10.10 It is hypothesized that there are two distinct schools of thought about strategic policy of superpowers in the nuclear age: those who feel a superpower should hold a “flexible response” posture, so that whatever weapons the enemy develops, the superpower should develop a capability to respond to these weapons; and those who feel the superpower should maintain an “assured destruction” posture, so that the enemy will be assured that they will also be destroyed if they choose to attack. To test this hypothesis 100 experts in military strategy were given a questionnaire with four items scored dichotomously as zero or one. Responses to the survey instrument are shown below.

Carry out a latent structure analysis of this data, and test the hypothesis that the data are consistent with the postulated two latent class model (use a 5% level of significance, and the MLE method). Estimate the recruitment probabilities and the latent probabilities. Assume the sample size is large enough for large sample results to be applicable.