The Intrinsic Psychological Health of Young Adults Through A Truncated Weibull Model

Abstract

The psychological data collected through questionnaires, extreme events such as total sickness or complete health, are very rare. This leads to an almost essential restriction of the data domain and hence demands truncation of data. Also, the data is essentially qualitative in nature (usually collected using a Likert scale). The objectives of the study were to model qualitative data using a continuous truncated Weibull model and to compare the three estimation techniques, namely, the Maximum Likelihood estimation, the Method of Moments (Cran) and the Bayesian Estimation method, all used under different circumstances, in case of this model. The choice of Weibull model was based on AIC and BIC criteria and was validated through the Kolmogorov-Smirnov test, prior to truncation. The parameters of the truncated model were estimated using the three estimation techniques on the data collected through the Strength and Difficulty Questionnaire (SDQ) 17+ extended version during Covid-19 pandemic period. The difficulty score component of SDQ (range 0-40) was truncated for total difficulty scores (i) less than 2; and (ii) more than 30. The estimates obtained through the three techniques were consistent up to two places after decimal.