Modelling Strategies for Repeated Multiple Response Data

This article discusses modelling strategies for repeated measurements of multiple response variables. Such data arise in the context of categorical variables where one can select more than one of the categories as the response. We consider each of the multiple responses as a binary outcome and use a marginal (or population‐averaged) modelling approach to analyse its means. Generalized estimating equations are used to account for different correlation structures, both over time and between items. We also discuss an alternative approach using a generalized linear mixed model with conditional interpretations. We illustrate the methods using data from a panel study in Australia called the Household, Income, and Labour Dynamics Survey.     

Penalized Regression with Ordinal Predictors

Ordered categorial predictors are a common case in regression modelling. In contrast to the case of ordinal response variables, ordinal predictors have been largely neglected in the literature. In this paper, existing methods are reviewed and the use of penalized regression techniques is proposed. Based on dummy coding two types of penalization are explicitly developed; the first imposes a difference penalty, the second is a ridge type refitting procedure. Also a Bayesian motivation is provided. The concept is generalized to the case of non-normal outcomes within the framework of generalized linear models by applying penalized likelihood estimation. Simulation studies and real world data serve for illustration and to compare the approaches to methods often seen in practice, namely simple linear regression on the group labels and pure dummy coding. Especially the proposed difference penalty turns out to be highly competitive.     

Bayesian prior elicitation in DSGE models: Macro- vs micropriors

Bayesian approaches to the estimation of DSGE models are becoming increasingly popular. Prior knowledge is normally formalized either directly on deep parameters' values (‘microprior’) or indirectly, on macroeconomic indicators, e.g. moments of observable variables (‘macroprior’). We introduce a non-parametric macroprior which is elicited from impulse response functions and assess its performance in shaping posterior estimates. We find that using a macroprior can lead to substantially different posterior estimates. We probe into the details of our result, showing that model misspecification is likely to be responsible of that. In addition, we assess to what extent the use of macropriors is impaired by the need of calibrating some hyperparameters.     

The wisdom of crowds: The potential of online communities as a tool for data analysis

Online communities have become an important source for knowledge and new ideas. This paper considers the potential of crowdsourcing as a tool for data analysis to address the increasing problems faced by companies in trying to deal with “Big Data”. By exposing the problem to a large number of participants proficient in different analytical techniques, crowd competitions can very quickly advance the technical frontier of what is possible using a given dataset. The empirical setting of the research is Kaggle, the world?s leading online platform for data analytics, which operates as a knowledge broker between companies aiming to outsource predictive modelling competitions and a network of over 100,000 data scientists that compete to produce the best solutions. The paper follows an exploratory case study design and focuses on the efforts by Dunnhumby, the consumer insight company behind the success of the Tesco Clubcard, to find and lever the enormous potential of the collective brain to predict shopper behaviour. By adopting a crowdsourcing approach to data analysis, Dunnhumby were able to extract information from their own data that was previously unavailable to them. Significantly, crowdsourcing effectively enabled Dunnhumby to experiment with over 2000 modelling approaches to their data rather than relying on the traditional internal biases within their R&D units.     

A study of the family service expenditures and the socio-demographic characteristics via fixed marginals correspondence analysis

Our study focuses on two data set, the former provides the expenditures for several services for each family and the latter contains socio-demographic variables for the same statistical units. The main aim is to analyze, in a Correspondence Analysis context, the service expenditure of families based on the whole given data-set under two types of constraints: the global relative expenses for a given service and the global relative expenses for a given socio-demographic category. The purpose of measuring the relationship between expenditure on social services and the socio-demographic characteristics of families is conducted in an exploratory and predictive perspective. A new approach is then introduced which ensures compliance with the required constraints. Moreover, through a procedure, we have obtained a table of regression coefficients. This table shows interesting properties and it is easy to interpret. Finally, the performance of the results has been evaluated using computer-based resampling techniques.     

Polytomous logistic regression

In this paper a review will be given of some methods available for modelling relationships between categorical response variables and explanatory variables. These methods are all classed under the name polytomous logistic regression (PLR). Models for PLR will be presented and compared; model parameters will be tested and estimated by weighted least squares and by likelihood. Usually, software is needed for computation, and available statistical software is reported.
An industrial problem is solved to some extent as an example to illustrate the use of PLR. The paper is concluded by a discussion on the various PLR-methods and some topics that need a further study are mentioned.     

Calibrating longitudinal models of residential mobility and migration: an assessment of a non-parametric marginal likelihood approach

"This paper discusses the problems of controlling for omitted variables in estimating the structural parameters of longitudinal models and focuses upon an assessment of a non-parametric marginal maximum likelihood approach suggested by the results of Laird....The approach is shown to be statistically valid for a plausible discrete-time model of the incidence of residential or migration moves, at least for data in which no household moves in every time period. Empirical evaluation with two large [U.S.] datasets on residential mobility indicates that the approach is also computationally feasible and provides a promising alternative to more conventional methods for controlling for omitted variables."     

Daily peak electrical load forecasting with a multi-resolution approach

In the context of smart grids and load balancing, daily peak load forecasting has become a critical activity for stakeholders in the energy industry. An understanding of peak magnitude and timing is paramount for the implementation of smart grid strategies such as peak shaving. The modelling approach proposed in this paper leverages high-resolution and low-resolution information to forecast daily peak demand size and timing. The resulting multi-resolution modelling framework can be adapted to different model classes. The key contributions of this paper are (a) a general and formal introduction to the multi-resolution modelling approach, (b) a discussion of modelling approaches at different resolutions implemented via generalised additive models and neural networks, and (c) experimental results on real data from the UK electricity market. The results confirm that the predictive performance of the proposed modelling approach is competitive with that of low- and high-resolution alternatives.     

Forecasting economic time series using score-driven dynamic models with mixed-data sampling

We introduce a mixed-frequency score-driven dynamic model for multiple time series where the score contributions from high-frequency variables are transformed by means of a mixed-data sampling weighting scheme. The resulting dynamic model delivers a flexible and easy-to-implement framework for the forecasting of low-frequency time series variables through the use of timely information from high-frequency variables. We verify the in-sample and out-of-sample performances of the model in an empirical study on the forecasting of U.S. headline inflation and GDP growth. In particular, we forecast monthly headline inflation using daily oil prices and quarterly GDP growth using a measure of financial risk. The forecasting results and other findings are promising. Our proposed score-driven dynamic model with mixed-data sampling weighting outperforms competing models in terms of both point and density forecasts.     

Cumulative and CUB Models for Rating Data: A Comparative Analysis

Ordinal measurements as ratings, preference and evaluation data are very common in applied disciplines, and their analysis requires a proper modelling approach for interpretation, classification and prediction of response patterns. This work proposes a comparative discussion between two statistical frameworks that serve these goals: the established class of cumulative models and a class of mixtures of discrete random variables, denoted as CUB models, whose peculiar feature is the specification of an uncertainty component to deal with indecision and heterogeneity. After surveying their definition and main features, we compare the performances of the selected paradigms by means of simulation experiments and selected case studies. The paper is tailored to enrich the understanding of the two approaches by running an extensive and comparative analysis of results, relative advantages and limitations, also at graphical level. In conclusion, a summarising review of the key issues of the alternative strategies and some final remarks are given, aimed to support a unifying setting.