These calculations were based on a liability threshold model, which assumes that the dichotomous distribution of Scheuermann's disease (affected versus not affected) reflects an underlying normally distributed liability in the population.
The model assumes that underlying a categorical diagnosis is a normally distributed liability continuum.
In genetics, models for dichotomous traits have traditionally been approached via the model of an underlying, normally distributed, liability.
However, it should be remembered that a normally distributed liability in the threshold model is also an assumption that can be challenged.
With ordinal item level data an underlying continuously distributed liability is assumed and thresholds that categorize the disorder are estimated based on the response frequencies (Flora and Curran 2004).
In the context of the model of an underlying normally distributed liability, it is natural to regard interaction on the probit scale as a natural generalization of Fisher's "epistacy".
MI was tested for the six age × sex groups with a multi-group confirmatory factor analysis (MGCFA) for ordinal data, assuming an underlying continuously distributed liability, which is subject to a series of thresholds that categorize the phenotype.
In medical conditions, behaviors similar to those observed for stochastic nonlinear systems manifest already in diseases whose pathogenesis may be less "complex" compared to MS. For instance, embolism that can be a casual response to normally distributed liability traits such as dyslipidemia or hypertension.
This can be calculated assuming a threshold ('all or none') model with an underlying normally distributed liability with heritability hL, which depends on the heritability of the binary trait (h01) as: h L 2 = p (1 - p ) z -2 h 01, where p is the prevalence of the binary trait and z is the ordinate of the standardised normal distribution corresponding to p [ 13].
Previous ground-breaking works have investigated the bounds prevalence and heritability impose on predictive accuracy using simulations [ 10], analytical results utilizing genotype relative risks and their frequencies [ 11], and analytical approximations under the assumption of a normally distributed liability [ 12, 13].
