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        Psychology 407

        Assignment \#9


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The data to be used in this assignment compares the previous
infant-loss histories of mothers of Baltimore school children who
had been identified by their teachers as behavior problems, with the
infant-loss histories of a comparable group whose children had not
been so designated.  The birth order of the ``index''child is an
important variable because the incidence of birth accidents such as
stillbirths increases with birth order.

\bigskip

We have 3 variables: Child (I), Loss (J), and Order (K) coded as
follows:

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i = 1 if child is a problem child

i  = 2 if child is a control child

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  j = 1 if mother suffered previous infant losses

  j  = 2 if there were no previous infant losses

  \bigskip

  k = 1 if birth order is 2

  k = 2 if birth order is 3 or 4

  k = 3 if birth order is 5 or more

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  The data, the fitted values and chi-square statistics for the
  model (I,JK) are given on the last page.

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a) Because this model ``fits'', specify in terms of $p_{ijk}$
exactly what probabilistic hypothesis is being ``accepted''?  Give
it a formal name and interpret it substantively.

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b) How does the probabilistic hypothesis in (a) translate into
expected frequencies?  Give a generic formula and show how it gives
the fitted value of 17.918 when $i = 1, j = 1, k = 1$.

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c) Given the model that is fit, what marginal tables are fit
exactly?  Show it numerically.  What marginal tables are not
necessarily fit exactly?  Show it numerically.

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d)  Indicate from a formula how the degrees of freedom are
calculated.

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e)  Generate the fitted values and the two chi-square statistics for
the model of complete independence.  Interpret the results
substantively.  Test formally the significance of the increase in
fit in moving from the complete independence model to (I,JK).

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f)  Because the model (I,JK) ``fits'', we would not ordinarily look
at more complicated models.  Suppose, however, (I,JK) did not fit
well but (IK,JK) did. Explain substantively what this would mean,
and specify explicitly the probabilistic hypothesis being accepted.
What marginal tables would be fit perfectly and which would not
necessarily be fit perfectly?  What is the formal name for this
model.


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