During the last thirty years, the LISREL model, methods and software have become synonymous with structural equation modeling (SEM). SEM allows researchers in the social sciences, management sciences, behavioral sciences, biological sciences, educational sciences and other fields to empirically assess their theories. These theories are usually formulated as theoretical models for observed and latent (unobservable) variables. If data are collected for the observed variables of the theoretical model, the LISREL program can be used to fit the model to the data. Today, however, LISREL for Windows is no longer limited to SEM.
LISREL for structural equation modeling.
Standard structural equation modeling
Complete and incomplete complex survey data on continuous variables
MULTILEV for hierarchical linear and non-linear modeling.
MAPGLIM implements the Maximum A Priori (MAP) method to fit generalized linear models to multilevel data.
|PRELIS for data manipulations and basic statistical analyses.
PRELIS is a 32-bit application which can be used for:
SURVEYGLIM fits Generalized LInear Models (GLIMs) to data from simple random and complex survey designs.
Models for the following sampling distributions are available.
SSI has enjoyed great success over the years in the development and publishing of statistical software and is proud to announce the release of LISREL 10.1.
In an effort to meet the growing demands of our LISREL 8 and 9 user community, SSI has developed LISREL 10, which is on the cutting edge of current technology. The program has been tested extensively on the Microsoft Windows platform with Windows7 and Windows 10 operating systems.
Structural equation modeling (SEM) was introduced initially as a way of analyzing a covariance or correlation matrix. Typically, one would read this matrix into LISREL and estimate the model by maximum likelihood. If raw data was available without missing values, one could also use PRELIS first to estimate an asymptotic covariance matrix to obtain robust estimates of standard errors and chi-squares.
Modern structural equation modeling is based on raw data. With LISREL 10, if raw data is available in a LISREL data system file or in a text file, one can read the data into LISREL and formulate the model using either SIMPLIS syntax or LISREL syntax.
LISREL 10 contains fixes to all bugs reported by users of LISREL 9. The new LISREL features are summarized next.
MULTIPLE GROUP ANALYSES USING A SINGLE DATA FILE
In practice, many multivariate data sets are observations from several groups. Examples of these groups are genders, languages, political parties, countries, faculties, colleges, schools, etc.
LISREL may be used to fit multiple group structural equation models to multiple group data. Traditional statistical methods such as Maximum Likelihood (ML), Robust Maximum Likelihood (RML), Weighted Least Squares (WLS), Diagonally Weighted Least Squares (DWLS), Generalized Least Squares (GLS) and Un-weighted Least Squares (ULS) are available for complete multiple group data while the Full Information Maximum Likelihood (FIML) method is available for incomplete multiple group data.
In previous versions of LISREL, the user was required to create separate data files for each group. Suppose that the groups to be analyzed consisted of data collected in eight countries, the implication is that eight datasets must to be created in order to fit a multiple group structural equation model.
A new feature implemented in LISREL 10 allows researchers to use a single dataset that contains a group variable that can be defined by
Using the Data Menu when a LISREL system file (.lsf) is opened
By inserting the line $GROUPS=<group variable name> anywhere in the syntax file.
Consider the dataset efficacy_4countries.lsf shown below. There are 4 countries and portion of the data from countries 2 and 3 are shown below.
To use this dataset in a multiple group analysis, use the Data menu from the main menu bar and select the Group Variable… option (see below)
Select COUNTRY from the list of variables and when done click the OK button.
The LISREL Examples folder contains a sub-folder named MGROUPS that contains examples for the following statistical procedures:
For a detailed example, see the Assessment of Invariance, (Section 2 in the “Additional Topics Guide.pdf”) that can be accessed via the Help option on the main menu bar:
P-VALUE FOR C1 STATISTIC UNDER NON-NORMALITY
Modern structural equation modeling is based on raw data. With LISREL 10, if raw data is available in a LISREL data system file or in a text file, one can read the data into LISREL and formulate the model using either SIMPLIS syntax or LISREL syntax. It is no longer necessary to estimate an asymptotic covariance matrix with PRELIS and read this into LISREL. The estimation of the asymptotic covariance matrix and the model is now done in LISREL. One can also use the EM or MCMC multiple imputation methods in LISREL to fit a model to the imputed data.
DATA CONVERSION USING STAT/TRANSFER
The data import/export software has been upgraded from Stat/Transfer Version 13 to the most recently released Version 14.
Selection of new features available Stat/Transfer Version 14
Version 14 has added support for the following formats:
BayesiaLab (Write Only)
JSON-Stat (Read Only)Version 14 has larger limits for:
Excel Files > 4 GB
SAS files > 32K variables
Stata Files > 32K variables
dBASE > 2GB
THRESS-LEVEL MULTILEVEL GENERALIZED LINEAR MODELS
Cluster or multi-stage samples designs are frequently used for populations with an inherent hierarchical structure. Ignoring the hierarchical structure of data has serious implications. The use of alternatives such as aggregation and disaggregation of information to another level can induce an increase in co-linearity among predictors and large or biased standard errors for the estimates.
The collection of models called Generalized Linear Models (GLIMs) have become important, and practical, statistical tools. The basic idea of GLIMs is an adaption of standard regression to quite different kinds of data. The variables may be dichotomous, ordinal (as with a 5-point Likert scale), counts (number of arrest records), or nominal. The motivation is to tailor the regression relationship connecting the outcome to relevant independent variables so that it is appropriate to the properties of the dependent variable. The statistical theory and methods for fitting Generalized Linear Models (GLIMs) to survey data was implemented in LISREL 8.8.
Researchers from the social and economic sciences are often applying these methods to multilevel data and consequently, inappropriate results are obtained. The LISREL statistical module for the analysis of multilevel data allows for design weights. Two estimation methods, MAP (maximization of the posterior distribution) and QUAD (adaptive quadrature) for fitting generalized linear models to multilevel data are available. The LISREL Multilevel Generalized Linear models module (MGLIM) allows for a wide variety of sampling distributions and link functions.
The LISREL 10 MGLIM module also include zero-inflated Poisson and zero-inflated Negative-Binomial models and prints results for unit-specific and population-average estimates of the fixed effects.
Examples in the folder mglimex illustrate these features.
These examples are based on a new book: “Multivariate Analysis with LISREL” authored by Karl G Jöreskog, Ulf H. Olsson & Fan Y. Wallentin (2017).
This book can be used by Master and PhD students and researchers in the economic, social, behavioral, and many other sciences that need to have a basic understanding of multivariate statistical theory and methods for their analysis of multivariate data. It can also be used as a text book for courses on multivariate statistical analysis. All examples are listed in the Table of Contents. All the syntax and data files for these examples are distributed with LISREL 10.1 and are located in
Program documentation is available as PDFs via the Help menu.
A list of PDF guides, accessible via the online Help menu is given below.
New features in LISREL
Graphical User’s Interface
PRELIS Examples Guide
LISREL Examples Guide
Multilevel Modeling Guide
Complex Survey Sampling
Generalized Linear Modeling Guide
Multilevel Generalized Linear Modeling Guide
Models for Proportional and Non-proportional Odds
Survival Models for Grouped Data
LISREL Syntax Guide
SIMPLIS Syntax Guide
PRELIS Syntax Guide
Additional Topics Guide
The complex Survey Sampling Guide includes structural equation modeling (SEM) for continuous variables and SEM for a mixture of ordinal and continuous variables. LISREL uses full information maximum likelihood under complex survey data with data missing at random.
The Additional Topics Guide includes sections on assessment of invariance, multiple imputation, multilevel structural equation modeling and multilevel non-linear regression.
ANALYSIS OF ORDINAL DATA USING IMPUTATION AND ACM (ls9ex)
Efficacy4a.spl: Model 2 Estimated by Robust Diagonally Weighted Least Squares
Raw Data from file EFFICACY.LSF
Multiple Imputation with MC
Latent Variables Efficacy Respons
NOSAY COMPLEX NOCARE = Efficacy
NOCARE – INTEREST = Respons
Method of Estimation: Diagonally Weighted Least Squares
End of Problem
Path Diagram Representation
Goodness of Fit Statistics
The last portion of the output file is a summary of fit statistics and confidence intervals. These statistics are discussed in the Appendix of the New Features in LISREL 9 guide, available in PDF format via the LISREL online Help menu.
A LEVEL-4 MODEL WITH CONTINUOS OUTCOME VARIABLE (mlevelex)
! Measurements made on 1,192 participants at three occasions.
! In the case of some of the participants, measurements were
! made on only one or two occasions.
OPTIONS OLS=YES CONVERGE=0.000100 MAXITER=15 OUTPUT=STANDARD;
TITLE=Analysis of level-4 repeated measurements data;
FIXED=gender occasion thera1 thera2 thera3 thera4;
Data for the first 10 participants on most of the variables are shown below in the form of a LISREL spreadsheet file, named therapist_L4.lsf.
The variables of interest are:
site is the level-4 identification variable (49 units in total).
therapis is the level-3 identification variable (187 units in total).
particip is the level-2 identification variable (1192 units in total).
assesmt is a score assigned by a therapist to a particular participant on occasion 0, 1 or 2.
gender is a gender indicator, with a value of 0 indicating a male participant and 1 a female participant.
occasion is a predictor variable coded 0, 1 and 2.
thera1 – thera4 are dummy coded variables indicating four types of therapy.Only selected parts of the output are shown. The output describing the estimated fixed effects after convergence is shown first. From the z-values and associated exceedance probabilities, we see that except for the coefficient associated with gender, the remaining coefficients are all highly significant.
A study of the random part of the model shows that all the intercept effects are highly significant, except for the level-3 (therapists) intercept. From this, we conclude that intercept estimates vary significantly over sites, but not over therapists.
MODELS FOR GROUPED- AND DISCRETE-TIE SURVIVAL DATA
Models for grouped-time survival data are useful for analysis of failure time data when subjects are measured repeatedly at fixed intervals in terms of the occurrence of some event, or when determination of the exact time of the event is only known within grouped intervals of time. Additionally, it is often the case that subjects are observed nested within clusters (i.e., schools, firms, clinics), or are repeatedly measured in terms of recurrent events. In this case, use of grouped-time models that assume independence of observations is problematic since observations from the same cluster or subject are usually correlated.
For data that are clustered and/or repeated, models including random effects provide a convenient way of accounting for association in correlated survival data.
Several authors have noted the relationship between ordinal regression models (using complementary log-log and logistic link functions) and survival analysis models for grouped and discrete time. In LISREL 10 a generalization of an ordinal random-effects regression model to handle correlated grouped-time survival data is implemented. This model accommodates multivariate normally-distributed random effects, and additionally, allows for a general form for model covariates.
Assuming a proportional or partial proportional, hazards or odds model, a maximum marginal likelihood solution is implemented using multi-dimensional quadrature to numerically integrate over the distribution of random-effects. The reference guide “Survival Models for grouped data.pdf” contains examples and references and is accessible via the online Help menu.
MODELS FOR ORDINAL OUTCOMES AND THE PROPORTIONAL ODDS VERSUS NON- PROPORTIONAL ODDS ASSUMPTION
The term “ordinal” is applied to variables where the response measure of interest is measured in a series of ordered categories. Examples of such variables include Likert scales and psychiatric ratings of severity. Nominal and ordinal outcome models can be seen as generalizations of the binary outcome model. The ordinal model becomes important when the outcome variable is not dichotomous, or not truly continuous. If an ordinal outcome is analyzed within a continuous model, such a model can yield predicted values outside the range of the ordinal variable. As with binary data, some transformation or link function becomes necessary to prevent this from happening. The continuous model can also yield correlated residuals and regressors when applied to ordinal outcomes because the continuous model does not take the ceiling and floor effects of the ordinal outcome into account. This can then result in biased estimates of regression coefficients, and is most critical when the ordinal variable in question is highly skewed.
Extensive work on the development of methods for the analysis of ordinal response data has been undertaken by numerous researchers. These developments have focused on the extension of methods for dichotomous variables to ordinal response data, and have been mainly in terms of logistic and probit regression models. The proportional odds model is a common choice for the analysis of ordinal data. In LISREL 10, it is possible to fit both proportional and non-proportional odds models to verify the proportional odds assumption using a chi-square difference test. The reference guide “Models for proportional and non-proportional odds.pdf” contains examples and references and is accessible via the online Help menu.
COMBINING LISREL AND PRELIS FUNCTIONALITY
Satorra & Bentler (1978) states that the asymptotic distribution of chi-square C1 is that of a linear combination of chi-squares with 1 degree of freedom, where the coefficients of the linear combination are the d (d = the degree of freedom) non-zero eigenvalues of UW_NNT, where U is defined in Satorra & Bentler (1978) and also in equation (45) in the document “New Features in LISREL 9” (available under “LISREL User & Reference Guides”) and W_NNT is an estimate of the asymptotic covariance matrix of the variances and covariance of the observed variables under non-normality, usually referred to as the ACM matrix.
LISREL 10 estimates the d eigenvalues and the p-value of the linear combination. Essentially, this makes the other chi-squares C2, C3, C4 and C5 less important, since they are based on approximations of the distribution using only the mean and variance of the eigenvalues.
FIML FOR ORDINAL AND CONTINUOS VARIABLES
LISREL 10 supports Structural Equation Modeling for a mixture of ordinal and continuous variables for simple random samples and complex survey data.
The LISREL implementation allows for the use of design weights to fit SEM models to a mixture of continuous and ordinal manifest variables with or without missing values with optional specification of stratum and/or cluster variables. It also deals with the issue of robust standard error estimation and the adjustment of the chi-square goodness of fit statistic.
This method is based on adaptive quadrature and a user can specify any one of the following four link functions:
Examples to illustrate this feature are given in the folders orfimlex and ls9ex.
FOUR AND FIVE-LEVEL MULTILEVEL LINEAR MODELS FOR CONTINUOS OUTCOME VARIABLES
Social science research often entails the analysis of data with a hierarchical structure. A frequently cited example of multilevel data is a dataset containing measurements on children nested within schools, with schools nested within education departments.
The need for statistical models that take account of the sampling scheme is well recognized and it has been shown that the analysis of survey data under the assumption of a simple random sampling scheme may give rise to misleading results.
Multilevel models are particularly useful in the modeling of data from complex surveys. Cluster or multi-stage samples designs are frequently used for populations with an inherent hierarchical structure. Ignoring the hierarchical structure of data has serious implications. The use of alternatives such as aggregation and disaggregation of information to another level can induce an increase in co-linearity among predictors and large or biased standard errors for the estimates. In order to address concerns regarding the appropriate analyses of survey data, the LISREL multilevel module for continuous data now also handles up to five levels and features an option for users to include design weights on levels 1, 2 , 3, 4 or 5 of the hierarchy.
Examples are given in the mlevelex folder.
RUNNING LISREL IN BATCH MODE
Any of the LISREL programs can be run into batch mode by using a .bat file with the following script:
“c:program files (x86)LISREL10MLISREL64_10”
Program name = LISREL, PRELIS, MULTILEV, MAPGLIM or SURVEYGLIM
Syntax File = “c:LISREL Examplesls9exnpv1a.spl”
Output File = “c:LISREL Examplesls9exnpv1a.out”
Examples of batch files (RunLISREL.bat and RunSIMPLIS.bat) are given in the ls9ex folder. These batch files will run all the LISREL and SIMPLIS syntax files in this folder.
ANALYSIS OF ORDINAL DATA USING QUADRATURE (ls9ex)
Efficacy3a.spl: Model 2 Estimated by FIML
Raw Data from file EFFICACY.LSF
$ADAPQ(8) PROBIT GR(5)
Latent Variables Efficacy Respons
NOSAY – NOCARE = Efficacy
NOCARE – INTEREST = Respons
End of Problem
Path Diagram Representation
Path Diagram (Standardized Solution)
Portion of output file
The last part of the output file is shown below.
For the moment we note the value of the deviance statistic −2 ln L = 19858.06. Since there is no value of −2 ln L for a saturated model, it is impossible to say whether this is large or small in some absolute sense. The deviance statistic can therefore only be used to compare different models for the same data.
To illustrate, the difference between the deviance statistic for this model and the deviance statistic for a model with one latent variable (Efficacy2a.spl) is 19934.57-19858.06 =76.51, which suggests that the two-dimensional model fits the data much better than the uni-dimensional model.
The output also gives estimates of the thresholds, their standard errors and z-values. The thresholds are parameters of the model but are seldom useful in analysis of a single sample.
THREE-LEVEL GENERALIZED LINEAR MODEL (mglimex)
MGlimOptions Converge=0.0001 MaxIter=500 MissingCode=-999999
Title=Level-3 Ordinal Model, random intercept and slope at level-2;
! Syntax file name is Tvsfpors_ORDINAL.prl
! The data for this example is from the Television School and
! Family Smoking Prevention
! and Cessation Project (TVSFP) and was downloaded from
! A description of the data is given in mixorcm.pdf, available ! from the URL above.
CoVars=PreTHKS CC TV ‘CC*TV’;
Selected portions of the output file are displayed below.
Parameter Estimates and Odds Ratios
Estimated variance components
Estimates of the variance components on levels 2 and 3 and the associated p-values indicate that the PreTHKS coefficient does not vary significantly over classes. Note however, that the covariance term is almost significant. The level-3 intercept effect is also not significant. These results seem to indicate a level-2 model random intercept model as being more appropriate.
All LISREL syntax files have extension .lis (since LISREL 9, previously .ls8), all PRELIS syntax files have extension .prl (since LISREL 9, previously .pr2). The LISREL spreadsheet has been renamed LISREL data system file and has extension .lsf (since LISREL 9, previously .psf).
To ensure backwards compatibility, users can still run previously created syntax files using a .psf file, but to open an existing .psf file using the graphical user’s interface, the user has to rename it to .lsf.
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|LISREL 10 is compatible with Windows 10. It has been tested on Windows 10 and no problems were reported.|
|LISREL 10 is compatible with Windows 8. It has been tested on Windows 8 and no problems were reported.|
|LISREL 10 is compatible with Windows 7. It has been tested on Windows 7 and no problems were reported.|
Additional Multilevel material not contained in the Multilevel Modeling Guide:
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Software originalmente sviluppato per la stima di modelli di equazioni strutturali (SEM). Oggi comprende molte altre applicazioni statistiche.