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Mplus

Mplus is a statistical software package that can implement a wide array of statistical models, but it is primarily known for its latent variable modeling capabilities. Latent variables are unobserved variables that are measured by multiple observed variables, also called items, indicators, or manifest variables, using a statistical model. Latent variables are typically used to summarize different measurements of the same unobserved characteristic that cannot be measured directly (e.g., student’s socioeconomic status) and represent the “true” outcomes as opposed to the observed variables, which are measured with an error.

Mplus is typically used by students, applied researchers, and practitioners interested in latent variables modeling, which is commonly used in the areas of education, psychology, and other social science disciplines. This entry first reviews improvements and add-on modules offered in updated versions of the statistical package. Next, applications for Mplus are considered. The entry also explains many of the functions of the Mplus interface and how to produce Mplus output files. The ability of Mplus to provide an evaluation of a statistical model is also discussed, and the entry concludes with a section about how to obtain Mplus and supporting materials.

Mplus Versions and Modules

Between version 1.0, released in 1998, and version 7.4 8.0, released in 2015, Mplus has introduced numerous developments and improvements that make possible estimations of many different latent variable models with different data conditions, choosing from a wide number of estimators and algorithms for the analysis (an extensive review of the Mplus version history and features can be found on the program’s website). The program is divided into the base program (Mplus Base) and three optional add-on modules. The base program allows the user to conduct exploratory factor analysis (EFA); confirmatory factor analysis (CFA); structural equation models; and regression, growth, and survival models with continuous, censored, binary, ordinal, nominal, and count variables or their combinations. The mixture add-on and multilevel add-on modules support a range of mixture models (such as latent class analysis) and multilevel models, respectively. The combination add-on module combines the features of the two individual add-ons and also enables estimation of several advanced models that combine the features of both modules (such as multilevel mixture models). Mplus can be installed on Windows, Mac OS, and Linux. The program is written in FORTRAN with graphical interface written in C and diagramming capabilities written in Java.

Applications

Mplus has flexible modeling capabilities, with the ability to estimate many different statistical models based on a wide variety of data types. The program can be applied to develop and validate scales (EFA and CFA), evaluate educational and psychological tests (categorical CFA and item response theory), discover unobserved groups in multivariate data (latent class and latent profile analyses), and estimate growth trajectory over time (latent growth analysis).

Mplus provides two approaches for analyzing complex survey data. The first approach takes into account stratification, nonindependence of observations due to cluster sampling, and/or unequal probability of selection when computing standard errors. The second approach, commonly referred to as multilevel or hierarchical modeling, models relationships between survey sampling and clustered standard errors by specifying a model for each level of the multilevel data.

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