Evaluating uncertainty of model acceptance in empirical applications. A Replacement Approach

A major problem in psychological measurements is that in some circumstances there is no basis to assume that subjects are responding honestly. Some individuals actually tend to distort their responses in order to reach specific goals. For example, in personnel selection some subjects are likely to fake a personality questionnaire to match the ideal candidate's profile (positive impression management). Similarly, in the administration of diagnostic tests individuals often attempt to malinger posttraumatic stress disorder (PTSD) in order to secure financial gain and/or treatment, or to avoid being charged with a crime. Possible fake data confront the researcher with a crucial question: If data included fake datapoints, would the answer to the research question be different from what it is? Even in the clearest case -- that is, randomly fake data -- the answer is not necessarily obvious, as even the random perturbation of data constitutes a biased information which decreases the efficiency of parameter estimates and weakens the accuracy of statistical results. In this paper we attempt to contribute to the modeling of methods of treating possible fake data in structural equation models. In particular, our study examines the uncertainty associated with the acceptability of a simple well fitting factorial model. A new approach, called SGR (Sample Generation by Replacements), is developed in order to provide a perturbation model and a sampling procedure to generate a structured collection of perturbations.