STA2201s06 Assignment 6

Read the data file fourvars.dat (the same data as for Assignment 3) in SAS, and use proc means to display the sample size, mean and standard deviation for each variable. Log and list files are due on Thursday March 16th at the beginning of class. This is just a warmup, to take care of any technical difficulties you might have running a SAS job.

Also, please read the rest of Chapter 4 (that is, pages 104-150), but read most of it lightly. Here are the high points as I see them.

• Under Estimation, the main method is Maximum Likelihood, and we have done it in detail already. A lot of the disucssion of maximum likelihood estimators is for the benefit of social scientists who may never have heard of it. On page 110, Bollen mentions the test for goodness of fit, the one comparing the model to a saturated model. Note that he multiplies the fitting function by (n-1) instead of n. This is what SAS does, too. Of course asymptotically it makes no difference. The other estimation methods discussed in this chapter (Unweighted least squares and Generalized least squares) are reasonable, but we will not use them in this course. We will explore Weighted least Squares (described later in the text) as a way of dealing with non-normal data.
• The Empirical Examples section starting on page 116 is optional. We are doing a different empirical example in class. We may revisit this one if I get around to doing it with SAS.
• The section entittled "Statndardized and unstandardized coefficients" is something you can skip. SAS does produce standardized estimates as part of the default output, but we can definitely live without it.
• The section entitled "Alternative assumptions for x" is worth a close look, because it leads to the conclusion that the distribution of the exogenous variables is not too important, provided that they are independent of the error terms. Remember, we're still dealing with just observed variables.
• If the distribution of X does not matter, it's okay to represent interactions with product terms as in ordinary multiple regression. Intercepts will be introduced later in the course. For now, we are staying with the assumtion that all the expected values are zero.
• You can skip the appendices, unless you are interested in the details of numerical minimization, which you may be. The stuff that is specific to the LISREL computer program (distinct from the LISREL model) you defnitely should ignore.