# Test of small differences in fit
#
# @author Timo Gnambs <timo@gnambs.at>
# @version 2008-09-29
#
# @source MacCallum, R. C., Browne, M. W. & Cai, L. (2006). 
#         Testing differences between nested covariance 
#         structure models: Power analysis and null 
#         hypotheses.Psychological Methods, 11, 19-35.
#




#################### SETTINGS ####################

dfa <- 22         # Degrees of freedom for model A
dfb <- 20         # Degrees of freedom for model B
alpha <- 0.05     # Significance level
n <- 200          # Sample size
rmseaa <- 0.06    # RMSEA for model A
rmseab <- 0.05    # RMSEA for model B
chidiff <- 18     # Observed chi-square difference
g <- 1            # Number of groups

################################################## 




# Test of small difference begins here
ddiff <- dfa-dfb                           #df difference
fa <- (dfa*rmseaa**2)/sqrt(g)             #model A discrepancy fn value
fb <- (dfb*rmseab**2)/sqrt(g)             #model B discrepancy fn value
ncp <- (n-1)*(fa-fb)                     #non-centrality parameter
cval <- qchisq(1-alpha,df=ddiff,ncp=ncp) #critical value from non-central chi^2
sig <- 1-pchisq(chidiff,df=ddiff,ncp=ncp)      #p-value from non-central chi^2
rm(ddiff, fa, fb, ncp, cval)
print(c('Test of small differences in fit (McCallum et al., 2006): p=', round(sig,3)))