The question of whether psychopathology constructs are discrete kinds or continuous dimensions represents an important issue in clinical psychology. The current setup of diagnostic systems such as the DSM and the ICD typically adheres to categorical models, in which discrete diagnoses are based on patterns of symptoms. This approach is rooted in psychiatric traditions that go back to the work op Kraeplin. In medicine, the successes of modern medicine are predicated on the insight that in many cases, treatment should be directed at diseases rather than, for instance, at the observable symptoms themselves, because in medicine diseases function as root causes. 

The current health care model assumes that psychiatric categorizations 'carve nature at its joints', as Plato puts it. But such categorizations often involve apparently arbitraty conventions. De DSM diagnoses of depression requires five or more symptoms to be present, but is unclear whether the resulting categorization is empirically superior to one that would require four or six symptoms for diagnosis. So, the question of whether psychopathology constructs are kinds or continua is of central importance to psychiatry and clinical psychology. 

The question of how to represent empirical phenomena using mathemetical structures is dealt with in measurement theory. All measurements starts with categorization of equivalence classes - these are sets of individuals who are exchangeable with respect to the attribute of interest. 

In psychological terms, categorical representations line up naturally with an interpretation of disorders as discrete disease entities, while continuum hypotheses are most naturally consistent with the idea that a construct varies continuously in a population. 

If mental disorders were directly observable, the task of categorizing them as continuous or categorical would be relatively straightforward. You could create equivalence classes of individuals with the same disorder status, see how many of these suffice, and test whether they conform to order relations. But unfortunately, in psychology, we have no way to decide conclusively whether two individuals are 'equally depressed'. So this also means we cannot form the equivalence classes necessary for measurement theory to operate. The standard procedure in psychology is to presume that, even though equivalence classes for theoretical entitities like depression and anxiety are not subject to direct empirical determination, we may still entertain them as hypothetical entitites purported to underlie the thoughts, feelings and behaviors that we observe. 

Alternatively, a model could hold that there are not just two discrete categories of individuals, but rather that individuals differ from each other in degree. This would yield a formal representation of a hypothesis that depression is not a kind but a continuum. 

Thus, the latent model assumes that, given a specific level of a latent variable (depression) the indicators (feelings of guilt, suicidal ideas) are uncorrelated. This feature is also known as local independence, and is consistent with a causal interpretation of the effects of the latent on the observed variables. 

If the underlying construct is continuous, then the covariance between any two indicators conditional on a given range of a proxy of the construct should be the same regardless of the exact range. To carry out a taxometric analysis, one arbitrarirly chosen variable is denoted the 'index' variable, and is assumed to be a proxy for the underlying construct. Despite its popularity, it should be noted that the taxometric approach is not uncontroversial in psychometrics. The reason is that it has long rested purely on the visual inspection of a plotted function instead of on a formal hypothesis test. Another reason is that one of its core assumptions is not necessarily true (that categorical latent structures will produce peaked covariance functions). Complementary to taxometrixs analysis, one may use latent variables modelling as a framework in which to query the structure of psychiatric constructs. 

Researchers have systematically evaluated the performance of latent variable models and taxometric proceudres, in which taxometric strategires are used to detect categorical structures, whereas latent class or profile models are used to select the optimal number of classes if the structure is determined to be categorical. 

Recent developments in statistical modelling have produced various models that blur the kinds-continua distinction, in the sense that they accomodate both categorical and continuous latent structures at the same time. Finite mixture models partition the population into distinct latent classes, but allow for continuous variation within these classes. However, observed variables are assumed to be conditionally independent given both the latent class and the latent continuous factor. Alternatively, the factor mixture model can be understood as a multi-group common factor model in which group membership is unknown. The latent class variable then takes the place of an observed grouping variable. 

Factor mixture models provide a useful framework for formalizing the distinction between categorical and continuous latent variables in terms of distributional assumptions and model constraints. Thus, while the factor model and the latent class model are distinct models, mixture modelling allows us to connect them by means of intermediate models and associate constraints. 

In GoM models, one can also depart from a simple latent class model to integrate continuous features. Here however, the continuous variation concerns group membership itself. Where the latent class model assumes that every person belongs to one and only one latent class, the GoM model allows individuals to be members of multiple classes at the same time. In the GoM model, the degree of membership is expressed in terms of a set of probabilities that sum to unity. 

In traditional models discussed so far, theoretical constructs are assumed to be either categorical or continuous for all elements of the population. Recently developed network models shed a new light on the question whether disorders should be thought of as categories or as continua. Psychometric latent variable models represent differences in the structure of psychiatric constructs as differences in the distributional form of a latent variable, which acts as a common cause of the indicators. 

Individual patterns in network structure may lead to different patterns of symptom dynamics. The reason for this difference is that, in strongly connected networks, symptom activation may be increased through feedback loops. The differences in dynamics across different network structures are important to the kinds vs. continua discussion, because they show that disorders may be discrete kinds for some people and continuous structures for others. 

Thus, network models provide a fresh way of thinking about the problem of kinds vs. continua, and suggest new avenues for research. The current evaluation of psychometric conceptualizations and models shows that the distinction between continua and kinds is considerably more subtle than has been presupposed in the literature.