Overdispersed generalized linear models for neuropsychological data analyses: a proof-of-concept study.

Introduction. Neuropsychological data from both patients and healthy subjects often do not meet normality and heteroscedasticity assumptions required to perform linear model (LM) analyses. Negatively skewed and overdispersed distribution are frequent findings due to ceiling effect and high interindividual variability respectively. Variance-stabilizing and normalizing transformations might not be adequate since data assume a count-like distribution. Non-parametric alternatives thereupon might lack statistical power too. This study aim is to provide a proof of concept that using generalized linear models (GLM) which assume overdispersed count-like distributions (Negative Binomial; NB) can obviate aforesaid issues. Methods. Data regarding a noun naming task (range=0-50) on which largely-cognitively-spared motor neuron disease patients (MND; N=30) were compared to healthy controls (HC; N=29) were retrieved from Aiello et al. (2019). MND patients can present with mild language deficits [2]. The number of errors on the task was computed for each subject and regarded as the outcome variable. Likelihood ratio tests between non-nested models with parametric-bootstrap-inferred distributions [3] were implemented in order to assess the goodness of fit of the NB GLM compared to a classical LM and the Poisson GLM (a widely used non-overdispersed GLM for count data) with regards to a case-control comparison. Results. The null hypothesis (H0) that the underlying distribution was a NB vs. a Gaussian could be accepted (p=.402). The H0 that the underlying probability distribution was a NB vs. a Poisson could be accepted (p=.527) as well as the H0 that the underlying probability distribution was a Poisson vs. a NB could be rejected (p<.001) .Those results collectively provide strong empirical evidence that the NB distribution should be adopted to model the data. Discussion. It has been provided a proof of concept that the NB GLM yield a better fit to overdispersed ceiling neuropsychological data when compared to both a classical LM and to the Poisson GLM if a case-control comparison is performed. It is therefore suggested that the NB GLM should be adopted in scenarios characterized by high interindividual variability when mildly-cognitively-impaired patients are compared to HCs and/or when to score high on a test is relatively easy even for mildly-cognitively-impaired patients. Since the presented method regards the number of errors as the outcome variable caution should be exercised when applying it to closed-range neuropsychological tests. The presented method is anyhow ostensibly indicated for the majority of linguistic measures. Aiello et al 5th Int Meet NeuroMI(2019,nov) Pinto-Grau et al Neuropsychol Rev(2018)28:251-68 Wahrendorf et al J R Stat Soc C-Appl(1987)36:72-81