ICPSR General Structural Equations (Baer)
Class Lab: Achievement Values Problem
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\Lab1. 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).
This exercise makes use of AMOS or SIMPLIS. This instruction sheet is designed for
use with AMOS; if you would like to use SIMPLIS, ask for the SIMPLIS instruction
sheet.
You might speed operations up slightly if you copy the file (achval81.sav) to a temporary
local disk and then work from there (optional).
First exercise:
Construct a single-factor model for the 6 achievement items using AMOS. First, use the
AMOS drawing tools to construct a diagram that should look like this:
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This was constructed using the “Draw Latent Variables and Indicators” button (normally,
the left button on the 2nd row). This tool automatically assigns the first indicator as a
reference indicator.
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Next, define the data set that AMOS will be analyzing. Press the “Specify Data Files”
button, which is located just past the “magic wand” button (the latter is officially called
the “Touch up a Variable” button). Press the File Name button and then navigate until
you find the file AchVal81.sav. The number of cases should appear in the column
marked N. Close this dialogue box when finished.
Next, put SPSS variable names into the “boxes” for the manifest variables. You can
either place the cursor next to the box and then right click (see the dialogue box below)
or click on the “View Variables in the Model” (normally underneath the “Title” and just
before the pointing hand) and then drag variable names into the manifest variable boxes.
If you type the names in yourself, the dialogue box will appear as shown below
after you select Object Properties. At this point, type in the Variable Name and then
close the dialogue box.
Your model should look like this:
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REDUCE
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NEW_GOAL
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ACHIEVE
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CONTENT
Long variable names (as opposed to names like “V1” “V2” etc.) tend to clutter AMOS
diagrams. There is nothing much to be done about this, though one could:
a) go into SPSS and delete all variable labels
b) right-click on the variable in the diagram, and delete the label or shorten the
variable name
c) type in the variable names (no labels) directly as opposed to using the
convenient AMOS “drag and drop” facility described above.
Next, place variable names in the circles. Any name can be used, but you might try
something like Ach1 for the latent variable and e1 through e6 for the error terms.
Click on the “Analysis Properties” button (normally underneath the magic wand button).
Under Output, click on the following:
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√ Standardized estimates
√ Squared multiple correlations
√ Modification indices
Run this model (press the button that looks like an abacus). When the program asks
you to give the model a file name (“Save as..”) provide any convenient name (e.g.,
Achieve1).
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
erase the fixed 1.0 associated with the first indicator and place a fixed 1 on a path
involving 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:
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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).
Construct two models:
A model with no correlation between the 2 latent variables.
A model with a correlation between the 2 latent variables.
Compare the results: - coefficients
- fit index values
Examine the size of the correlation in the model where the 2 latent variables are
correlated.
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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?
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Fifth exercise
Add the four single-indicator exogenous variables to your model.
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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.
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).
Briefly make note of how the various exogenous variables affect achievement values.
For your information: AMOS has an alternative way of specifying coefficients or
correlations between exogenous variables when the number of variables is large. Click
view/set and then Matrix Representation to see this feature.
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.
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Initially, you might 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).
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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.