fCFA {cfa}

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

m.i

Vector of observed frequencies.

X

Design Matrix of the base model.

tabdim

Vector of table dimensions.

alpha

Significance level.

Value

restable

Fit results for each step

design.mat

Final design matrix

struc.mat

Structural part of the design matrix for each step

typevec

Type or antitype for each step

resstep

Design matrix, expected frequency vector, and fit results for each step

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)