This file contains an R program to obtain the test statistics proposed in paper “Four New Corrected Statistics for SEM With Small Samples and Nonnormally Distributed Data”.

For citation of this article, please consider:

Jiang, G., & Yuan, K.-H. (2017). Four New Corrected Statistics for SEM With Small Samples and Nonnormally Distributed Data. *Structural Equation Modeling: A Multidisciplinary Journal, 24*, 479-494. doi: 10.1080/10705511.2016.1277726

Authors: Ge Jiang and Ke-Hai Yuan

##=======================================================================================##

## This program requires the input of 1) likelihood ratio statistic, 2) Satorra-Bentler’s mean rescaled statistic,

## 3) Satorra-Bentler’s mean and variance adjusted statistic, and 4) their degrees of freedom

## from standard output from any major statistic packages (Mplus, SAS, EQS, R:lavaan)

##=======================================================================================##

# The likelihood ratio statistic:

T_ml;

# Satorra-Bentler’s mean rescaled statistic:

T_rml;

# Degrees of freedom:

df;

# Satorra-Bentler’s mean and variance adjusted statistic:

T_aml; df_aml;

# Scaling factor in T_rml:

r_1 = T_ml/T_rml

# trace of the UGamma matrix:

tr = r_1*df

# rank of the UGamma matrix:

rk = min(df, n-1)

# First Corrected Statistic

const1 = tr/rk

T_cor1 = T_ml/const1

p_cor1 = 1-pchisq(T_cor1, df)

# Second Corrected Statistic

const2 = (r_1+const1)/2

T_cor2 = T_ml/const2

p_cor2 = 1-pchisq(T_cor2, df)

# Third Corrected Statistic

T_cor3 = (T_rml+T_cor1)/2

p_cor3 = 1-pchisq(T_cor3, df)

# Fourth Corrected Statistic

p_rml = 1-pchisq(T_rml, df)

p_aml = 1-pchisq(T_aml, df_aml)

p_cor4 = (p_rml+p_aml)/2