The danger of using a dichotomous system when it comes to mental disorders is not treating people who require treatment or treating people who do not require treatment. It is unclear where the boundary between disorder and no disorder is and this is not progressive for science and research as a whole.

Equivalence classes refers to sets of individuals who are exchangeable with respect to the attribute of interest. Measurement starts with categorization. The continuity hypothesis states that in between any two positions lies a third that can be empirically confirmed (1) and that there are no gaps in the continuum (2).

In a continuous interpretation, the distinction between people that have a disorder and do not have a disorder depends on the imposition of a cut-off score that does not reflect a gap in the inherent attribute itself (e.g. difference between average length and being tall). However, there is no way of measuring how depressed someone is (i.e. there is no scale).

Local independence states that given a specific level of a latent variable, the observed variables are uncorrelated (e.g. guilt and suicide ideation is uncorrelated in healthy individuals).

The form of the latent structure can be assessed by inspecting particular consequences of the model for specific statistical properties of items (1) and on the basis of the global fit measures that allow one to compare whether a model with a categorical latent structure fits better than a model with a continuous latent structure on the observed data.(2).

Taxometrics refers to inspecting particular consequences of the model for specific statistical properties of items. If an underlying construct is continuous, then the covariance between any two observed variables should be the same regardless of the exact range. This analysis can be done by choosing a variable and denoting it as the index variable. In other words, the covariance between A and B should be the same on different levels of index variable C if the index variable is continuous. If it is categorical, then the covariance between A and B should differ on different levels of the index variable and be 0 at the ‘no disorder’ level of the index variable.

ALTERNATIVE LATENT VARIABLE MODELS
The factor mixture models subdivide the population into different categories but there is a continuous scale within categories. It is a model in which each category is characterized by its own common factor model. It is a multi-group common factor model in which group membership is unknown. The class variable takes the place of an observed grouping variable.  

Grade of membership (GoM) models can integrate continuous features. This continuous variation concerns group membership. This model allows individuals to be members of multiple classes at the same time but to different degrees. This model is useful if there is no clear distinction between classes.

In a network model, modes are causally related to each other and this network leads to a disorder. Individual differences in network structure may lead to different patterns of symptom dynamics. There could be individual differences in the strength of connection between nodes. In a network that is strongly connected, an external stressor will cause the symptoms and these symptoms will activate other symptoms. This will create a disordered state which will remain stable even when the external stressor is taken away.

In strongly connected networks, symptom activation may be increased through feedback loops. There could be early warning signals of when the tipping point is arriving. This makes the system’s state at a given point more predictable based on previous time points.