Psychology 407 Assignment #9

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.

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

i = 1 if child is a problem child i = 2 if child is a control child

j = 1 if mother suffered previous infant losses j = 2 if there were no previous infant losses

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

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

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.

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.

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.

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

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).

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.

3