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Mplus——结构方程模型

Mplus是一款统计建模程序,给研究人员提供了一个灵活的分析数据的工具。Mplus界面简单、数据和分析结果以图形显示,为研究人员提供广泛的模型、估计和算法的选择。Mplus允许进行横截面和纵向、单级和多级数据分析;来自不同人群的观测数据或未观测到的异质性数据,以及包含缺失值的数据都可以进行分析。可以对连续、删失、二进制、有序分类(序数)、无序类别(计数)、计数或这些变量类型的组合观测变量都可以进行分析。此外,Mplus还具有广泛的蒙特卡罗模拟功能,程序中包含的任何模型,都可以生成和分析数据。

Mplus的建模框架借鉴了潜变量的统一主题。而且一般的建模框架来自连续和分类潜变量的使用。连续潜变量用于表示与未观测到的构造相对应的因素,随机效应与发展中的个体差异相对应,随机效应与分层数据中各组间系数变化相对应,弱点对应于生存时间的异质性,责任与疾病遗传易感性相对应,潜在响应变量值与缺失数据相对应。分类潜变量对应于均质个体群,潜在的轨迹分类对应于未观测种群的发展类型,混合组件对应于未观测种群的有限混合,潜在响应变量类别对应于缺失数据。


Mplus建模框架
建模数据的目的是以简单的方式描述数据结构,便于理解和解释。本质上,数据建模相当于指定变量之间的一组关系。下图表示了在Mplus建模中的关系类型。矩形表示观测变量,观测变量可以是结果变量或背景变量。背景变量为X,连续和截尾结果变量为y,二元、有序范畴(序数),无序分类(名词)和计数结果变量为u。圆圈代表潜变量。允许连续变量和类别变量,连续潜变量为f,分类潜变量为c。


图中的箭头表示变量之间的回归关系。回归关系是允许的,但在图中没有具体说明,包括观测到的结果变量之间的回归,连续潜变量之间的回归以及类别潜变量的回归。对于连续结果变量,使用的是线性回归模型。对于结果变量,在删截点有或没有通货膨胀,审查(tobit)都使用回归模型。对于二进制和有序分类结果,使用概率或logistic回归模型。对于无序的分类结果,使用多项式logistic回归模型。对于计数结果,不管通货膨胀率是否为零,都使用Poisson和负二项回归模型。

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Mplus模型包括连续的潜变量、分类潜变量、连续变量和类别潜变量的组合。上图中,圆柱A描述只有潜在连续变量的模型。圆柱B描述只有特定潜变量的模型。完整的建模框架描述了连续变量和类别变量相结合的模型。上图表明,Mplus估计的描述个体水平的多层次模型(内部)和集群水平(之间)的变量。


Mplus Base Program
Mplus Base Program可以估计回归、路径分析、探索性因素分析和验证性因素分析(EFA和CFA)、结构方程模型(SEM)、增长以及离散和连续时间生存分析模型。在回归和路径分析模型中,观测到的因变量可以是连续的、删失的、二进制的、有序的(序数)、计数或这些变量类型的组合。此外,对于非中介变量的回归分析和路径分析,观测到的因变量可以是无序的分类(名义上)。在探索性因素分析中,因素指标可以是连续的、二进制的、有序的分类(排序)或是这些变量类型的组合。在CFA、SEM和增长模型中,观测到的因变量可以是连续的、删失的、二元的、有序的(序数)、无序的分类(名词)、计数或这些变量类型的组合。其他特殊的功能包括单组或多组分析,缺失数据估计;复杂的调查数据分析,包括分层,聚类,和不平等的选择概率(抽样权重);用极大似然法分析潜在变量相互作用和非线性因素;随机斜率;个体变化的观测次数;非线性参数约束;间接影响;所有结果类型的极大似然估计。引导的标准误差和置信区间;贝叶斯分析与多重归责原则;蒙特卡罗模拟功能以及后处理图形模型。


Mplus Base Program and Mixture Add-On
包含了所有Mplus Base Program的功能。此外,估计回归混合模型;路径分析混合模型;潜在类别分析;具有多分类潜变量的潜类分析;对数线性模型;有限混合模型;编译器的平均因果关系(CACE)模型;潜在类增长分析;潜在转移分析;隐马尔可夫模型以及离散和连续时间生存混合分析。观测到的因变量可以是连续的、删失的、二元的、有序的(序数)、无序的分类(名词)、计数或这些变量类型的组合。其他特殊功能包括单组或多组分析;缺失数据估计;复杂的调查数据分析,包括分层、聚类和不平等的选择概率(抽样权重);用极大似然法分析潜在变量相互作用和非线性因素;随机斜率;个体变化的观测次数;非线性参数约束;所有结果类型的极大似然估计。引导的标准误差和置信区间;贝叶斯分析与多重归责原则;蒙特卡罗模拟功能以及后处理图形模型。


Mplus Base Program and Combination Add-On
Mplus Base Program and Combination Add-On包含了Mplus Base Program and the Mixture and Multilevel Add-Ons的所有功能。此外,它还包括处理同一模型中的集群数据和潜在类的模型。例如,两级回归混合分析、二级混合验证因子分析(CFA)和结构方程模型(SEM)、二级潜类分析、多层增长混合模型、二级离散和连续时间生存混合分析。其他特殊功能包括缺失数据估计;复杂的调查数据分析,包括分层、聚类和不平等的选择概率(抽样权重);用极大似然法分析潜在变量相互作用和非线性因素;随机斜率;个体变化的观测次数;非线性参数约束;所有结果类型的极大似然估计。贝叶斯分析与多重归责原则;蒙特卡罗模拟功能以及后处理图形模型。

适用平台
Microsoft Windows 7/8/10
Mac OS X 10.8或更高版本
Linux (已在下面的平台中测试过: Ubuntu, RedHat, Fedora, Debian和Gentoo)
至少1GB以上的内存
至少120 MB硬盘空间


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.