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MLwiN Textbook Examples
Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence
by Judith D. Singer and John B. Willett
Chapter 7: Examining the multilevel model’s error covariance structure

Table 7.2, page 246 using data set opposites_pp.ws.

In this model, the intercept, called cons, is random at both levels 1 and 2.  We manually created a variable called time*ccog for the interaction of time and ccog. The variable time is random at level 2 and ccog and time*ccog are fixed.  We used the RILGS method of estimation, which you can select by clicking on "estimation" from the pull-down menus at the top of the program screen and then selecting "RILGS" (the default is ILGS).

The results of running the above model are shown below.  NOTE:  Our results for the variance components differ slightly from those shown in the text.  We do not know why.

Table 7.3, pages 258-259 using the same data set as the example above.

Unstructured:

The results of running the above model are shown below.

Compound symmetry:

Compound symmetry is a set of linear constraints on the variance and covariance matrix. We can impose it using Constrain Parameters from the Model menu. Enter the number of constraints in the specified field before entering the constraints.

We pick c16 to store the constraint matrix and we need to click on attach random constraints before running the model again.

Heterogeneous compound symmetry:

MLwiN can only deal with linear constraints. We don't know how to do this in MLwiN.

Autoregressive:

For the same reason as in the above case, we don't know how to do this in MLwiN.

Heterogeneous autoregressive:

We do not know how to do this in MLwiN.

Toeplitz:

This is another example of linear constraints. The first three columns are for the constraints on the variance and the last three on the covariance.

Table 7.4, page 265

Standard error covariance structure:

This is the same equation that we ran for Table 7.2.

The results of running the above model are shown below.

Toeplitz error covariance structure:

Unstructured error covariance structure:

The results of running the above model are shown below.

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