Applied Psychometric Strategies Lab Applied Quantitative and Psychometric
Applied Psychometric Strategies Lab Applied Quantitative and Psychometric Series David Dueber, MA Michael Toland, Ph. D Introduction to Mplus October 4, 2016
What is Mplus? • Mplus is a powerful statistical program specifically designed for latent variable modeling – Handles continuous and ordinal (categorical) data – New versions roughly every year implementing common user-requested • Mplus uses syntax-based input files and textbased data files • Developed by Muthén, L. K. , & Muthén, B. O. (1998 -2015)
What is latent variable modeling? • A latent variable model is a statistical model that relates a set of observed variables to a set of latent variables • For example, there is no way to directly measure self-efficacy – But, participants respond to items intended to measure self-efficacy – Mplus can model a latent variable representing self-efficacy based on observed responses to those items
What are some advantages of Mplus? • It’s highly versatile, supporting many different types of modeling – Supports a wide variety of different latent variable models and can freely combine them • Has a very simple syntax language, compared to R or SAS. – No programming expertise is required
What are some capabilities of Mplus? • • • Exploratory and Confirmatory Factor Analysis Structural Equation Modeling Multilevel Modeling Item Response Theory Bayesian Analysis Latent Class Analysis Mixture Modeling Monte Carlo Simulations Longitudinal Analysis Multiple Imputation for Missing Data Any combination of these!!
Comparison of Some Common Statistical Software Mplus SPSS R SAS Structural Equation Modeling Yes, with AMOS Yes (lavaan) Yes (Proc CALIS, TCALIS) Bayesian Analysis Yes No Yes Mixture Modeling Yes No Yes (with package*) Yes (limited) Multiple Imputation for Multilevel (MLM) data Yes No Yes Pooling of MLM data Yes ? Yes Item response theory Yes (with R plugin) Yes (Proc IRT, NLMIXED) * R packages all require their own syntax, and usually cannot be used together (https: //cran. r-project. org/web/views/Psychometrics. html)
What are some examples of cool things Mplus can do? • Combine capabilities seamlessly – Use Bayesian analysis to perform multilevel mixture modeling with one of the levels being longitudinal • Thurstonian IRT, a method for analyzing forcedchoice data, is only available in Mplus and R • Testing many different mediation pathways can easily be performed using the “Model Constraint” command
Mplus sounds great! What’s the catch? • Cost - $350 student version – However, three computers in TEB 151 have Mplus installed – Grants may be available if required for your dissertation • Need to learn syntax language • Lacks some bells-and-whistles – e. g. , M 2 limited information GOF statistics in IRT • As with every program, it cannot do everything
What are some key points about Mplus? • Mplus can handle (combinations of) a wide array of statistical analyses • Mplus uses a simple, generic syntax language • Mplus can natively handle both ordinal and continuous variables
Questions?
Regression Example: Research Question • NASCAR races are run on 21 different tracks. • Tracks vary based on length, banking of curves, and various other factors • Research Question: Can we predict record lap speeds (DV) for tracks based on the length of the track (IV 1) and the banking of the curves (IV 2)?
Regression Example: Path Diagram Track Length Top Speed Degrees of Banking res
Regression Example: Data File (. csv) • In SPSS, Save As Comma Delimited (*. csv) Uncheck “Write variable names to spreadsheet” • In Excel file, Save As CSV (Comma Delimited) (*. csv) • May also use *. txt or *. dat (comma separated or tab separated both work)
Regression Example: Data File • First column is track length, measured in miles • Second column is maximum banking, measured in degrees • Third column is the record top lap speed, measured in mph • Fourth column is the year in which the record was set
Regression Example: Input File
Regression Example: Sample Statistics • Mplus uses population formulas for covariances and correlations, so if you have a very small sample size, you may need to adjust
Regression Example: Output (z) The p-value for R 2 is from a z test. You can perform the Ftest manually.
From R 2 to F •
Regression Example: Standardized Output
Regression Example: Plots
Regression Example: APA Style Writeup The multiple regression model with track length and banking steepness was statistically significant at explaining variability in top speed, R 2 =. 61, z = 4. 64, p <. 001. Track length had a statistically significant positive regression weight, but the regression weight for banking steepness was not statistically significant.
Questions?
Correlation Example: Research Question • In an instrument you have written with a Likert-type response format with four options, you suspect that two items are too similar to each other and are considering dropping one of them* • What is the correlation between the scores of these two items? * This example is entirely made-up
Correlation Example: Input File
Correlation Example: Output The results of a “WITH” model are covariances The standardized model results is the correlation (correlation is standardized covariance)
Correlation Example: Reviewer Number 2 • A psychometrician was assigned to review your manuscript and gave the following objection: “It is not appropriate to use the Pearson correlation coefficient for data which is not continuous. Please re-run your analysis accounting for the categorical nature of your data. ”
Correlation Example: Categorical Variables
Correlation Example: New Output In this example, Mplus models latent continuous variables (which it automatically standardizes) for the observed categorical variable. This is why both results are correlations.
Categorical Example: Second Time’s The Charm • New input file was generated simply by adding a single line • Categorical data is handled natively with no need for special scripts or packages
Do any textbooks present data analytic topics with Mplus? • Geiser, C. (2012). Data analysis with Mplus. Guilford Press. • Muthén, B. O. , Muthén, L. K. , & Asparouhov, T. (2016). Regression and Mediation Analysis Using Mplus. Muthén and Muthén. • Byrne, B. M. (2013). Structural equation modeling with Mplus: Basic concepts, applications, and programming. Routledge. • Heck, R. H. , & Thomas, S. L. (2015). An introduction to multilevel modeling techniques: MLM and SEM approaches using Mplus. Routledge. • Wickrama, K. K. , Lee, T. K. , O’Neal, C. W. , & Lorenz, F. O. (2016). Higher-Order Growth Curves and Mixture Modeling with Mplus: A Practical Guide. Routledge.
Helpful Mplus Resources • https: //www. statmodel. com/language. html • http: //www. statmodel. com/download/usersg uide/Mplus. User. Guide. Ver_7. pdf • http: //www. lesahoffman. com/943/Introductio n_to_Mplus_Syntax. pdf • http: //statmodel. com/course_materials. shtml • Google your question with “Mplus” in there somewhere. The Muthéns have answered thousands of questions on their forums
Applied Psychometric Strategies Lab Applied Quantitative and Psychometric Series • Thank you for attending – Go forth and use Mplus • Questions?
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