1. Figure 17.13 shows a model to test the effects of participation in Head Start on children’s cognitive ability. This example is a classic reanalysis of a controversial quasiexperiment; I have seen variations of it presented in Kenny (1979) and Bentler and Woodward (1978), among others. The measured background variables in the model include measures of mother’s and father’s educational attainment, father’s occupational status, and family income. Head Start was hoped to improve participants’ cognitive
skills, and the latent Cognitive Ability outcome was indexed by scores on two tests: the Illinois Test of Psycholinguistic Abilities (ITPA) and the Metropolitan Readiness Test (MRT). The Head Start variable is a dummy variable coded 1 for those who participated in Head Start and 0 for children in the control group. The data are shown in Table 17.4. These are data from 303 white children from an early Head Start evaluation, 148 who attended Head Start in the summer and 155 who did not. To understand
why the example is so controversial, note the correlation between Head Start and the two cognitive outcomes: both are negative (–.10, –.09), suggesting that Head Start may have negative effects on Ability! The model is one of several possible models designed to determine what the outcomes of Head Start are after taking the family’s background characteristics into account. The correlations and
SDs are also included here and in the Excel file “head start.xls” (the SDs are not included in most presentations of these data. I estimated these and the means from data presented in Magidson & Sörbom, 1982).
All continuous variables are standardized.
a. Draw (set up) and estimate the model. Is the structural portion of the model justidentified or overidentified? Evaluate the fit of the model and, if adequate, focus on parameter estimates. Interpret the model. According to these results, does Head Start have a positive effect on cognitive ability, a negative effect, or no effect at all? Interpret the other aspects of the model.
Figure 17.13
Model testing the potential effects of Head Start participation on children’s cognitive
Ability
b. Fix the path from Head Start to Cognitive Ability to zero; compare the fit of this model to the initial model. Do you still come to the same conclusion as before?
c. Are there other alternative models that you are interested in testing? Are they equivalent to the initial model? Test these models; be sure to evaluate the relative fit of the model and to interpret your findings.
d. Are there any common causes that the research may have neglected? How could you investigate the possibility of unmeasured common causes more completely?