Theoretical Foundations and Clinical Implications of Formal Psychological Assessment

criterion for obsessive-compulsive disorder a8 ( table 1 ) can represent an attribute investigated by i2. Starting from a set of objects (MOCQ-R items) and a set of attributes (the DSM-IV-TR criteria for obsessive-compulsive disorder), a Boolean matrix (‘formal context’) is built. From a deterministic perspective, whenever an item investigates the specific symptom, 1 is reported in the cell that, otherwise, would contain 0. Defining the whole set of items as the ‘domain’ of the formal context, the ‘clinical state’ of a patient is the subset of the domain he/she affirmatively answers. Each clinical state is uniquely defined by a subset of attributes. Therefore, even if two different clinical states may score the same (2 different patients affirmatively answer the same number of items), their attribute configurations systematically differ. The formal context is used to build the ‘clinical structure’, i.e. the set representation of the implications among the items of the domain [4, 9] , including all the ‘admissible response patterns’ (i.e. the clinical states) and their respective set of attributes. An admissible response pattern is a set of items consistent with the implications postulated by a theoretical framework. For example, answering ‘true’ to item 20 (‘I get into a lot of physical fights’) of the Personality Diagnostic Questionnaire-4+ [10] reasonably implicates answering ‘true’ to item 12 (‘Sometimes I get upset’), whereas the inverse implication may not occur. To summarize, FPA both deterministically maps sets of items to sets of attributes, by investigating the cognitive processes involved in answering behavior, and identifies and uses implications among items to implement an adaptive methodology. Thus, FPA offers the possibility to adaptively collect the same information of a clinical interview through the administration of selfreport questionnaires. Nonetheless, a deterministic approach is inadequate in clinical practice, since neither the observed answers necessarily convey the exact information about the patient nor do all clinical states have the same probability to occur. Therefore, a probabilistic model taking into account both these issues is needed. The basic local independence model [6] addresses them by introducing ‘false negative’ ( ) and ‘false positive’ ( ) rates for each item. The application of FPA to obsessive-compulsive disorder, as described by the DSM-IV-TR and assessed by the ‘cleaning’ subscale of the MOCQ-R [7] , is used to illustrate its implications in clinical assessment. The model was tested on 4,412 subjects (3,775 males and 637 females), aged 21–65 years. Participants gave written informed consent to enter the study. The first step of the procedure was to construct the deterministic model, i.e. the formal context. The list of items and attributes is displayed in table 1 . The second step of the procedure involved the construction of the clinical structure from the context. The quality of the initial assessment represents one of the predictors of positive therapeutic outcomes, thus an increasing amount of research focuses on the development of more accurate assessment tools [1] . In clinical practice, the most widely adopted tools for assessment are clinical interview, semistructured interviews and psychological testing. Clinicians follow two main criteria in developing the sequence of questions to ask: (1) choosing questions to collect information for both diagnosis and case formulation and (2) trying to reduce redundancy. These criteria are not satisfied by self-report questionnaires because of methodological problems deriving from adopting a psychometric approach in psychodiagnosis. Since questionnaires mainly provide quantitative information (scores), they are unsuitable for collecting structured qualitative information. Furthermore, psychometric theory emphasizes the importance of obtaining reliable measures even through redundancy [2] . Thus, having an assessment methodology that is as informative as a clinical interview, as time consuming as a psychological test, able to collect information useful for case formulation, reliable, valid, adaptive and nonredundant, is needed. Clinimetrics is an attempt to address this request, focusing on the quality of clinical measurements [3] . Formal psychological assessment (FPA) [4] can integrate the principles of clinimetrics through formal representation. FPA is the formal conjunction and the clinical application of two mathematical psychology theories: formal concept analysis [5] and knowledge space theory [6] . The present paper briefly introduces FPA foundations and explores the main implications following from its use in clinical assessment. Consider item i2 ( table 1 ) of the Maudsley Obsessional-Compulsive Questionnaire-Reduced (MOCQ-R) [7] . In FPA, i2 is an ‘object’, defined on the basis of a given theoretical framework, which could be arbitrarily chosen without effect on the application of the methodology, thus resulting in extreme flexibility. If the DSM-IV-TR [8] is selected, one could check the diagnostic criteria for a disorder investigated through i2. Each criterion is then defined as an ‘attribute’. In the case at hand, the diagnostic Received: July 13, 2012 Accepted after revision: October 18, 2012 Published online: March 28, 2013