Most Frequently Asked Questions about Amos

Where has Amos been referenced in the scientific literature?

What are the differences between Amos and LISREL?

What are the differences between Amos and EQS?

What does the name "Amos" stand for?

Can Amos read SPSS LISREL files?

Does Amos use polychoric correlations? Are poly/tetrachoric correlations available in Amos?

What is Amos's FIML estimation?

This question is also posed in the form: "My advisor (or: A reviewer) tells me that I will not get my research published unless I use ... <insert name of another SEM program here> ... to analyze my data. What should I do?"

Advisors and journal reviewer sometimes like a little convincing before they will accept a relatively new research tool such as Amos. You can supply your critic(s) with a list of Amos in print references to alleviate these concerns.

We are often asked in which respects Amos is different from other structural equation programs such as LISREL (written by Karl Jöreskog and Dag Sörbom). As a general rule, SmallWaters tries to avoid comparative advertising because easily degenerates into pettiness and featuritis.

For evaluating specific features of Amos, the reader is advised to download the Amos student version, try it out, and evaluate the online documentation (Amos Help).

Most structural equation models can be set up and estimated with either Amos or LISREL -- which program to use is often a matter of price, support and personal preference. Some of the specific differences between Amos and LISREL are:

1. Amos is written with teaching and consulting applications in mind first. Fully-interactive path diagram input and display options make it easy to discuss and evaluate models with applied researchers and students.

The interface is object oriented and follows the MS Windows standard guidelines for graphical user interfaces. Amos Graphics has an extensive online help system. Anybody used to other Windows programs, such as MathCAD or MS Word, will have little or no trouble getting started with Amos Graphics.

2. In Amos, the path diagram is the model and the user does not have to manipulate sets of equations or matrices with Greek names. Thus, modeling with Amos is a complete change from the old ways of doing SEM.

Amos reads its model specifications only in the form of equations or path diagrams. Even complex models can be drawn out as path diagrams, and at the press of a button (literally) Amos goes ahead and calculates the estimates. The graphics are always in publication quality.

3. By the same token, and in contrast to LISREL, Amos does not support model specifications in matrix notation.

4. Mean models, and multi-group models, can be specified with either program. However, it can be done very easily with Amos.

5. Similarly, bootstrapping and Monte Carlo simulations are very easily set up in Amos, and there are sophisticated output options. For instance, the following three commands will cause amos Amos to produce 1000 bootstrap replications of the current structural model and compute 95% confidence intervals with bias correction:

$bootstrap=1000	! 1000 bootstrap replications
$seed=123489	! pick some seed value for the random number generator
$confidencebc=95	! compute bias-corrected confidence intervals

6. Analysis of missing data is by full-information maximum likelihood in Amos. The full-information method used by Amos are more efficient in the missing-at-random case. If missingness is not at random, Amos's estimates are generally less biased than those produced by ad-hoc methods as pairwise or listwise deletion.

7. LISREL 8 excels in ordinal data modeling via polychoric/serial correlations. However, there has been some debate about the asymptotic covariance matrices computed by Prelis 2. Methods for ordinal-categorical data are still subject of ongoing research. While it was clear from early on that the polychoric approach can remove, or largely reduce, bias due to discrete measurement, the asymptotically distribution-free estimation employed by LISREL and EQS is limited to a maximum of 25 observed variables and appears to require formidable sample sizes of at least 2,000-5,000 observations per group.

8. Lisrel also features instrumental variables (IV) and two-stage least-squares (TSLS) as estimation methods, although in non-standard implementations. Amos does not provide any IV or TSLS estimation methods.

9. Lisrel 8 allows general polynomial parameter constraints.

Another comparison we are often asked to make is the one between Amos and the EQS program (by Peter Bentler). Several aspects from the Amos-vs.-LISREL discussion (above) apply to EQS as well, so the comparison with EQS can be kept short.

Most structural equation models can be set up and estimated with either Amos or EQS -- which program to use is often a matter of price, support and personal preference. Apparently the difference between Amos and EQS is not terribly great. EQS has somewhat of a niche in methods for elliptical distribution methods, robustified chi-square tests, and integrated exploratory data analysis modules. On the other hand, Amos features full-information ML model estimation with incomplete (or missing) data, and has a variety of sophisticated bootstrap simulation tools for analyzing non-normal data.

The following third-party comments appeared on the SEMNET discussion list:

Editorial correction: Normal-theory Monte-Carlo simulation is implemented in Amos as a parametric bootstrap option, and can be invoked with the $bootnormal   command.

There are two schools of thought (at least).

The pseudo-biblical school originated in this SEMNET discussion thread of February 1996:

Notwithstanding this colorful (and certainly noteworthy) school of thought championed by Professors Kaplan and Powell, the more traditional school contends that SmallWaters has been using the name "Amos" merely as an acronym for "Analysis of moment structures." Make up your own mind which school to believe.

SPSS's technical support group has documented several LISREL-to-Amos data conversion issues in a technical paper (sorry, last time we looked, on Sept 4, 1997, this link was broken; a fix is in progress) located on the SPSS web page. The document contains SPSS macro code to take covariance and correlation matrices stored as SPSS system files and transform them into the ASCII format that Amos understands.

The current version 4.0 of Amos does not offer polychoric/polyserial correlations, nor any other estimation method specific to ordered categorical data.

When Likert scales are modeled as ordinal data, one might consider using the ADF estimation incorporated in LISCOMP, LISREL and EQS for polychoric/polyserial correlations, provided that the following two conditions are met:

1. The sample size is exceptionally large. The simulation study by Yung and Bentler (1994) indicates that that the sample size should be at least 2000, and possibly 5000, to obtain satisfactory results.
2. The number of observed variables is not too big, because the number of elements in the (ADF) weight matrix increases with the fourth power of the number of observed variables. EQS, for instance, imposes an upper limit of twenty (20) observed variables for ADF estimation, and PRELIS 2 reaches its technical limitation for computing the weight matrix at twenty-five (25) observed variables. The LISCOMP program must have similar limitations, but they are not documented.

If the sample is too small to support the use of ADF estimation with polychoric/polyserial correlations, or if there are too many observed variables, it might be more efficient treating the Likert scale as an interval scale, and using either ML or GLS estimation methods.

In our opinion, a method that requires a sample size of a few thousands (like the method in Lisrel/Prelis) is not worth very much in practice, but the absence of such a method in Amos presents somewhat of a marketing problem. An alternative method for ordered categorical data is scheduled to be included in a future release Amos. Our hope is that the Amos method will give acceptable results for more typical sample sizes. Reference:

Yuan, K.H. & Bentler, P.M. (1994) Bootstrap-corrected ADF test statistics in covariance structure analysis. British Journal of Mathematical and Statistical Psychology, 47, 63-84.

See also: Ordinal data

What is Amos's FIML estimation? What is the difference between Full Information Maximum Likelihood (FIML) and Maximum likelihood? Or they do not have any difference?

Maximum likelihood comes in a variety of flavors, even with just the multivariate normal case. For instance, sociology has seen Pseudo-ML (PML, Arminger), and econometrics knows of limited information ML (or LIML).

The importance of Amos's full information maximum likelihood (FIML) estimation lies in its treatment of missing data. Amos uses all information of the observed data, while many other methods do not. The likelihood is computed for the observed portion of each case's data and then accumulated and maximized. Amos's ML approach usually yields results equivalent to Don Rubin's EM approach, except that Amos also incorporates constrained moment matrix estimation. In addition, FIML requires no imputation (or E-step) and typically converges faster.

An introduction to FIML estimation is given by Jim Arbuckle in the edited volume by Marcoulides and Schumacker (1996) and by Werner Wothke in the edited volume by T.D. Little, K.U. Schnabel, and J. Baumert [Eds.] (2000) Modeling longitudinal and multiple group data: Practical issues, applied approaches and specific examples. Mahwah, NJ: Lawrence Erlbaum Associates, also available online.

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