Symptoms Measurement, Community Sampling and the Zero-Problem: A Case for Two-Part Modeling

Abstract

The difference between mental health and mental ability measurement hinges on a single concept-zero. Dysfunctional mental health is manifested by symptoms defined as self-reported feelings of unpleasantness due to pathological causes. Symptoms can be meaningfully reported as present or absent whereas mental abilities are generally considered to be ever present in some positive amount. Absence of symptoms creates a population zero class with unknown membership and proportion. Inadvertent mixture of zero-and non-zero classes, as often occurs in community samples, biases symptom estimates of means, variances, and covariance for the non-zero class, resulting in what is herein referred to as the zero-problem.Two-part modeling is proposed as a means of circumventing the zero-problem. In Part I, zero-class sample members are identified and deleted. Part II provides users a symptoms research paradigm based on a multiplicative measurement model. Data are logarithmically transformed, and the log-normal distribution assumed. The hypothesis that symptom statements are unidimensional is tested by confirmatory factor analysis (CFA). If accepted, statements are combined into a weighted pathology score. Pathology scores can be correlated, corrected for attenuation, and used as input to multivariate statistical applications. Computer routines are provided as a user service.

On establishing that pathology scores are quantitative

“…The psychopathology microworld of two-part modeling [1] is populated by a countable infinity of human objects. Human objects function as transducers converting the felt impact of wirklichkeit into symptom data elicited via scale instrumentation.…”

“…For the two-part symptom model [1], two contributing explanatory factors to responses from a symptomatic subpopulation are envisioned: pathological human life conditions and nonpathological human life conditions. Life condition is defined as a prolonged state of being.…”

“…The same procedure is used to generate a continous positive random variable E for nonpathological life conditions. The random variables P and E are combined multiplicatively to create a random variable Y = P·E [1]. It is the natural log transform of the Y random variable that when digitalized via scalar quantization comprises the symptom scale scores in two-part modeling [1].…”

“…The indirect means herein proposed is the estimation of standardized latent pathology scores as defined in [1]. The conditional expectation of the latent pathology score is shown to be an unbiased estimate of the conditioned pathology score.…”

“…Two-part symptom modeling as previously presented [1] envisions a medical reality in which a pathology underlying symptom response exists in varying amounts referred to as magnitudes. Magnitudes are said to sustain the qualitative ordering relations "more than" denoted by , "less than" denoted by , and the equivalence relation "same as" denoted by ~.…”