STA 431 Assignment Seven:

Quiz in Tutorial on Friday March 4th

Please start this one early!

As part of a much larger study, farmers filled out questionnaires about various aspects of their farms. Some questions were asked twice, on two different questionnaires several months apart. Buried in all the questions were

There are two readings of these variables, one from each questionnaire. We will assume (maybe incorrectly) that because the questions were buried in a lot of other material and were asked months apart, that errors of measurement are independent between the two questionnaires. However, errors of measurement might be correlated within a questionnaire.

Here are the homework questions. You can save work by using lecture material and your work from earlier assignments.

  1. Write down a reasonable model for these data. I know that usually you are given a model, but in practice you get a data set and must come up with the model yourself -- maybe in consultation with a researcher who knows the data. But that researcher will typically be unable to stand looking at a Greek letter.
  2. Of course it is hopeless to identify the expected values and intercepts, so we will concentrate on the covariance matrix. Calculate the covariance matrix of the observable data.
  3. If there are any equality constraints, say what they are.
  4. Based on your answer to the last question, how many degrees of freedom should there be in the chisquare tests for model fit?
  5. If there are and inequality constraints, say what they are.
  6. How do you know the parameters appearing in the covariance matrix are identifiable? You don't have to show any work.
  7. The raw data are available in the file pigs.data.
    1. Use proc calis to fit your model. If you experience numerical problems you are doing something differently from the way I did it. When I fit a good model everything was fine. When I fit a poor model there was trouble.
    2. Does your model fit the data adequately? Answer Yes or No and give three numbers: a chisquare statistic, the degrees of freedom, and a p-value.
    3. For each breeding sow present in September, what is the expected number giving birth that summer? Your answer is a single number from the list file.
    4. What is the estimated reliability of number of breeding sows from questionnaire one? The answer is a number, which you get with a calculator and the list file.
    5. What is the estimated reliability of number of sows giving birth from questionnaire two? The answer is a number, which you get with a calculator and the list file.
    6. Is there evidence of correlated measurement error within questionnaires? Answer Yes or No and give some numbers from the list file to support your conclusion.