
Muthén, B. (2002).
Using Mplus Monte Carlo simulations in practice: A note on
assessing estimation quality and power in latent variable models.
Version 2, March 22, 2002.

Muthén, B. and Asparouhov, T. (2002).
Using Mplus Monte Carlo simulations in practice: A note on
nonnormal missing data in latent variable models.
Version 2, March 22, 2002.

Muthén, B. and Asparouhov, T. (2002).
Modeling of Heteroscedastic Measurement Errors.
Version 1, July 19, 2002.

Muthén, B. and Asparouhov, T. (2002).
Latent Variable Analysis With Categorical Outcomes: MultipleGroup And Growth Modeling In Mplus.
Version 5, December 9, 2002.

Muthén, B. (2002).
Supplementary Analyses for the Article "Assessment of Treatment Effects
Using Latent Variable Modeling: Comments on the New York School Choice Study".
Version 1, December 20, 2002.

Muthén, B. and Asparouhov, T. (2003).
Modeling interactions between latent and observed continuous variables using maximumlikelihood
estimation in Mplus.
Version 1, March 5, 2003.

Asparouhov, T. (2004). Weighting for unequal probability of selection in latent
variable modeling. Mplus Web Notes: No. 7. Refer to Mplus Papers
for the abstract. Mplus inputs and outputs used in section 10 of this paper can be downloaded from
here.
MLwiN runs used in section 10 of this paper can be downloaded from
here.
HLM runs used in section 10 of this paper can be downloaded from
here.

Asparouhov, T. (2004). Weighting for unequal probability of selection in multilevel
modeling. Mplus Web Notes: No. 8. Refer to Mplus Papers
for the abstract.

Asparouhov, T. (2004). Stratification in multivariate modeling. Mplus Web Notes: No. 9. December 16, 2004.
Refer to Mplus Papers for the abstract. Mplus inputs and outputs used in this paper can be downloaded from here.
 Asparouhov, T. & Muthén, B. (2006).
Robust Chi Square Difference Testing with mean and variance adjusted test statistics. Mplus Web Notes: No. 10. May 26, 2006.
 Asparouhov, T. & Muthén, B. (2006). Constructing covariates in multilevel regression. Mplus Web Notes: No. 11. February 15, 2006.
 Asparouhov, T. & Muthén, B. (2010).
Computing the strictly positive SatorraBentler chisquare test in Mplus. Paper can be downloaded from here. Mplus Web Notes: No. 12. January 24, 2012.
 Muthén, B. & Asparouhov, T. (2011). LTA in Mplus: Transition probabilities influenced by covariates. Mplus Web Notes: No. 13. July 27, 2011.
 Asparouhov, T. & Muthén, B. (2012). Using Mplus TECH11 and TECH14 to test the number of latent classes.
Paper can be downloaded from here. Mplus Web Notes: No. 14. May 22, 2012.
 Asparouhov, T. & Muthén, B. (2014). Auxiliary variables in mixture modeling: Threestep approaches using Mplus. Structural Equation Modeling:
A Multidisciplinary Journal, 21:3, 329341. DOI: 10.1080/10705511.2014.915181. The posted version corrects several typos in the published version.
An earlier version of this paper was posted as web note 15. Appendices with Mplus scripts are available here.
 Asparouhov, T. & Muthén, B. (2012). Multiple group multilevel analysis. Mplus Web Notes: No. 16. November 15, 2012.
 Muthén, B. & Asparouhov, T. (2013). BSEM measurement invariance analysis. Mplus Web Notes: No. 17. January 11, 2013.
 Asparouhov, T. & Muthén, B. (2014). Multiplegroup factor analysis alignment. Structural
Equation Modeling: A Multidisciplinary Journal, 21:4, 495508. DOI: 10.1080/10705511.2014.919210. An earlier version of this paper was posted as web note 18.
Mplus input, output, and data files for Web Note 18 Monte Carlo simulations are available here. Realdata analyses of the traditionconformity
items for 26 countries and corresponding Monte Carlo simulation are available here. For further information,
see the 2013 July Ljubljana talk here.
 Asparouhov, T. & Muthén B. (2015). Structural equation models and mixture models with continuous nonnormal skewed distributions. Structural equation models and mixture models with continuous nonnormal skewed distributions. Structural Equation Modeling: A Multidisciplinary Journal, DOI:
10.1080/10705511.2014.947375. An earlier version of this paper was posted as web note 19. Mplus inputs and outputs used in this paper can be downloaded here.
 Asparouhov, T. & Muthén, B. (2014). Using Mplus individual residual plots for diagnostic and model evaluation in SEM. Mplus Web Notes: No. 20. October 6, 2014. Revised October 31, 2017.
 Asparouhov, T. & Muthén, B. (2020). Auxiliary variables in mixture modeling: Using the BCH method in Mplus to estimate a distal outcome model and an arbitrary second model. Mplus Web Notes: No. 21. May 14, 2014. Revised April 27, 2020 with added Section 7 for missing data. Download scripts.
 Asparouhov, T, & Muthén, B. (2017). PriorPosterior Predictive Pvalues. Mplus Web Notes: No. 22. Version 2. April 27, 2017. (Download Mplus analyses)
 Asparouhov, T, & Muthén, B. (2019). Latent variable interactions using maximumlikelihood and Bayesian estimation for single and twolevel models. Mplus Web Notes: No. 23. May 3, 2019. (Download the Section 4 Bayes examples)
Type of Analysis 
Input file 
Data file 
View output 

1. Muthén, B. (2002). Using Mplus Monte Carlo simulations in practice: A note on
assessing estimation quality and power in latent variable models. Version 2, March 22, 2002.
Contact the author. Download this
web note or the corresponding
set of examples. 
Study A. Linear growth model: no covariates, no missing data

mca.inp 
N/A 
mca.std 
Study B. Linear growth model: covariate, no missing data

mcb.inp 
N/A 
mcb.std 
Study C. Linear growth model: covariate, MAR missing data

mcc.inp 
N/A 
mcc.std 
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Type of Analysis 
Input file 
Data file 
View output 

2. Muthén, B. and Asparouhov, T. (2002). Using Mplus Monte Carlo simulations in practice: A note on
nonnormal missing data in latent variable models. Version 2, March 22, 2002.
Contact the first author. Download this
web note or the corresponding
set of examples. 
Study A. Linear growth model with nonnormal data: no covariate, no missing data, ML estimator

mc2a.inp 
N/A 
mc2a.std 
Study A. Linear growth model with nonnormal data: no covariate, no missing data, MLR estimator

mc2b.inp 
N/A 
mc2b.std 
Study B. Linear growth model with nonnormal data: covariate, MAR missing data, ML estimator

mc2c.inp 
N/A 
mc2c.std 
Study B. Linear growth model with nonnormal data: covariate, MAR missing data, MLR estimator

mc2d.inp 
N/A 
mc2d.std 
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Type of Analysis 
Input file 
Data file 
View output 

3. Muthén, B. and Asparouhov, T. (2002). Modeling of Heteroscedastic Measurement Errors.
Version 1, July 19, 2002.
Contact the first author. Download this
web note or the corresponding
set of examples. 
Model 1. Full model. 5 parameters.

model1.inp 
stationary_oddsratio.dat 
model1.std 
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Type of Analysis 
Input file 
Data file 
View output 

4.
Muthén, B. and Asparouhov, T. (2002).
Latent Variable Analysis With Categorical Outcomes: MultipleGroup And Growth Modeling In Mplus.
Version 5, December 9, 2002.
Contact the first author. Download this
web note or the corresponding
set of examples.

Example 1. ASB EFA

catex1.inp 
asb.dat 
catex1.std 
Example 2. ASB CFA

catex2.inp 
asb.dat 
catex2.std 
Example 3. ASB factor analysis (MIMIC) with gender as covariate

catex3.inp 
asb.dat 
catex3.std 
Example 4. ASB factor analysis (MIMIC) with gender as covariate and gender noninvariance

catex4.inp 
asb.dat 
catex4.std 
Example 5. ASB multiplegroup analysis

catex5.inp 
asb.dat 
catex5.std 
Example 6. ASB multiplegroup analysis with gender noninvariance

catex6.inp 
asb.dat 
catex6.std 
Study A. Multiplegroup modeling: full invariance

catstudya.inp 
mc.dat 
catstudya.std 
Study B. Multiplegroup modeling: partial threshold invariance

catstudyb.inp 
mc.dat 
catstudyb.std 
Study C. Growth modeling: binary outcomes

catstudyc.inp 
mcgrowth.dat 
catstudyc.std 
Study D. Growth modeling: polytomous outcomes

catstudyd.inp 
mcgrowth.dat 
catstudyd.std 
Study E. Growth modeling: multipleindicator, polytomous outcomes

catstudye.inp 
mcgrowth3.dat 
catstudye.std 
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Type of Analysis 
Input file 
Data file 
View output 

5.
Muthén, B. (2002). Supplementary Analyses for the Article "Assessment of Treatment Effects
Using Latent Variable Modeling: Comments on the New York School Choice Study".
Version 1, December 20, 2002.
Contact the author. Download this
web note or the corresponding
set of examples.

Study A. 2class scenario with 3 time points

jasaa.inp 
N/A 
jasaa.std 
Study B. 3class scenario with 3 time points

jasab.inp 
N/A 
jasab.std 
Study C. 2class scenario with 2 time points

jasac.inp 
N/A 
jasac.std 
Study D. 3class scenario with 2 time points

jasad.inp 
N/A 
jasad.std 
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Type of Analysis 
Input file 
Data file 
View output 

6.
Muthén, B. and Asparouhov, T. (2003).
Modeling interactions between latent and observed continuous variables using maximumlikelihood
estimation in Mplus. Version 1, March 5, 2003.
Contact the first author. Download this
web note or the corresponding
set of examples.

Example 1. Monte Carlo example

web6ex1.inp 
N/A 
web6ex1.std 
Example 2. Crosssectional example of behavior

web6ex2.inp 
web6cross.dat 
web6ex2.std 
Example 3. Growth modeling example

web6ex3.inp 
web6growth.dat 
web6ex3.std 
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Type of Analysis 
Input file 
Data file 
View output 

10.
Asparouhov, T. and Muthen, B. (2006).
Robust Chi Square Difference Testing with Mean and Variance Adjusted Test Statistics.
Mplus Web Notes: No. 10. May 26, 2006.
Contact the second author. Download this
web note or the corresponding
set of examples.
The set of examples includes a DOS batch file called ALL.BAT which executes
Step 2 and Step 3 for each data set created in Step 1. The DOS batch file uses
a utility called Extractor to extract
the pvalue for the ChiSquare Test for Difference Testing from the H0 analysis in Step 3.
The pvalues are extracted and placed into the file pval.txt.
The data sets created in Step 1 are not included.

Step 1: Data generation

gendata.inp 
N/A 
gendata.out 
Step 2: H1 analysis (shown for one data set)

difinp1.inp 
mcdiff.dat 
difinp1.out 
Step 3: H0 analysis (shown for one data set)

difinp0.inp 
mcdiff.dat 
difinp0.out 
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Type of Analysis 
Input file 
Data file 
View output 

12.
Asparouhov, T. and Muthen, B. (2010).
Computing the strictly positive SatorraBentler chisquare test in Mplus.
Contact the second author.
Download this
web note.

Example 1, M0 model

run1.inp 
1.dat 
run1.out 
Example 1, M1 model

run2.inp 
1.dat 
run2.out 
Example 1, M10 model

run3.inp 
1.dat 
run3.out 
Example 2, M0 model

run4.inp 
1.dat 
run4.out 
Example 2, M1 model

run5.inp 
1.dat 
run5.out 
Example 2, M10 model

run6.inp 
1.dat 
run6.out 
Example 3, M0 model

run7.inp 
2.dat 
run7.out 
Example 3, M1 model

run8.inp 
2.dat 
run8.out 
Example 3, M10 model

run9.inp 
2.dat 
run9.out 
Example 4, M0 model

run10.inp 
2.dat 
run10.out 
Example 4, M1 model

run11.inp 
2.dat 
run11.out 
Example 4, M10 model

run12.inp 
2.dat 
run12.out 
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