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Methods for Constructing Normalised Reference Scores: An Application for Assessing Child Development at 24 Months of
Vasiliki Bountziouka1,2,3,4, Samantha Johnson2, Bradley N Manktelow2
1Department of Food Science and Nutrition, University of the Aegean.
Insights
The lambda-mu-sigma (LMS) method for reference ranges is limited with bounded data. This study introduces methods to improve centile estimation for bounded scores, addressing ceiling effects using specific distributions for accurate developmental assessments.
Area of Science:
- Biostatistics
- Developmental Psychology
- Psychometrics
Background:
- The lambda-mu-sigma (LMS) method is widely used for estimating centiles and reference ranges, particularly in childhood growth assessment.
- Standard LMS methods assume normality, which is violated when data are bounded (e.g., psychometric scores with ceiling/floor effects).
- This violation leads to biased centile estimations in clinical practice.
Purpose of the Study:
- To describe methodology for constructing reference intervals for bounded response variables.
- To explore different distribution families for centile estimation in psychometric data.
- To address limitations of the LMS method in the presence of ceiling effects.
Main Methods:
- Developed and applied methods for centile estimation with bounded data.
- Utilized a parent-completed assessment of cognitive and language development in 24-month-old children.
- Explored various distribution families, including the inflated binomial distribution, to model bounded scores.
Main Results:
- Modeling kurtosis improved z-scores and centile extraction.
- The inflated binomial distribution effectively addressed ceiling effects.
- Accurate centile curves for bounded data require careful selection of distribution families.
Conclusions:
- The standard LMS method requires adaptation for bounded psychometric measures.
- Appropriate distribution selection is critical for accurate centile estimation in bounded data.
- This methodology enhances the reliability of developmental assessments for young children.
Abstract:
The use of the lambda-mu-sigma (LMS) method for estimating centiles and producing reference ranges has received much interest in clinical practice, especially for assessing growth in childhood. However, this method may not be directly applicable where measures are based on a score calculated from question response categories that is bounded within finite intervals, for example, in psychometrics. In such cases, the main assumption of normality of the conditional distribution of the transformed response measurement is violated due to the presence of ceiling (and floor) effects, leading to biased fitted centiles when derived using the common LMS method. This paper describes the methodology for constructing reference intervals when the response variable is bounded and explores different distribution families for the centile estimation, using a score derived from a parent-completed assessment of cognitive and language development in 24 month-old children. Results indicated that the z-scores, and thus the extracted centiles, improved when kurtosis was also modeled and that the ceiling effect was addressed with the use of the inflated binomial distribution. Therefore, the selection of the appropriate distribution when constructing centile curves is crucial.
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