Methods for Constructing Normalised Reference Scores: An Application for Assessing Child Development at 24 Months of...

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.