Mplus is a statistical modeling program that provides researchers with a flexible tool to analyze their data. Mplus offers researchers a wide choice of models, estimators, and algorithms in a program that has an easy-to-use interface and graphical displays of data and analysis results. Mplus allows the analysis of both cross-sectional and longitudinal data, single-level and multilevel data, data that come from different populations with either observed or unobserved heterogeneity, and data that contain missing values. Analyses can be carried out for observed variables that are continuous, censored, binary, ordered categorical (ordinal), unordered categorical (nominal), counts, or combinations of these variable types. In addition, Mplus has extensive capabilities for Monte Carlo simulation studies, where data can be generated and analyzed according to any of the models included in the program.
The Mplus modeling framework draws on the unifying theme of latent variables. The generality of the Mplus modeling framework comes from the unique use of both continuous and categorical latent variables. Continuous latent variables are used to represent factors corresponding to unobserved constructs, random effects corresponding to individual differences in development, random effects corresponding to variation in coefficients across groups in hierarchical data, frailties corresponding to unobserved heterogeneity in survival time, liabilities corresponding to genetic susceptibility to disease, and latent response variable values corresponding to missing data. Categorical latent variables are used to represent latent classes corresponding to homogeneous groups of individuals, latent trajectory classes corresponding to types of development in unobserved populations, mixture components corresponding to finite mixtures of unobserved populations, and latent response variable categories corresponding to missing data.
The Mplus Modeling Framework
The purpose of modeling data is to describe the structure of data in a simple way so that it is understandable and interpretable. Essentially, the modeling of data amounts to specifying a set of relationships between variables. The figure below shows the types of relationships that can be modeled in Mplus. The rectangles represent observed variables. Observed variables can be outcome variables or background variables. Background variables are referred to as x; continuous and censored outcome variables are referred to as y; and binary, ordered categorical (ordinal), unordered categorical (nominal), and count outcome variables are referred to as u. The circles represent latent variables. Both continuous and categorical latent variables are allowed. Continuous latent variables are referred to as f. Categorical latent variables are referred to as c.
The arrows in the figure represent regression relationships between variables. Regressions relationships that are allowed but not specifically shown in the figure include regressions among observed outcome variables, among continuous latent variables, and among categorical latent variables. For continuous outcome variables, linear regression models are used. For censored outcome variables, censored (tobit) regression models are used, with or without inflation at the censoring point. For binary and ordered categorical outcomes, probit or logistic regressions models are used. For unordered categorical outcomes, multinomial logistic regression models are used. For count outcomes, Poisson and negative binomial regression models are used, with or without inflation at the zero point.
Models in Mplus can include continuous latent variables, categorical latent variables, or a combination of continuous and categorical latent variables. In the figure above, Ellipse A describes models with only continuous latent variables. Ellipse B describes models with only categorical latent variables. The full modeling framework describes models with a combination of continuous and categorical latent variables. The Within and Between parts of the figure above indicate that multilevel models that describe individual-level (within) and cluster-level (between) variation can be estimated using Mplus.
Mplus Base Program
The Mplus Base Program estimates regression, path analysis, exploratory and confirmatory factor analysis (EFA and CFA), structural equation (SEM), growth, and discrete- and continuous-time survival analysis models. In regression and path analysis models, observed dependent variables can be continuous, censored, binary, ordered categorical (ordinal), counts, or a combination of these variable types. In addition, for regression analysis and path analysis for non-mediating variables, observed dependent variables can be unordered categorical (nominal). In EFA, factor indicators can be continuous, binary, ordered categorical (ordinal), or a combination of these variable types. In CFA, SEM, and growth models, observed dependent variables can be continuous, censored, binary, ordered categorical (ordinal), unordered categorical (nominal), counts, or a combination of these variable types. Other special features include single or multiple group analysis; missing data estimation; complex survey data analysis including stratification, clustering, and unequal probabilities of selection (sampling weights); latent variable interactions and non-linear factor analysis using maximum likelihood; random slopes; individually-varying times of observation; non-linear parameter constraints; indirect effects; maximum likelihood estimation for all outcomes types; bootstrap standard errors and confidence intervals; Bayesian analysis and multiple imputation; Monte Carlo simulation facilities; and a post-processing graphics module.
Mplus Base Program and Mixture Add-On
The Mplus Base Program and Mixture Add-On contains all of the features of the Mplus Base Program. In addition, it estimates regression mixture models; path analysis mixture models; latent class analysis; latent class analysis with multiple categorical latent variables; loglinear models; finite mixture models; Complier Average Causal Effect (CACE) models; latent class growth analysis; latent transition analysis; hidden Markov models; and discrete- and continuous-time survival mixture analysis. Observed dependent variables can be continuous, censored, binary, ordered categorical (ordinal), unordered categorical (nominal), counts, or a combination of these variable types. Other special features include single or multiple group analysis; missing data estimation; complex survey data analysis including stratification, clustering, and unequal probabilities of selection (sampling weights); latent variable interactions and non-linear factor analysis using maximum likelihood; random slopes; individually-varying times of observation; non-linear parameter constraints; indirect effects; maximum likelihood estimation for all outcomes types; bootstrap standard errors and confidence intervals; automatic starting values with random starts; Bayesian analysis and multiple imputation; Monte Carlo simulation facilities; and a post-processing graphics module.
Mplus Base Program and Multilevel Add-On
The Mplus Base Program and Multilevel Add-On contains all of the features of the Mplus Base Program. In addition, it estimates models for clustered data using multilevel models. These models include multilevel regression analysis, multilevel path analysis, multilevel factor analysis, multilevel structural equation modeling, multilevel growth modeling, and multilevel discrete- and continuous-time survival models. In multilevel analysis, observed dependent variables can be continuous, censored, binary, ordered categorical (ordinal), unordered categorical (nominal), counts, or a combination of these variable types. Other special features include single or multiple group analysis; missing data estimation; complex survey data analysis including stratification, clustering, and unequal probabilities of selection (sampling weights); latent variable interactions and non-linear factor analysis using maximum likelihood; random slopes; individually-varying times of observation; non-linear parameter constraints; maximum likelihood estimation for all outcomes types; Bayesian analysis and multiple imputation; Monte Carlo simulation facilities; and a post-processing graphics module.
Mplus Base Program and Combination Add-On
The Mplus Base Program and Combination Add-On contains all of the features of the Mplus Base Program and the Mixture and Multilevel Add-Ons. In addition, it includes models that handle both clustered data and latent classes in the same model, for example, two-level regression mixture analysis, two-level mixture confirmatory factor analysis (CFA) and structural equation modeling (SEM), and two-level latent class analysis, multilevel growth mixture modeling, and two-level discrete- and continuous-time survival mixture analysis. Other special features include missing data estimation; complex survey data analysis including stratification, clustering, and unequal probabilities of selection (sampling weights); latent variable interactions and non-linear factor analysis using maximum likelihood; random slopes; individually-varying times of observation; non-linear parameter constraints; maximum likelihood estimation for all outcomes types; Bayesian analysis and multiple imputation; Monte Carlo simulation facilities; and a post-processing graphics module.
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