ICPSR General Structural Equations (Baer)

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ICPSR General Structural Equations (Baer)

Class Lab: Achievement Values Problem (SIMPLIS Version)

The Data:

The data are taken from a Canadian survey undertaken in the 1980s. A small subset using listwise deletion has been constructed as an SPSS save file (.sav). This file is called Achval81.sav and is located in \baer\ExtraLab1. The codebook for this small variable set is contained in the MS Word file ValuesCodebook.doc. The original survey involved 3288 interviews; due to listwise deletion, the N has been reduced to 3086.

(Later in the course we will discuss better approaches to missing data from a SEM perspective).

To use a file with SIMPLIS, PRELIS must be used to construct a covariance matrix. This covariance matrix could be a text file, or it could be a special “system file” (a .dsf file). For today’s exercise, we will use a covariance matrix stored in a text file called

\baer\Extralab1\achval81.cov

First exercise:

Construct a single-factor model for the 6 achievement items using SIMPLIS. Your model will look like this:

The basic SIMPLIS syntax for a model like this would be as follows:

TITLE (any title)

System File from file z:\baer\AchVal81.dsf

Latent Variables: Achvmt

Relationships:

NEVHAPP NEW_GOAL IMPROVE ACHIEVE CONTENT = Achvmt

REDUCE = 1*Achvmt

Options: MI SC ND=3

End of program

If you wish, you may add the instruction

Path Diagram

-on the second last line.

The options are as follows:

MI = modification indices

SC = standardized estimates

ND=3 provide 3 digits of accuracy when printing out parameter estimates

Type this model in a syntax box in LISREL. First, open LISREL 8.54. Then go through the menus: File  New  Syntax Only.

Next, type the program into this text box, and then click on File  Save (save your model on a temporary disk). After you have saved the file, you may press the run LISREL button.

Note: Make sure to save you file to a read/write disk and not to a read-only file area on the server.

Examine the parameter estimates for this model. Note that all of the regression coefficients for the measurement model equations are greater than or equal to 1. This is because the first indicator, REDUCE, is fairly weak (at least in the context of this model). Examine the standardized estimates to get a sense of the strength of relationships.

Try re-running this model with a different reference indicator. You will need to change the *1 specification for the first indicator and use a different variable. Give this new program a different name before you run it. Compare the results with the previous model. (What to look for: Has the chi-square changed? Has the ratio of the coefficients (e.g., the ratio of the coefficient for indicator #2 to indicator #3) changed?)

Examine the model to ask the question, “is this a well-fitting model?”

We will normally want fairly high (>.90 if possible) values for the various 0 to 1 fit index measures such as GFI, Tucker-Lewis, CFI, Normed Fit Index.

Second exercise

Examine the modification indices in the first model. Add a parameter to correspond to the highest MI value (in the context of your model, this will be a correlated error term).

Run the model with this new parameter added. Examine the results of this model, and add another parameter to correspond to the highest MI value in this new model. Continue until you have added three new parameters to the model.

 While one might be tempted to add more than one new parameter at a time, technically MIs represent “one at a time” estimates of the degree to which a model will improve when a parameter is added. There can be cases where trying to add 2-3 parameters at a time will result in a model where one of these parameters adds little to the model, or even creates identification problems.

Briefly, make note of the fit index values for this model.

Third exercise

Try a model with 2 latent variables instead of one. This model will have 3 indicators per variable. Which indicators should be used for each construct? Figure this out by either:

a) using some logical a priori criterion (conceptually, which variables might you expect to go together) or b) using the grouping suggested by the correlated error terms in the 2nd part of this exercise for one latent variable and then using the other 3 indicators for the other latent variable or c) both (a) and (b).

The general form of a two latent variable model is as follows:

V1 V2 = Latent1

V3 = 1*Latent1

V4 V5 = Latent2

V6 = 1*Latent2

Construct two models:

A model with no correlation between the 2 latent variables.

By default, with 2 latent variables, LISREL/SIMPLISincludes the

correlation (covariance) between the latent variables. To exclude it,

you will need the following line:

Let the Covariance between Latent1 and Latent2 be zero.

A model with a correlation between the 2 latent variables.

Drop the line above.

Compare the results: - coefficients

-fit index values

Examine the size of the correlation in the model where the 2 latent variables are correlated.

Fourth exercise:

Examine the modification indices for the model with the 2 latent variables correlated. Look for the highest MI involving a path from a latent variable to a manifest variable (we usually prefer to add “paths” as opposed to correlated errors if possible). Construct a model where this added path is included in the model. Carefully examine the coefficients that have been generated (especially for this indicator) to determine if this improvement makes sense. If the MI was not very high, you could have simply reverted to the earlier model without the added term. If, however, the new parameter “makes sense,” it can be included in the model. Which is preferable?

Programming:

Imagine variable V3 is connected with 2 latent variables instead of one

(viz., it is “factorally complex”):

V1 V2 = Latent1

V3 = 1*Latent1

V4 = Latent1 Latent2

V5 = 1*Latent2

V6 = Latent2

Fifth exercise

Add the four single-indicator exogenous variables to your model.

Notes:

1. Since the 2 latent variables are now endogenous, the correlation between the two of them is no longer a model parameter. However, we will expect the errors to be correlated.

Add: Let the Error Covariance of Latent 1 and Latent2 be Free

2. We will normally correlate all exogenous variables. In large models, it is easy to neglect one of these (notice there are 6 curved arrows in the diagram above).

SIMPLIS normally includes these by default. It is thus less

prone to errors (that occur when one of these is missed) than

AMOS

3. You can use statements such as the following to include the paths

from the exogenous variables:

Equations:

Latent1 = GENDER EDUC AGE INCOME

Briefly make note of how the various exogenous variables affect achievement values.

Sixth exercise (optional/if time permits):

Reconstruct the exogenous variables so that these are linked, as single indicators, to latent variables. You will need to fix the values of the error variances.

Example for education:

Add LEduc as a latent variable under Latent Variables:

Add:

Relationships:

EDUC = 1*Leduc

Add

Let the error variance of Educ be zero

(or Set the error variance of Educ to zero)

Initially, you will fix the variances to zero (to give you a model equivalent to the one you estimated above, just to make sure you are doing it correctly).

Try ultimately to fix the variances so that the percentage of error variance differs across the different variables:

Gender 0% error

Education 20% error

Age 10% error

Income 30% error

Examine the results to see how much the parameter estimates linking the exogenous variables with the endogenous variables have changed from the earlier model where you assumed no error.