Quantitative Psychology Research Laboratory

Variable System (VS) Program

VS (Variable System) is a computer software program for the analysis of conditional path models based on structural equation modeling (SEM). It can be used to examine models with simple mediation, simple moderation, moderated mediation (moME), mediated moderation (meMO), and any combinations of them such as the one shown below:

 VS Model


VS runs on Windows environment together with the R system for statistical computing (R Development Core Team, 2015) that implements the package lavaan (Rosseel, 2012). In other words, you need to have R and the lavaan package installed on your PC in order to activate VS.

VS is easy to use. Users only need to specify the conceptual model using simple control languages in VS and the program will automatically (1) transform the conceptual model into a testable SEM-based model, (2) estimate the basic model parameters, (3) compute and test the conditional effects of interest, and (4) evaluate the model goodness-of-fit. 

Kwan, J. L.-Y., & Chan, W. (2017). Variable system: An alternative approach for the analysis of mediated moderation.*  Psychological Methods, 23, 262-277.  doi: 10.1037/met0000160

*This paper has won the 2018 Quality Journal Article Awards by the Faculty of Education and Human Development, The Education University of Hong Kong


Download VS

VS v1.2 is now available. Download VS v1.2 Here

VS Version History 

Version 1.0 (First release, March 2016)

Version 1.1 (April 2017)

  What's New: 

  • New working model for mediated moderation
  • Minor bug fixes 


Version 1.2 (November 2017)

  What's New: 

  • Minor bug fixes 

VS for Latent Variables

To test models with latent variables, we follow a three-step approach:

Step 1: Compute Factor Scores.  Given a conditional process model (which could be a model of mediated moderation, moderated mediation, or simple moderation) with latent variables, compute the factor scores of the latent variables based on confirmatory factor analysis.  Run the R program in the VS for Latent Variable Package, FS_program, to compute the factor scores.  This program computes two types of factor scores based on (1) the regression method and (2) Bartlett method.  The computed factor scores will be saved as an excel file in the user-specified folder. 

Step 2: Generate Modified Model.  Replace the latent variables that appear in the original model with the computed factor scores derived in Step 1.  The modified model, therefore, operates on the factor scores as if they were measured variables.  We follow Skrondal and Laake's (2001) bias avoiding procedure.  Specifically, we recommend to use the regression-type factor scores to replace those exogeneous latent variables, and the Bartlett-type factor scores for those endogeneous latent variables in this step.

Step 3: Analyze Modified Model.  Submit the modified model with factor scores to the standard VS program. 


Download the VS for Latent Variables Package here.

An illustrative example is available here.

VS Project Team

VS is developed by the VS Project Team:



Department of Psychology
The Chinese University of Hong Kong


KWAN, Joyce L.-Y.

Department of Psychology
The Education University of Hong Kong


NG, Jacky C.-K.

Department of Psychology
The Chinese University of Hong Kong


CHOI, Cherry Y.-T.

Department of Psychology
The Chinese University of Hong Kong



Contact Us

VS is a new product and it is undergoing a continuous development. We are working towards a better version with additional programming features. To help us improve our system, your comments and feedback are important. Please leave us a message at This email address is being protected from spambots. You need JavaScript enabled to view it..



This work was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administration Region, China (Project No.: CUHK 441113).