#The code is to evaluate the cutoff values CFI_e in equivalence testing
#corresponding to the conventional cutoff values of CFI=.99, .95, .92, and .90, respectively;
#as described in the article
#"Confirm Structural Equation Models by Equivalence Testing with Adjusted Fit Indices"
#by Yuan, Chan, Marcoulides and Bentler;

#needed inputs are degrees of freedom (df), sample size (N), and number of observed variables (p);

df=23; N=145; p=9; 
n=N-1; df_i=p*(p-1)/2;

CFI_e99=1-exp(
 4.67603-.50827*log(df)+.87087*(df^(1/5))-.59613*((df_i)^(1/5))-1.89602*log(n)
+ .10190*((log(n))^2)+ .03729*log(df)*log(n)
);
#corresponding to R-square=.9836;

CFI_e95=1-exp(
 4.12132-.46285*log(df)+.52478*(df^(1/5))-.31832*((df_i)^(1/5))-1.74422*log(n)
+.13042*((log(n))^2)-.02360*(n^(1/2))+.04215*log(df)*log(n)
);
#corresponding to R-square=.9748;

CFI_e92=1-exp(
6.31234-.41762*log(df)+.01554*((log(df))^2)-.00563*((log(df_i))^2)-1.30229*log(n)
+.19999*((log(n))^2)-2.17429*(n^(1/5))+.05342*log(df)*log(n)-.01520*log(df_i)*log(n)
);
#corresponding to R-square=.9724;


CFI_e90=1-exp(
5.96633-.40425*log(df)+.01384*((log(df))^2)-.00411*((log(df_i))^2)-1.20242*log(n)
+.18763*((log(n))^2)-2.06704*(n^(1/5))+.05245*log(df)*log(n)-.01533*log(df_i)*log(n)
);
#corresponding to R-square=.9713;

cutoff=cbind(CFI_e90, CFI_e92, CFI_e95, CFI_e99);

cutoff_3=round(cutoff,3);
print(cutoff);

cat('--poor--', cutoff_3[1], '--mediocre--', cutoff_3[2], '--fair--', cutoff_3[3], '--close--', cutoff_3[4], '--excellent--',"\n")