Modelling neuromotor ratings with floor-effects.
Associated movements (AMs) are a classical diagnostic tool to assess differences between normal children and children with some motor dysfunction. This paper presents a methodology to produce age- and gender-dependent reference-curves for AMs of normal children, for various tasks of a test battery. Data available consist of separate ratings of duration and extent of AMs, which are ordinal quantities with few levels. Other problems are severe age- and gender-dependent floor-effects (as well as some ceiling-effects), leaving little information for analysis at older ages. To get a better scale, we combined the two ordinal ratings into one meaningful and quasi-continuous quantity referred to as intensity of AMs. In order to solve problems due to floor-effects, ceiling-effects and discreteness, we assumed left- , right- and interval-censored values, respectively. We considered a censored regression problem and postulated a truncated normal distribution for the non-censored values (after an appropriate transformation of the data). Using Wei and Tanner's poor man's data augmentation algorithm, together with the technique of linear mixed effects modelling, useful reference-curves could be produced. In contrast to the cumulative probabilities approach for ordinal data, our methodology allows the calculation of individual age- and gender-standardized values, which puts us in a position to investigate numerous scientific questions.