IBM® SPSS® Amos™ 28
Hypothesis testing procedures, confidence intervals and claims for efficiency in maximum likelihood or generalized least squares estimation by Amos depend on certain statistical distribution assumptions. First, observations must be independent. For instance, the forty young people in the Attig study have to be picked independently from the population of young people. Second, the exogenous variables must meet certain distributional requirements. For instance, if the exogenous variables have a multivariate normal distribution, that will suffice. Otherwise, there is one other, general situation under which maximum likelihood estimation can be applied. If some exogenous variables are random while others are fixed, i.e., they are either known beforehand or measured without error, then the fixed variables may have an arbitrary joint distribution, provided that
1.For any value pattern of the fixed variables, the remaining (random) variables have a (conditional) normal distribution.
2.The (conditional) variance-covariance matrix of the random variables is the same for every pattern of fixed variables.
3.The (conditional) expected values of the random variables depend linearly on the values of the fixed variables.
A typical example of a fixed variable would be an experimental treatment, classifying respondents into a study and a control group, respectively. This is all right as long as the other exogenous variables are normally distributed for study and control cases alike, and with the same conditional variance-covariance matrix. Note that an experimental grouping variable must be regarded as fixed, because the group assignment is completely determined by the experimenter.
Many people are accustomed to the requirements for normality and independent observations, since these are the usual requirements for many conventional procedures. However, with Amos, you have to remember that meeting these requirements leads only to asymptotic conclusions (i.e., conclusions that are approximately true for large samples).
