Robert Gilchrist

The logistic regression model with response variables subject to randomized response

The univariate and multivariate logistic regression model is discussed where response variables are subject to randomized response (RR). RR is an interview technique that can be used when sensitive questions have to be asked and respondents are reluctant to answer directly. RR variables may be described as misclassified categorical variables where conditional misclassification probabilities are known. The univariate model is revisited and is presented as a generalized linear model. Standard software can be easily adjusted to take into account the RR design. The multivariate model does not appear to have been considered elsewhere in an RR setting; it is shown how a Fisher scoring algorithm can be used to take the RR aspect into account. The approach is illustrated by analyzing RR data taken from a study in regulatory non-compliance regarding unemployment benefit.

Modelling Skewness and Kurtosis with the Bcpe Density in Gamlss

This paper illustrates the power of modern statistical modelling in understanding processes characterised by data that are skewed and have heavy tails. Our particular substantive problem concerns film box-office revenues. We are able to show that traditional modelling techniques based on the Pareto–Levy–Mandelbrot distribution led to what is actually a poorly supported conclusion that these data have infinite variance. This in turn led to the dominant paradigm of the movie business that ‘nobody knows anything’ and hence that box-office revenues cannot be predicted. Using the Box–Cox power exponential distribution within the generalized additive models for location, scale and shape framework, we are able to model box-office revenues and develop probabilistic statements about revenues.

Investigation of the Properties of the HEAF Estimator Using Simulation Experiments and MPEG-encoded Video Traces

It was discovered that some LAN traffic exhibits self-similar rather than Poisson behaviour and there is ongoing research towards finding and improving suitable estimators which may help to characterize various types of network traffic. Such characterization can be potentially applied for control purposes such as traffic shaping, load balancing, etc. The Hurst exponent is used to measure the intensity of long-range dependence (LRD) in the network traffic. Despite having several existing estimators, LRD analysis is still impeded by the difficulty of actual identification of its intensity. This paper continues work on estimating the Hurst exponent from the autocorrelation function, a so-called HEAF estimator introduced earlier by the authors. It also compares HEAF with a few existing estimators such as wavelet, Higuchi, aggregated variance time (V/T) and rescaled-range (R/S). The simulation studies show that HEAF can be used to capture the LRD in the network traffic if true process is fGn and FARIMA

Forecasting Film Revenues Using GAMLSS

This paper utilises the GAMLSS framework for the statistical modelling of movie box-office revenues. The dominant modelling paradigm of the film industry, traditionally exemplified by the nobody knows principle is based upon the infinite variance of the Pareto distribution. Using GAMLSS we have the flexibility to model up to 4 parameters of any distribution in terms of the avail- able explanatory variates, including a predictor that has smooth non-parametric functions. We here show that total box-office revenue can be better modelled by distributions with finite variance contradicting the Paretian hypothesis. Moreover the final version of the paper will illustrate that the Box-Cox power exponential distribution gives models where the parameters vary smoothly with an important explanatory variable, leading to the substantive conclusion that the post-opening revenue can, in fact, be explained by the opening box-office

The randomized response log linear model as a composite link model

In randomized response (RR) designs, misclassification is used to protect the privacy of respondents when sensitive questions are asked. A generalized linear model with a composite link function is presented to formulate log linear models that take the RR design into account. The approach is extended to model the situation where some respondents do not follow the instructions of the RR design. For example, if there are three binary RR variables with regard to practicing fraud, the 2 × 2 × 2 cross-classification of the true answers is latent due to the misclassification. Using composite link functions, log linear models can be specified for the latent table to investigate possible association between the variables. Fast iteratively re-weighted least squares algorithms are presented.