be adjusted.

The object returned has the class scfa if a one-sample CFA was performed or the class mcfa if a repeated-measures CFA was performed. cfa() decides which one is appropriate by looking at cnts: If it is a vector, it will do a simple CFA. If it is a dataframe or matrix with 2 or more columns, a repeated-measures CFA ist done.

Author(s)

Stefan Funke <s.funke@t-online.de>

References

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

See Also

scfa, mcfa

Examples

# 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) 

Stepwise CFA approaches

Description

These CFA methods detect and eliminate stepwise types/antitypes cells by specifying an appropriate contrast in the design matrix. The procedures stop when model fit is achieved. Functional CFA (fCFA) uses a residual criterion, Kieser-Victor CFA (kvCFA) a LR-criterion.

Usage

fCFA(m.i,  X, tabdim, alpha = 0.05)
kvCFA(m.i, X, tabdim, alpha = 0.05)

Arguments

Value

Author(s)

Patrick Mair, Alexander von Eye

References

von Eye, A., and Mair, P. (2008). A functional approach to configural frequency analysis. Austrian Journal of Statistics, 37, 161-173.

Kieser, M., and Victor, N. (1999). Configural frequency analysis (CFA) revisited: A new look at an old approach. Biometrical Journal, 41, 967-983.

Examples

#Functional CFA for a internet terminal usage data set by Wurzer 
#(An application of configural frequency analysis: Evaluation of the
#usage of internet terminals, 2005, p.82)
dd <- data.frame(a1=gl(3,4),b1=gl(2,2,12),c1=gl(2,1,12))
X <- model.matrix(~a1+b1+c1,dd,contrasts=list(a1="contr.sum",b1="contr.sum",
    c1="contr.sum"))
ofreq <- c(121,13,44,37,158,69,100,79,24,0,26,3)
tabdim <- c(3,2,2)

res1 <- fCFA(ofreq, X, tabdim=tabdim)
res1
summary(res1)


# Kieser-Vector CFA for Children's temperament data from 
# von Eye  (Configural Frequency Analysis, 2002, p. 192) 
dd <- data.frame(a1=gl(3,9),b1=gl(3,3,27),c1=gl(3,1,27))
X <- model.matrix(~a1+b1+c1,dd,contrasts=list(a1="contr.sum",
    b1="contr.sum",c1="contr.sum"))
ofreq <- c(3,2,4,23,23,6,39,33,9,11,29,13,19,36,19,21,26,18,13,30,
         41,12,14,23,8,6,7)
tabdim <- c(3,3,3)

res2 <- kvCFA(ofreq, X, tabdim=tabdim)
res2
summary(res2)

Hierachical analysis of configuration frequencies

Description

Recursively eliminates one variable in the configuration to generate all possible sub-tables and performs a global chi-squared-test on them

Usage

hcfa(configs, cnts)

Arguments

Details

The hierarchical CFA assists in the selection of configuration variables by showing which variables contribute the most to the variability. If eliminating a variable does not markedly decrease the global chi squared the variable is likely to be redundant, provided there are no extraneous reasons for retaining it.

The output is in decreasing order of chi squared so the most useful combinations of variables come first.

Value

Note

The p for the test of significance ist provided by the print method

Author(s)

Stefan Funke <s.funke@t-online.de>

References

Lautsch, E., von Weber S. (1995) Methoden und Anwendungen der Konfigurationsfrequenzanalyse in Psychologie und Medizin, Beltz Psychologie Verlagsunion

See Also

cfa, scfa, mcfa

Examples

# 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)
hcfa(configs,counts) 

Two or more-sample CFA

Description

Performs an analysis of configuration frequencies for two or more sets of counts. This function is not designed to be called directly by the user but will only be used internally by cfa(). Both the simple an the multiple cfa are handled by cfa()

Usage

mcfa(cfg, cnts, sorton="chisq", sort.descending=TRUE, format.labels=TRUE)

Arguments

Details

This function is the "engine" cfa() will use. It does the aggregation, summing up, and will calculate chi squared. All tests of significance are left to cfa()

Value

The function returns the following list:

Note

There are no hard-coded limits in the program so even large tables can be processed.

Author(s)

Stefan Funke <s.funke@t-online.de>

References

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

See Also

cfa, scfa

Examples

 
# 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])
counts1<-trunc(runif(250)*10) 
counts2<-trunc(runif(250)*10)
cfa(configs,cbind(counts1,counts2))
# cfa rather than mcfa!

Plotting method for a bcfa object

Description

Plots an object of the class bcfa

Usage

## S3 method for class 'bcfa'
plot(x,...)

Arguments

Details

Plots the number of cases considered significant vs. the number of cases considered to be a type (n > expected).

This is in some way like other plots of quality versus quantity.

Configurations can be identified by left-clicking on them until the right mouse button is pressed. The labels of the configurations selected will be displayed in the text window.

Value

Returns a vector of the configurations selected with their name set to the labels

Note

This function is usually invoked plotting an object returned by bcfa

Author(s)

Stefan Funke <s.funke@t-online.de>

References

None - plots have been rarely used with the CFA

See Also

bcfa

Examples

# 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)
plot(bcfa(configs,counts,runs=25))

Plotting method for a hcfa object

Description

Plots an object of the class hcfa

Usage

## S3 method for class 'hcfa'
plot(x,...)

Arguments

Details

A dotchart is generated which plots chi squared vs. the order of the configuration (i.e. the number of configuration variables it contains).

Value

Returns NULL.

Note

This function is usually invoked plotting an object returned by hcfa

Author(s)

Stefan Funke <s.funke@t-online.de>

References

None - plots have been rarely used with the CFA

See Also

cfa, hcfa

Examples

#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)
#plot(hcfa(configs,counts))

Plotting method for a mcfa object

Description

Plots an object of the class mcfa

Usage

## S3 method for class 'mcfa'
plot(x,...)

Arguments

Details

Plots chi squared vs. the sum of all counts for this configuration which indicates pronouncedness of the configuration vs. practical importance. Configurations can be identified by left-clicking on them until the right mouse button is pressed. The labels of the configurations selected will be displayed in the text window.

Value

Returns a list of the labels of the configurations selected.

Note

This function is usually invoked plotting an object returned by cfa

Author(s)

Stefan Funke <s.funke@t-online.de>

References

None - plots have been rarely used with the CFA

See Also

cfa, mcfa

Examples

# 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])
counts1<-trunc(runif(250)*10)
counts2<-trunc(runif(250)*10)

plot(cfa(configs,cbind(counts1,counts2)))

Plotting method for a scfa object

Description

Plots an object of the class scfa

Usage

## S3 method for class 'scfa'
plot(x,...)

Arguments

Details

Plots chi squared vs. n which indicates pronouncedness of the configuration vs. practical importance. Configurations can be identified by left-clicking on them until the right mouse button is pressed. The labels of the configurations selected will be displayed in the text window.

Value

Returns a list of the labels of the configurations selected.

Note

This function is usually invoked plotting an object returned by cfa

Author(s)

Stefan Funke <s.funke@t-online.de>

References

None - plots have been rarely used with the CFA

See Also

cfa, scfa

Examples

# 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)
plot(cfa(configs,counts))

Print an object of the class hcfa

Description

Printing method for an object returned by boot.cfa()

Usage

## S3 method for class 'bcfa'
print(x,...)

Arguments

Details

This function is usually called implicitely.

Value

Returns NULL

Author(s)

Stefan Funke <s.funke@t-online.de>

References

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

See Also

bcfa

Examples

# 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)
result<-bcfa(configs,counts,runs=25) 
print(result)

Print an object of the class hcfa

Description

Printing method for an object returned by hier.cfa()

Usage

## S3 method for class 'hcfa'
print(x,...)

Arguments

Details

This function is usually called implicitely.

Value

Returns NULL.

Author(s)

Stefan Funke <s.funke@t-online.de>

References

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

See Also

hcfa

Examples

#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)
#result<-hcfa(configs,counts) 
#print(result)

Print an object of the class mcfa

Description

Printing method for one of two possible objects returned by cfa()

Usage

## S3 method for class 'mcfa'
print(x,...)

Arguments

Details

This function is usually called implicitely.

Value

Returns NULL

Note

Note that cfa() will return an object with the class scfa if there is only one row of counts. If there are two or more of them, an object with the class mcfa is returned. In contrast scfa() and mcfa() return a list which has no class of it's own.

Author(s)

Stefan Funke <s.funke@t-online.de>

References

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

See Also

cfa, mcfa

Examples

# 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])
counts1<-trunc(runif(250)*10) 
counts2<-trunc(runif(250)*10)
result<-cfa(configs,cbind(counts1,counts2))
print(result)

Print an object of the class scfa

Description

Printing method for one of two possible objects returned by cfa()

Usage

## S3 method for class 'scfa'
print(x,...)

Arguments

Details

This function is usually called implicitely.

Value

Returns NULL

Note

Note that cfa() will return an object with the class scfa if there is only one row of counts. If there are two or more of them, an object with the class mcfa is returned. In contrast scfa() and mcfa() return a list which has no class of it's own.

Author(s)

Stefan Funke <s.funke@t-online.de>

References

Krauth J., Lienert G. A. (1973, Reprint 1995) Die Konfigurationsfrequenzanalyse (KFA) und ihre Anwendung in 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

See Also

cfa, scfa

Examples

# 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)
result<-cfa(configs,counts) 
print(result)

One sample CFA

Description

Performs a configuration frequency analysis if only one set of counts exists. This function is not designed to be called directly by the user but will only be used internally by by cfa(). Both the simple an the multiple cfa are handled by cfa()

Usage

scfa(cfg, cnt=NA, sorton="chisq", sort.descending=TRUE, format.labels=TRUE)

Arguments

Details

This function is the "engine" cfa() will use. It does the aggregation, summing up, and will calculate chi squared. All tests of significance are left to cfa()

Value

The function returns the following list:

Note

There are no hard-coded limits in the program so even large tables can be processed.

Author(s)

Stefan Funke <s.funke@t-online.de>

References

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 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

See Also

cfa, mcfa

Examples

 
# 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) 
# cfa rather than scfa!