Longitudinal Analysis of the Strengths and Difficulties Questionnaire Scores of the Millennium Cohort Study Children in England UsingM-Quantile Random-Effects Regression

Abstract

SummaryMultilevel modelling is a popular approach for longitudinal data analysis. Statistical models conventionally target a parameter at the centre of a distribution. However, when the distribution of the data is asymmetric, modelling other location parameters, e.g. percentiles, may be more informative. We present a new approach, M‐quantile random‐effects regression, for modelling multilevel data. The proposed method is used for modelling location parameters of the distribution of the strengths and difficulties questionnaire scores of children in England who participate in the Millennium Cohort Study. Quantile mixed models are also considered. The analyses offer insights to child psychologists about the differential effects of risk factors on children's outcomes.

Mixed hidden Markov quantile regression models for longitudinal data with possibly incomplete sequences

“…3 , Geraci and Bottai 4 , Tzavidis et al 5 and, in a Bayesian framework, by Reich et al 6 and Yuan and Yin 7 . When the assumption of time-constant random coefficients does not hold, adopting the above model specifications may lead to biased parameter estimates 13 .…”

Modelling the distribution of health-related quality of life of advanced melanoma patients in a longitudinal multi-centre clinical trial using M-quantile random effects regression

“…For describing the relationship between y and a set of covariates X at other parts of a conditional distribution we extend the two level M-quantile random effects regression model (Tzavidis et al, 2015) to a three-level M-quantile random effects regression model. In particular, we propose using asymmetric loss functions for this purpose when the data are hierarchically structured.…”

“…A function that fits the three-levels M-quantile (expectile) random effects regression has been in written in R. Some asymptotic properties of the estimators and their variance parameters for the MQRE models of order q are discussed in Tzavidis et al (2015).…”

“…Tzavidis et al (2015) propose the extension of M-quantile regression to two-levels M-quantile random effects regression for multilevel-type data. This paper is, to the best of our knowledge, the first attempt to apply a quantile-like random effects model to complex data from longitudinal and multi-centre studies (threelevels models).…”

“…In this paper we use M-estimation because it offers some advantages: (i) it easily allows for robust estimation of both fixed and random effects; (ii) it can trade robustness for efficiency in inference by selecting the tuning constant of the influence function; (iii) it can offer computational stability because it can use a wide range of continuous influence functions instead of the absolute value used in the quantile regression. Tzavidis et al (2015) extended M-quantile regression to include random effects to account for a two-level hierarchical structure in the data and used maximum likelihood to estimate the parameters of the model. In this paper we extend this approach to a three-level random effects model, which is appropriate for the analysis of the data we consider in Section 2 and we propose a maximum likelihood approach to estimate the model parameters.…”