Development and performance of npd for the evaluation of models with ordinal data
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915977125429248 |
|---|---|
| author | Cerou, Marc Chenel, Marylore Comets, Emmanuelle |
| author_facet | Cerou, Marc Chenel, Marylore Comets, Emmanuelle |
| contents | Introduction: Normalised prediction distribution errors (npde) are used to graphically and statistically evaluate continuous responses in non-linear mixed effect models. Here, our aim was to extend npde for categorical data and to evaluate their performance. We applied our approach to a real case-study describing the evolution of severe onychomycosis (toenail infection) in a trial comparing two treatment groups.
Methods: Let V denote a dataset with categorical observations. The null hypothesis H0 is that observations in V can be described by a model M. Residuals called npde can be adapted to categorical observations using jittering techniques. Their theoretical standard normal distribution can be evaluated through the Kolmogorov-Smirnov test. We evaluated the performance in terms of power through a simulation and compared it to a Chi-square. We illustrated the test and graphs on a real case-study.
Results: npd were able to detect misspecifications in the structural model and model parameter value. As expected, the power to detect model misspecifications increased both with the difference in the shape of the probability, and with the sample size. Chi-square test performed better but npd could be readily applied in all type of design. Based on the toe-nail data, graphs reveal a huge discrepancy of the base model, and a good adequation for the best model we found.
Conclusions: npde can be extended to categorical data, particularly in clinical settings with unbalanced design and graphs can be useful to evaluate the model as well as the covariate effects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02403 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Development and performance of npd for the evaluation of models with ordinal data Cerou, Marc Chenel, Marylore Comets, Emmanuelle Methodology Other Statistics Introduction: Normalised prediction distribution errors (npde) are used to graphically and statistically evaluate continuous responses in non-linear mixed effect models. Here, our aim was to extend npde for categorical data and to evaluate their performance. We applied our approach to a real case-study describing the evolution of severe onychomycosis (toenail infection) in a trial comparing two treatment groups. Methods: Let V denote a dataset with categorical observations. The null hypothesis H0 is that observations in V can be described by a model M. Residuals called npde can be adapted to categorical observations using jittering techniques. Their theoretical standard normal distribution can be evaluated through the Kolmogorov-Smirnov test. We evaluated the performance in terms of power through a simulation and compared it to a Chi-square. We illustrated the test and graphs on a real case-study. Results: npd were able to detect misspecifications in the structural model and model parameter value. As expected, the power to detect model misspecifications increased both with the difference in the shape of the probability, and with the sample size. Chi-square test performed better but npd could be readily applied in all type of design. Based on the toe-nail data, graphs reveal a huge discrepancy of the base model, and a good adequation for the best model we found. Conclusions: npde can be extended to categorical data, particularly in clinical settings with unbalanced design and graphs can be useful to evaluate the model as well as the covariate effects. |
| title | Development and performance of npd for the evaluation of models with ordinal data |
| topic | Methodology Other Statistics |
| url | https://arxiv.org/abs/2605.02403 |