1. Accessing LISREL on Terminal Server Systems

2. Heywood cases and LISREL

3. Covariance matrix not positive definite

4. Total coefficient of determination for structural equations

5. P-values for coefficient tests

6. Reading missing data directly into LISREL

7. Comparing groups using LISREL

8. Assessing model identification

9. Access Violation using LISREL on the Stat Apps Terminal Server

### Accessing LISREL on Terminal Server Systems

#### Question:

Where is the LISREL structural equations modeling program available on timesharing systems?

#### Answer:

LISREL is only available on the stat apps server. Lisrel 8 is a stand-alone product which can read a variety of different datasets. See the Stat Apps Server page on how to connect to the stat apps server.

### Heywood cases and LISREL

#### Question:

I am using LISREL 8 to do some structural equation modeling and am having trouble with a recurring error message. This message states: WARNING: THETA EPS NOT POSITIVE DEFINITE. The result is that the modification indices, t-values, residuals, etc. can't be computed, and I assume that the final parameter estimates are somewhat arbitrary. Is there any solution to this?

#### Answer:

LISREL's Theta Epsilon (Theta EPS) matrix is the error matrix associated with Y-residuals (i.e., downstream variable residuals). A negative variance estimate in this matrix makes it "not positive definite"; the variance estimate for the measurement error is negative. Negative variance estimates are a result of a communality (squared correlation between the latent variable and a measurement variable) estimate larger than 1.00.

This situation is called a Heywood case in the factor analysis literature. Heywood cases have many possible causes, including insufficient data, bad prior estimates, and a poorly specified model. Thus, possible solutions include collecting more data, making better prior estimates, and specifying a better-fitting model.

The possible solutions related to computer code include a) providing better prior estimates, and b) using different methods of solving for estimates.

A) Replace the default starting values: some users have had moderate success with using ST .5 ALL.

B) Replace the default maximum-likelihood-based solution with an ordinary least-squares or a generalized least-squares solution, since the former method is particularly prone to produce Heywood cases . Ordinary least-squares and generalized least-squares solutions are available by typing UL or GLS on the OU line, respectively.

Poor model specification can also produce Heywood cases; one example is called "empirical under-identification". This occurs when there are an infinite number of solutions possible for the path values (parameter estimates). This is particularly likely when the correlation or covariance matrix linking the latent variables to the measured variables has a small number of entries (e.g., only one or two measured variables per latent variable). To determine if this situation is present, check whether the standard error of the estimates is large. You can try to get around this difficulty by setting your residuals equal to one another with EQ statements.

Heywood cases are a problem for any software. SAS has added the HEYWOOD option to PROC CALIS that sets communality estimates greater than 1.0 to 1. LISREL contains no such luxury, but with a little more work the LISREL user can do the same thing through the use of the techniques described above.

### Covariance matrix not positive definite

#### Question:

When I run my data I get an error message that states that my covariance matrix is not positive definite. I have searched the LISREL book that I have and it doesn't provide any explanation for this error message.

#### Answer:

This message generally means one or more of the following things is happening:

1) There are redundancies among the correlation matrices- in other words, some of the correlations may be a linear function of some of the other correlations.

You can fix this by removing the redundant variables or collecting more data.

2) Your model may be estimating more parameters than you have degrees of freedom to use. You can check this by examining how many degrees of freedom you have and the number of parameters you are estimating.

The formula for calculating the number of degrees of freedom available to you is q(q+1)/2, where q is the number of measured variables. If you have 9 measured variables, then you must estimate, (9(9+1)/2 = 45), less than 45 parameters. As part of its standard output, LISREL will count the number of parameters it estimates. The difference between the number of estimable parameters and the number of estimated parameters is the number of degrees of freedom used in the chi-square test by LISREL (the first chi-square test to appear on the printout, not the Independence Model chi-square test).

3) LISREL is not correctly reading the raw data, correlation matrix, or covariance matrix. Alternatively, you may be inputting a correlation or covariance matrix which is based on incorrectly read raw data values via PRELIS, SPSS, or another program which has the capability to convert raw data into correlation or covariance matrix form.

4) You computed a covariance or correlation matrix using pairwise deletion of missing data. The solution here is to use a different method of handling missing data.

Be sure to check the accuracy of the raw data, correlation, or covariance matrices before you proceed further with your analyses.

### Total coefficient of determination for structural equations

#### Question:

I'm using LISREL. On my printouts under LISREL 7, I used to get a statistic called "Total coefficient of determination for structural equations". I can't seem to get it when I use LISREL 8. How can I get this information using LISREL 8?

#### Answer:

The authors of LISREL 8 decided not to include this statistic as part of the available LISREL output. This means that you must compute it based on other portions of the LISREL output.

### P-values for coefficient tests

#### Question:

I am using LISREL 8 to do some structural equation modeling. LISREL prints the coefficient estimates, standard errors, and t-values for each path, but I don't see a P-value associated with the t-values. How can I tell if my path is significant?

#### Answer:

The writers of the LISREL program assume, for better or worse, that LISREL users will be using sample sizes above 120, the point at which most tables of the t-distribution assign a value of infinity to the t-distribution. At this point, the t-distribution can be approximated by the z (standard normal) distribution.

For the z distribution, an obtained value less than -1.96 or larger than +1.96 suggests a statistically significant result at the alpha = .05 level, two-tailed. The critical value is -/+ 1.64 for a one-tailed test.

For an alpha = .01, the critical values of Z are -/+ 2.58 for a two-tailed test, -/+ 2.33 for a one-tailed test.

The null hypothesis under test is that the coefficient is statistically significantly different than zero, much as one might test the null hypothesis that a correlation value or a regression beta weight is equal to zero in the population from which one drew one's sample.

Practically speaking, then, you need not evaluate the obtained t-values from a LISREL printout on a t-table unless your sample size is 120 cases or fewer. Otherwise, if your sample is sufficiently large (or you are willing to make this assumption with a smaller sample), you can evaluate your obtained value of t, shown on the LISREL printout, against the critical value of z you select based upon your choice of alpha level. If your obtained value is larger than the positive critical value or smaller than the negative critical value, you would reject the null hypothesis and conclude that the path coefficient is significantly different than zero.

For instance, suppose you chose an alpha level of .05, two-tailed. The critical values of t would thus be -1.96 and +1.96. If you obtained a t of 2.92, you would reject the null hypothesis. Similarly, if you obtained a t value of -2.45, you would also reject the null hypothesis. On the other hand, if you obtained a t-value of 1.76, you would fail to reject the null hypothesis. In this last case, there would not be sufficient evidence to conclude that the path coefficient was significantly different from zero in the population from which you drew your sample.

### Reading missing data directly into LISREL

#### Question:

I am using LISREL to read my raw data directly instead of preprocessing it using PRELIS. I know that I can use the MISSING=99 option in PRELIS to tell PRELIS that 99's represent missing data points in my data file. Is there something similar I can use with LISREL?

#### Answer:

Yes. You can use the XM=99 option on the LISREL DA command line. If your missing value code is something other than 99, then you would replace the 99 value in the statement shown above with your missing data code.

### To View Questions Number 7, 8 and 9 - click on links below:

7. Comparing groups using LISREL

8. Assessing model identification

9. Access Violation using LISREL on the Stat Apps Terminal Server