An analogy may help give a context for heywood cases: ML estimation (and related methods) is like a religious fanatic in that it so believes  the models spesification that it will do anything, no matter how implausible, to force the model on the data (e.g., estimated correlation > 1.0). note that some SEM computer programs do not permit certain heywood cases to appear in the solution. For example, EQS does not allow the estimate of an error variance to be less than zero; that is, it sets a lower bound of zero (i.e, an inequality constraint) that prevents a negative variance estimate. However, solutions in which one or more estimates have been constrained by the computer to prevent an illogical value may indicate a problem (i.e., they should not be trusted). Researchers should also attempt to determine the source of the problem instead of constraining an error variance to be positive in a computer program for SEM and then rerunning the analysis (chen et al., 2001).

                The ML methods is generally both scale in variant. The former means that if a variable’s scale is linearly transformed, a parameter estimated for the transformed variable can be algebraically converted back to the original metric. The latter means the value of the ML fitting function in a particular sample remains the same regardless of the scale of the observed variables(kaplan, 2000). However, ML estimation may lose these properties if a correlation matrix is analyzed instead of a covariance matrix. Some special methods to correctly analyze a correlation matrix are discussed in Chapter 7.

                When a raw data file is analyzed, standard ML estimation assumes there are no missing values. A special form of ML estimation available for raw data files where some observations are missing at random was described earlier section 3.2).