# fCFA: Stepwise CFA approaches In cfa: Configural Frequency Analysis (CFA)

## 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

 ```1 2``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```#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) ```

cfa documentation built on May 2, 2019, 1:46 p.m.