Kline R.B. Principles and Practice of Structural Equation Modeling

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74 CONCEPTS AND TOOLS

5. Use a computer tool for statistics to construct the normal probability plot for

the data in Figure 3.2.

6. Remove the outlier (the score of 27) from the distribution in Figure 3.2 and

recalculate the skew index and the kurtosis index for N = 63.

7. Why is it necessary to add a constant to the scores so that the lowest score

equals 1.0 before applying a square root transformation or a logarithmic trans-

formation?

8. Apply the square root transformation to the scores in Figure 3.2, but apply it

to the original scores, not to the rescaled scores where a constant is added so

that the lowest score equals 1.0. Then calculate the skew index and the kurtosis

index. Compare these results to those reported in the text for the data in Figure

3.2 but rescaled where the lowest score is 1.0.

9. Presented next are scores on ﬁve dichotomously scored items (0 = wrong, 1 =

correct) for eight cases (A–H). Use a computer tool for general statistical analy-

ses to calculate internal consistency reliability using Equation 3.6 for these

scores. If your computer tool has a reliability analysis procedure, then use it to

verify your calculations:

A: 1, 1, 0, 1, 1 B: 0, 0, 0, 0, 0

C: 1, 1, 1, 1, 0 D: 1, 1, 1, 0, 1

E: 1, 0, 1, 1, 1 F: 0, 1, 1, 1 ,1

G: 1, 1, 1, 1, 1 H: 1, 1, 0, 1, 1

Computer Tools

Described in this chapter are major software tools. These include eight programs or

procedures speciﬁcally intended for SEM: Amos, CALIS/TCALIS of SAS/STAT, EQS,

LISREL, Mplus, Mx, RAMONA of SYSTAT, and SEPATH of STATISTICA. Two other

programs originally created for other kinds of statistical analyses but with SEM capa-

bilities are R and MATLAB, which are also described. Ways of interacting with SEM

computer tools are outlined, and pros and con of different methods are considered.

A major theme of this chapter is that the relative ease of use of modern computer

tools should not lull you into thinking that SEM is easy or requires minimal conceptual

understanding. In this sense, this adage by the Canadian scholar Marshall McLuhan is

appropriate: We shape our tools and afterwards our tools shape us. I hope that com-

puter tool use sharpens, rather than dulls, your ability to think critically about SEM.

ease oF use, not susPensIon oF JudgMent

Computer programs are critical tools for the conduct of SEM. About 30 years ago, LIS-

REL was essentially the only widely available SEM program. At that time, LISREL and

related programs were rather difﬁcult to use because they (1) required users to gener-

ate a lot of rather arcane code for each analysis and (2) were generally available only on

mainframe computers with stark command-line user interfaces. The abundance of rela-

tively inexpensive yet powerful personal computers has dramatically changed this situa-

tion. Speciﬁcally, statistical software for personal computers with a graphical user inter-

face (GUI) is easier to use than their character-based predecessors. “User friendliness”

in contemporary SEM computer tools—and others for general statistical analyses—is a

near-revolution compared with older programs.

For example, consider a feature of the most recent versions of Amos, EQS, LISREL,

and the graphical version of Mx for personal computers. Users of any of these packages

can still choose to write code in each application’s native syntax. As an alternative, they

76 CONCEPTS AND TOOLS

can use a graphical editor to draw the model on the screen with geometric symbols such

as boxes, circles, and arrows. The program then translates the ﬁgure into lines of code,

which are then used to generate the output. Thus, (1) the user need not know very much

(if anything) about how to write code in order to run a sophisticated statistical analysis,

and (2) the importance of highly technical programming skills for conducting SEM is

likely to diminish even further. For researchers who understand the fundamental con-

cepts of SEM, this development can only be a boon—anything that reduces the drudgery

and gets one to the results quicker is a beneﬁt.

There are some potential drawbacks to “push-button modeling.” For example, no-

or low-effort programming could encourage the use of SEM in uninformed or careless

ways. Thus, it is more important than ever to be familiar with the conceptual and statis-

tical bases of SEM. Computer programs, however easy to use, should be only the tools

of your knowledge and not its master. Steiger (2001) makes the related point that the

emphasis on ease of use of computer tools can give beginners the false impression that

SEM itself is easy. Indeed, some computer tools for SEM have been advertised with the

tagline “SEM made easy!” This message may give the false impression that all one has

to do is draw the model on the screen and let the computer take care of the rest. Nothing

could be further from the truth! The reality is that things can and do go wrong in SEM.

Speciﬁcally, beginners often quickly discover that analyses fail because of technical

problems, including a terminated program run with cryptic error messages or uninter-

pretable output (Steiger, 2001). These things happen because actual research problems

can be technical, and the availability of user-friendly computer tools does not change

No, you won’t need computer gurus to learn how to use modern SEM computer tools. Copyright

2009 by Clive Goddard. Reprinted with permission from CartoonStock Ltd. (www.cartoonstock.

com)

Computer Tools 77

this fact. This is why there is so much emphasis in this book on conceptual knowledge

instead of teaching you how to use a particular computer tool: In order to deal with prob-

lems in the analysis, you must understand what went wrong and why.

huMan–CoMPuter InteraCtIon

There are basically three ways to interact with SEM computer tools:

1. Batch mode processing is the method for users who already know a program’s

syntax. Lines of code that describe the model, data, and analysis are entered directly

into an editor window that may be saved as an ASCII (text) ﬁle. Program code entered

by the user is then executed with a “run” command. Virtually all SEM computer tools

support this mode.

2. One method that does not require knowledge of program syntax uses “wiz-

ards,” which are a series of templates (dialog boxes) that build the model and analysis

as the user clicks with the mouse cursor on GUI elements such as text ﬁelds or check

boxes. Once the wizard has all the information, it automatically writes the program

code, which can then be run.

3. Another method that requires no programming is based on a drawing editor,

which is a GUI that allows the user to specify the model by drawing it on the screen.

The model is drawn using a set of more-or-less standard graphical symbols for model

diagrams, including squares or rectangles for observed variables and circles or ellipses

for latent variables (Chapter 5). When the diagram is ﬁnished, the analysis is run within

the program’s GUI. Although drawing editors are popular with beginners, you should

note that there are times when using a drawing editor is actually a hindrance—see Topic

Box 4.1 for more information.

Core seM PrograMs and Book WeBsIte resourCes

There are a total of eight computer programs speciﬁcally constructed for SEM, each of

which is used by many researchers today. Listed alphabetically, they are:

Amos Mplus

CALIS/TCALIS procedures (SAS/STAT) Mx

EQS RAMONA procedure (SYSTAT)

LISREL SEPATH procedure (STATISTICA)

There are free student versions of Amos, LISREL, and Mplus that place a limit on the size

of the model or the number of variables that can be analyzed, but they are good learning

tools. One of these programs, Mx, is a full-featured computer tool for model ﬁtting that

is available at no cost because it is not a commercial product. Other software programs

78 CONCEPTS AND TOOLS

toPIC BoX 4.1

graphical Isn’t always Better

There are some possible drawbacks to controlling an SEM analysis by drawing

the model on the computer screen:

1. It can be tedious to specify a complex model—one with lots of variables

and paths—in a drawing editor. This is because the screen tends to ﬁll up

quickly with numerous graphical elements. The resulting visual clutter can

make it difﬁcult to keep track of what you are doing.

2. Conducting a multiple-group analysis where a model is simultaneously ﬁt-

ted to data from two or more independent samples can be difﬁcult to carry

out in a drawing editor. This is because it may be necessary to look through

several different screens or windows in order to get all the information

about model speciﬁcation and data for each group.

3. Standard graphical symbols for model diagrams in SEM do not “translate”

well for doing a multilevel analysis. The issue is considered in Chapter 12,

but it would be hard to use a drawing editor to conduct a multilevel SEM

analysis.

4. It seems that it would be easy to produce a publication-quality model dia-

gram in a drawing editor, but this is not exactly true. Drawing editors in

SEM programs offer limited options for “tweaking” the appearance of the

diagram (e.g., changing line widths) compared with full-ﬂedged drawing

programs, such as Microsoft Visio.

To tell the truth, it takes a lot of time and

fussing to make a publication-quality diagram in any drawing editor. But

once you make a few examples, you can reuse graphical elements, such

as those for error terms, in future diagrams.

As many researchers become more experienced using SEM computer tools, they

tend to stop using a drawing editor to specify their models. For example, they

may discover that it can be easier to specify a complicated model through a

wizard that presents a series of templates. Other researchers eventually learn the

syntax of their SEM computer tool and start working in batch mode. There are

advantages to doing so. For example, it is often possible to work faster in batch

mode than by using a drawing editor. All of the syntax for a complex model plus

a matrix summary of the data may ﬁt within a single screen of a text editor. The

text ﬁle in which syntax is saved also serves as an archive that records the “his-

*I’ll share a trade secret with you: All model diagrams in this book were created using noth-

ing more than Microsoft Word AutoShapes. Maybe I’m biased, but I think these diagrams

are not too bad. Sometimes you can do a lot with a simple but ﬂexible tool. In this case,

you do not need a professional-grade drawing program to make publication-quality model

diagrams.

Computer Tools 79

can analyze structural equation models, but they are not used as often as the eight listed

here. Some of these other computer tools are described later in this chapter.

The eight core SEM computer tools can analyze all of the structural equation mod-

els described in Part II of this book. Most of these programs can also analyze means or

models across multiple samples, and EQS, LISREL, and Mplus each have special syntax

for multilevel analyses (Chapter 12). The descriptions that follow emphasize the major

features of each program. Speciﬁc capabilities of computer tools can change quickly as

new versions are released, so refer to the websites listed here for the most current infor-

mation.

The website for this book (see p. 3) has resources to help you learn how to work in

the syntax of EQS, LISREL, or Mplus, three of the most widely used computer tools. For

each detailed example in Chapters 7–10, you can download all computer ﬁles (syntax,

data, output) for analyzing that example in EQS, LISREL, and Mplus. This will allow to

you to run the input ﬁles in the corresponding computer tool. All syntax ﬁles are anno-

tated with comments that help to explain model speciﬁcation in a particular analysis.

In addition, you can compare the contents of each syntax ﬁle with the corresponding

model diagram in this book as a learning aid. Computer ﬁles can also be downloaded

for research examples in Chapters 11–12.

amos

Version 18.0 of Amos

(Analysis of Moment Structures) (Arbuckle, 1995–2009) is a

Microsoft Windows program sold by SPSS, Inc., as either a stand-alone application (it

does not need the SPSS environment to run) or as an optional part of SPSS. The version

number of Amos reﬂects the current version number of SPSS, now known as PASW Sta-

tistics. The Amos program is made up of two modules, Amos Graphics and Amos Basic.

Amos Graphics provides a GUI through which the user can specify the model by draw-

ing it on the screen and control other aspects of the analysis. A set of graphical wizards

is available that can automatically draw an entire latent growth model, among other

tory” of the analysis (model, data, output options, etc.). Syntax for modern SEM

computer programs is not all that difﬁcult to learn, no more so than, say, learn-

ing syntax for SPSS or SAS/STAT. Yes, there is tedium in working with syntax

because every single line must be correct, but the same is true about working in

a drawing editor: every single graphical element must be correct, or the analysis

might fail. So don’t fear the prospect of learning syntax and working in batch

mode for your SEM analyses. Indeed, doing so is probably in your future, too.

www.spss.com/AMOS/

80 CONCEPTS AND TOOLS

tasks. A special utility for testing alternative models is available through the Speciﬁca-

tion Search toolbar. In this utility, the user can designate particular paths in the model

as optional, and Speciﬁcation Search will analyze models with all possible subsets of the

designated paths. Values of ﬁt statistics for all tested models appear in a summary table,

and the corresponding model diagram can be viewed by clicking with the mouse cursor

in the table.

Amos Basic works in batch mode. Its syntax is ﬂexible in that it does not use a ﬁxed

set of keywords for variable names. Instead, the user supplies labels for all variables. The

Amos Basic editor is also a language interpreter for Microsoft Visual Basic. This means

that users can write scripts in Visual Basic that modify the functionality of Amos Graph-

ics, such as calculating a model ﬁt statistic that is not otherwise reported in default

program output.

Special features of Amos include the capability to generate bootstrapped estimates of

standard errors and conﬁdence intervals for all parameter estimates. Both nonparamet-

ric and parametric bootstrapping are available. Amos has a special maximum likelihood

(ML) method for raw data ﬁles, in which some observations are missing at random and

special estimation methods for censored data and ordered-categorical (ordinal) outcome

variables. It has extensive capabilities for Bayesian estimation of model parameters, but

their correct use requires knowledge of Bayesian statistics (Kline, 2004, chap. 9). Amos

can also analyze mixture models with latent categorical factors that represent class

membership. A free student version is available. It is identical to Amos 5.0 except that

the student version is limited to eight observed variables and 54 model parameters.

There are also training videos available for the Amos student version.

CalIs and tCalIs

The CALIS (Covariance Analysis and Linear Structural Equations) procedure is part

of SAS/STAT 9.2,

a comprehensive package for general statistical analyses that runs

under Microsoft Windows and operating systems for workstation computers, includ-

ing Linux, OpenVMS, AIX, and Solaris. It analyzes a wide variety of structural equa-

tion models and also estimates parameters in analyses such as MR or multivariate

linear regression. The TCALIS procedure is a new (“experimental”) procedure in SAS/

STAT 9.2. It allows greater ﬂexibility than CALIS in testing structural equation mod-

els across multiple samples and in analyzing models with both a covariance structure

and a mean structure. Because TCALIS is more capable than CALIS, the latter is not

described further.

The TCALIS procedure runs only in batch mode; that is, the user must type com-

mands in an editor window that describe the data and model and then run the program

www.amosdevelopment.com/download/

www.amosdevelopment.com/video/index.htm

www.sas.com/technologies/analytics/statistics/stat/index.html

Computer Tools 81

in the SAS environment. Models can be speciﬁed in TCALIS using one of seven different

representational notations. These include LISREL-type matrix-based syntax, EQS-type

equations-based syntax, and a notational system based on an approach to causal model-

ing known as the reticular action model (RAM) (McArdle & McDonald, 1984). The

RAM approach includes a matrix-based system for specifying structural equation mod-

els and a set of graphical symbols for model diagrams. The RAM symbolism for model

diagrams is used in this book and is introduced in the next chapter. Special features of

TCALIS include the possibility of selecting from among eight different methods for cal-

culating start values, or initial estimates of model parameters. Other options control the

estimation process, such as the particular statistical search method used to ﬁnd optimal

parameter estimates. Output from an analysis in TCALIS can be automatically saved for

input into the next run of the program for the same model and data. This capability is

handy for checking whether or not a complex model is identiﬁed (Chapter 9).

eqs

Version 6.1 of EQS

(Equations) (Bentler, 2006) is a Microsoft Windows program that

can be used for all stages of the analysis from data entry and screening to exploratory

statistical analyses to SEM. There are also versions of EQS for UNIX or LINUX environ-

ments. The EQS data editor has many of the capabilities of a general statistical package,

including conditional case selection, variable transformation, and merging of separate

data ﬁles. Exploratory statistical analyses that can be conducted in EQS include ANOVA,

covariate analysis, and factor analysis. There are also options for analyzing missing data

patterns and model-based imputation of missing observations with the EM algorithm

(Chapter 3).

The user can interact with EQS in three different ways: through batch mode; through

wizards that collect information about the model and data and automatically write EQS

programming syntax; or through a drawing editor. The last two ways do not require

knowledge of EQS syntax. The drawing editor in EQS is its Diagrammer, which offers

graphical tools for drawing the model on the screen. Tools available in the Diagrammer

can automatically draw an entire path, factor, or latent growth curve model after the user

completes a few templates about the variables, direct effects, measurement occasions, or

residual terms. Both the Diagrammer and template-based wizards automatically write

EQS syntax into a background window, which is then run by the user.

The syntax of EQS is based on the Bentler–Weeks representational system, in

which the parameters of any covariance structure are regression coefﬁcients for effects

on dependent variables and the variances and covariances of independent variables. In

the Bentler–Weeks model, dependent variables have error terms, but not the indepen-

dent variables. All types of models in EQS are thus set up in a consistent way. Special

strengths of EQS include the availability of several different estimation methods for non-

www.mvsoft.com/

82 CONCEPTS AND TOOLS

normal data, model-based bootstrapping, and the ability to correctly analyze a correla-

tion matrix without standard deviations. The latest version features built-in syntax and

special estimation methods for multilevel analyses. A future version of EQS will include

capabilities for mixture modeling, latent class modeling, and analysis of item response

theory measurement models.

lIsrel

Version 8.8 of LISREL

(Linear Structural Relationships) for Microsoft Windows

(Jöreskog & Sörbom, 2006) is an integrated suite of programs for all stages of the analy-

sis, from data entry and management to exploratory data analyses to the evaluation of

a wide range of structural equation models. Included with LISREL is PRELIS, which

prepares raw data ﬁles and matrix summaries for analysis in LISREL or other computer

programs. Many multivariate data screening and summarization options are available in

PRELIS, including model-based imputation of missing data. The PRELIS program can

also generate bootstrapped estimates, conduct simulation studies with variables speci-

ﬁed to have particular distributional characteristics, and calculate polychoric and poly-

serial correlations.

The LISREL program offers an interactive mode that consists of a series of wizards

that prompt the user for information about the model and data and then automatically

write command syntax in a separate window. Interactive LISREL also allows the user

to specify the model by drawing it onscreen through the Path Diagram functionality.

Users already familiar with one of two different LISREL command syntaxes can as an

alternative directly enter code into the LISREL editor and then run it by clicking with

the mouse cursor on an icon. If the command “Path Diagram” is placed at the end of

the editor ﬁle, LISREL will also automatically draw the model diagram that corresponds

to the syntax ﬁle. This unique feature provides a way for the user to verify whether the

model speciﬁed in syntax and estimated by LISREL is actually the one that he or she

intended to analyze.

The original (classic) LISREL syntax is based on matrix algebra. This command

syntax is not easy to use until after one has memorized the whole system. An advantage

of the classic syntax is efﬁciency: one can often specify a complex model in relatively few

lines of code. The other LISREL programming language is SIMPLIS (“simple LISREL”),

which is not based on matrix algebra, nor does it require familiarity with the classic syn-

tax. Programming in SIMPLIS requires little more than naming the observed and latent

variables (but not error terms) and specifying paths with equation-type statements.

Residual terms are automatically speciﬁed when SIMPLIS is used, which is convenient.

Features of the latest version of LISREL include the capability to conduct exploratory

factor analyses of ordinal variables in PRELIS and the addition of syntax commands

in LISREL’s classic, matrix-based programming language for multilevel analyses. (The

www.ssicentral.com/

Computer Tools 83

latter is not available in SIMPLIS.) The full commercial version of LISREL can be down-

loaded for a free 15-day trial. There are also free student versions of LISREL available for

the Microsoft Windows, Apple Macintosh OS 9 and X, and LINUX operating systems.

The student versions are restricted to a total of 15 observed variables for both SEM

analyses and multilevel analyses.

Mplus

Version 6.0 of Mplus

(Muthén & Muthén, 1998–2010) runs under Microsoft Windows

and is divided into a program for SEM, Mplus Basic, and three add-on modules for ana-

lyzing additional kinds of latent variable models. Mplus Base analyzes all core types of

structural equation models plus discrete- and continuous-time survival models. A spe-

cial strength of Mplus is that it can analyze outcome variables that are any combination

of continuous, dichotomous, ordinal, or count variables. For example, it automatically

calculates odds ratios for dichotomous outcomes (Chapter 2). Also available in Mplus

Base is an ML method for incomplete raw data ﬁles, special syntax for handling complex

survey data (e.g., with stratiﬁcation), and Monte Carlo methods for generating simulated

random samples. Versions 5.1 and later feature the capability for exploratory structural

equation modeling (ESEM) (Asparouhov & Muthén, 2009), which combines features of

SEM and exploratory factor analysis. The logic of ESEM is introduced in the next chap-

ter. Version 6.0 includes capabilities for Bayesian estimation (Asparouhov & Muthén,

2010).

The Mplus Base user interacts with the program in one of two different ways, in

batch mode by writing programs in the Mplus language that specify the model and data

or through a language generator (wizard) that prepares ﬁles for batch analysis. Through

the Mplus language generator, the user completes templates about analysis details, such

as where the data ﬁle is to be found and variable names. The user’s responses are then

automatically converted to Mplus language statements that are written to an editor win-

dow, but the user must write the syntax that speciﬁes the model. There is no model dia-

gram input or output in Mplus Basic. However, it has a template-based module for gener-

ating data graphics, including histograms, scatterplots, and item characteristic curves.

The Multilevel Add-On to Mplus Basic is for the multilevel analyses. It estimates

multilevel versions of models for regression analysis, factor analysis, SEM, and time

survival analysis. The Mixture Model Add-On analyzes mixture models with categori-

cal latent variables. Mplus Base together with this add-on can analyze “classical” struc-

tural equation models with continuous latent variables, latent structure models with

categorical latent variables, and models with both continuous and categorical latent

variables. The third optional module is the Combination Add-On, which contains all the

features of the other two add-ons. It also supports the analysis of multilevel models with