A hierarchical latent variable model for data visualization

Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images.

An illustration of variable precision rough sets model:an analysis of the findings of the UK Monopolies and Mergers Commission

This paper introduces a new technique in the investigation of limited-dependent variable models. This paper illustrates that variable precision rough set theory (VPRS), allied with the use of a modern method of classification, or discretisation of data, can out-perform the more standard approaches that are employed in economics, such as a probit model. These approaches and certain inductive decision tree methods are compared (through a Monte Carlo simulation approach) in the analysis of the decisions reached by the UK Monopolies and Mergers Committee. We show that, particularly in small samples, the VPRS model can improve on more traditional models, both in-sample, and particularly in out-of-sample prediction. A similar improvement in out-of-sample prediction over the decision tree methods is also shown.

Pricing-to-market using EGARCH-error correction model

In this paper, the authors use an exponential generalized autoregressive conditional heteroscedastic (EGARCH) error-correction model (ECM), that is, EGARCH-ECM, to estimate the pass-through effects of foreign exchange (FX) rates and producers’ prices for 20 U.K. export sectors. The long-run adjustment of export prices to FX rates and producers’ prices is within the range of -1.02% (for the Textiles sector) and -17.22% (for the Meat sector). The contemporaneous pricing-to-market (PTM) coefficient is within the range of -72.84% (for the Fuels sector) and -8.05% (for the Textiles sector). Short-run FX rate pass-through is not complete even after several months. Rolling EGARCH-ECMs show that the short and long-run effects of FX rate and producers’ prices fluctuate substantially as are asymmetry and volatility estimates before equilibrium is achieved.

Semi-supervised Gaussian process latent variable model with pairwise constraints

In machine learning, Gaussian process latent variable model (GP-LVM) has been extensively applied in the field of unsupervised dimensionality reduction. When some supervised information, e.g., pairwise constraints or labels of the data, is available, the traditional GP-LVM cannot directly utilize such supervised information to improve the performance of dimensionality reduction. In this case, it is necessary to modify the traditional GP-LVM to make it capable of handing the supervised or semi-supervised learning tasks. For this purpose, we propose a new semi-supervised GP-LVM framework under the pairwise constraints. Through transferring the pairwise constraints in the observed space to the latent space, the constrained priori information on the latent variables can be obtained. Under this constrained priori, the latent variables are optimized by the maximum a posteriori (MAP) algorithm. The effectiveness of the proposed algorithm is demonstrated with experiments on a variety of data sets. © 2010 Elsevier B.V.

EM optimization of latent-variable density models

There is currently considerable interest in developing general non-linear density models based on latent, or hidden, variables. Such models have the ability to discover the presence of a relatively small number of underlying `causes' which, acting in combination, give rise to the apparent complexity of the observed data set. Unfortunately, to train such models generally requires large computational effort. In this paper we introduce a novel latent variable algorithm which retains the general non-linear capabilities of previous models but which uses a training procedure based on the EM algorithm. We demonstrate the performance of the model on a toy problem and on data from flow diagnostics for a multi-phase oil pipeline.

Model specification and forecasting foreign exchange rates with vector autoregressions

This study examines the forecasting accuracy of alternative vector autoregressive models each in a seven-variable system that comprises in turn of daily, weekly and monthly foreign exchange (FX) spot rates. The vector autoregressions (VARs) are in non-stationary, stationary and error-correction forms and are estimated using OLS. The imposition of Bayesian priors in the OLS estimations also allowed us to obtain another set of results. We find that there is some tendency for the Bayesian estimation method to generate superior forecast measures relatively to the OLS method. This result holds whether or not the data sets contain outliers. Also, the best forecasts under the non-stationary specification outperformed those of the stationary and error-correction specifications, particularly at long forecast horizons, while the best forecasts under the stationary and error-correction specifications are generally similar. The findings for the OLS forecasts are consistent with recent simulation results. The predictive ability of the VARs is very weak.

Fixed or variable noise in contrast discrimination? The jury's still out

The ability to distinguish one visual stimulus from another slightly different one depends on the variability of their internal representations. In a recent paper on human visual-contrast discrimination, Kontsevich et al (2002 Vision Research 42 1771 - 1784) re-considered the long-standing question whether the internal noise that limits discrimination is fixed (contrast-invariant) or variable (contrast-dependent). They tested discrimination performance for 3 cycles deg-1 gratings over a wide range of incremental contrast levels at three masking contrasts, and showed that a simple model with an expansive response function and response-dependent noise could fit the data very well. Their conclusion - that noise in visual-discrimination tasks increases markedly with contrast - has profound implications for our understanding and modelling of vision. Here, however, we re-analyse their data, and report that a standard gain-control model with a compressive response function and fixed additive noise can also fit the data remarkably well. Thus these experimental data do not allow us to decide between the two models. The question remains open. [Supported by EPSRC grant GR/S74515/01]

Chain-store pricing and the structure of retail markets

This paper investigates competition between chain-stores and independents in the UK opticians' industry, using the relationship between the number of outlets present in a local market and the market size. Chain-stores are shown to have a significant effect on local market competition. In addition, the empirical approach is extended to allow inferences on the nature and extent of product differentiation. The results are broadly consistent with a model of vertical product differentiation in which chain-stores adopt national pricing strategies. The evidence suggests that the nature of competition between independent retailers depends on whether a chain-store is present.

Pricing-to-market for UK export sector

This thesis investigates the pricing-to-market (PTM) behaviour of the UK export sector. Unlike previous studies, this study econometrically tests for seasonal unit roots in the export prices prior to estimating PTM behaviour. Prior studies have seasonally adjusted the data automatically. This study’s results show that monthly export prices contain very little seasonal unit roots implying that there is a loss of information in the data generating process of the series when estimating PTM using seasonally-adjusted data. Prior studies have also ignored the econometric properties of the data despite the existence of ARCH effects in such data. The standard approach has been to estimate PTM models using Ordinary Least Square (OLS). For this reason, both EGARCH and GJR-EGARCH (hereafter GJR) estimation methods are used to estimate both a standard and an Error Correction model (ECM) of PTM. The results indicate that PTM behaviour varies across UK sectors. The variables used in the PTM models are co-integrated and an ECM is a valid representation of pricing behaviour. The study also finds that the price adjustment is slower when the analysis is performed on real prices, i.e., data that are adjusted for inflation. There is strong evidence of auto-regressive condition heteroscedasticity (ARCH) effects – meaning that the PTM parameter estimates of prior studies have been ineffectively estimated. Surprisingly, there is very little evidence of asymmetry. This suggests that exporters appear to PTM at a relatively constant rate. This finding might also explain the failure of prior studies to find evidence of asymmetric exposure in foreign exchange (FX) rates. This study also provides a cross sectional analysis to explain the implications of the observed PTM of producers’ marginal cost, market share and product differentiation. The cross-sectional regressions are estimated using OLS, Generalised Method of Moment (GMM) and Logit estimations. Overall, the results suggest that market share affects PTM positively.Exporters with smaller market share are more likely to operate PTM. Alternatively, product differentiation is negatively associated with PTM. So industries with highly differentiated products are less likely to adjust their prices. However, marginal costs seem not to be significantly associated with PTM. Exporters perform PTM to limit the FX rate effect pass-through to their foreign customers, but they also avoided exploiting PTM to the full, since to do so can substantially reduce their profits.

Electromagnetic interference from variable speed motor drives

A methodology is presented which can be used to produce the level of electromagnetic interference, in the form of conducted and radiated emissions, from variable speed drives, the drive that was modelled being a Eurotherm 583 drive. The conducted emissions are predicted using an accurate circuit model of the drive and its associated equipment. The circuit model was constructed from a number of different areas, these being: the power electronics of the drive, the line impedance stabilising network used during the experimental work to measure the conducted emissions, a model of an induction motor assuming near zero load, an accurate model of the shielded cable which connected the drive to the motor, and finally the parasitic capacitances that were present in the drive modelled. The conducted emissions were predicted with an error of +/-6dB over the frequency range 150kHz to 16MHz, which compares well with the limits set in the standards which specify a frequency range of 150kHz to 30MHz. The conducted emissions model was also used to predict the current and voltage sources which were used to predict the radiated emissions from the drive. Two methods for the prediction of the radiated emissions from the drive were investigated, the first being two-dimensional finite element analysis and the second three-dimensional transmission line matrix modelling. The finite element model took account of the features of the drive that were considered to produce the majority of the radiation, these features being the switching of the IGBT's in the inverter, the shielded cable which connected the drive to the motor as well as some of the cables that were present in the drive.The model also took account of the structure of the test rig used to measure the radiated emissions. It was found that the majority of the radiation produced came from the shielded cable and the common mode currents that were flowing in the shield, and that it was feasible to model the radiation from the drive by only modelling the shielded cable. The radiated emissions were correctly predicted in the frequency range 30MHz to 200MHz with an error of +10dB/-6dB. The transmission line matrix method modelled the shielded cable which connected the drive to the motor and also took account of the architecture of the test rig. Only limited simulations were performed using the transmission line matrix model as it was found to be a very slow method and not an ideal solution to the problem. However the limited results obtained were comparable, to within 5%, to the results obtained using the finite element model.

A new fuzzy additive model for determining the common set of weights in Data Envelopment Analysis

The main advantage of Data Envelopment Analysis (DEA) is that it does not require any priori weights for inputs and outputs and allows individual DMUs to evaluate their efficiencies with the input and output weights that are only most favorable weights for calculating their efficiency. It can be argued that if DMUs are experiencing similar circumstances, then the pricing of inputs and outputs should apply uniformly across all DMUs. That is using of different weights for DMUs makes their efficiencies unable to be compared and not possible to rank them on the same basis. This is a significant drawback of DEA; however literature observed many solutions including the use of common set of weights (CSW). Besides, the conventional DEA methods require accurate measurement of both the inputs and outputs; however, crisp input and output data may not relevant be available in real world applications. This paper develops a new model for the calculation of CSW in fuzzy environments using fuzzy DEA. Further, a numerical example is used to show the validity and efficacy of the proposed model and to compare the results with previous models available in the literature.

On a distinction between casual and formative variable models:theoretical issues and practical implications for organizational researchers

Formative measurement has seen increasing acceptance in organizational research since the turn of the 21st Century. However, in more recent times, a number of criticisms of the formative approach have appeared. Such work argues that formatively-measured constructs are empirically ambiguous and thus flawed in a theory-testing context. The aim of the present paper is to examine the underpinnings of formative measurement theory in light of theories of causality and ontology in measurement in general. In doing so, a thesis is advanced which draws a distinction between reflective, formative, and causal theories of latent variables. This distinction is shown to be advantageous in that it clarifies the ontological status of each type of latent variable, and thus provides advice on appropriate conceptualization and application. The distinction also reconciles in part both recent supportive and critical perspectives on formative measurement. In light of this, advice is given on how most appropriately to model formative composites in theory-testing applications, placing the onus on the researcher to make clear their conceptualization and operationalisation.

Wealth effects of mergers and acquisitions for US firms: using alternative pricing models

This empirical study employs a different methodology to examine the change in wealth associated with mergers and acquisitions (M&As) for US firms. Specifically, we employ the standard CAPM, the Fama-French three-factor model and the Carhart four-factor models within the OLS and GJR-GARCH estimation methods to test the behaviour of the cumulative abnormal returns (CARs). Whilst the standard CAPM captures the variability of stock returns with the overall market, the Fama-French factors capture the risk factors that are important to investors. Additionally, augmenting the Fama-French three-factor model with the Carhart momentum factor to generate the four-factor captures additional pricing elements that may affect stock returns. Traditionally, estimates of abnormal returns (ARs) in M&As situations rely on the standard OLS estimation method. However, the standard OLS will provide inefficient estimates of the ARs if the data contain ARCH and asymmetric effects. To minimise this problem of estimation efficiency we re-estimated the ARs using GJR-GARCH estimation method. We find that there is variation in the results both as regards the choice models and estimation methods. Besides these variations in the estimated models and the choice of estimation methods, we also tested whether the ARs are affected by the degree of liquidity of the stocks and the size of the firm. We document significant positive post-announcement cumulative ARs (CARs) for target firm shareholders under both the OLS and GJR-GARCH methods across all three methodologies. However, post-event CARs for acquiring firm shareholders were insignificant for both sets of estimation methods under the three methodologies. The GJR-GARCH method seems to generate larger CARs than those of the OLS method. Using both market capitalization and trading volume as a measure of liquidity and the size of the firm, we observed strong return continuations in the medium firms relative to small and large firms for target shareholders. We consistently observed market efficiency in small and large firm. This implies that target firms for small and large firms overreact to new information resulting in a more efficient market. For acquirer firms, our measure of liquidity captures strong return continuations for small firms under the OLS estimates for both CAPM and Fama-French three-factor models, whilst under the GJR-GARCH estimates only for Carhart model. Post-announcement bootstrapping simulated CARs confirmed our earlier results.

A flexible cost function model with risk

In examining bank cost efficiency in banking inclusion of risk-taking of banks is very important. In this paper we depart from the standard modeling approach and view risk intimately related to the technology. Thus, instead of controlling for risk by viewing them as covariates in the standard cost function we argue that the technology differs with risk, thereby meaning that the parameters of the parametric cost function changes with risk in a fully flexible manner. This is accomplished by viewing the parameters of the cost function as nonparametric functions of risk. We also control for country-specific effects in a fully flexible manner by using them as arguments of the nonparametric functions along with the risk variable. The resulting cost function then becomes semiparametric. The standard parametric model becomes a special case of our semiparametric model. We use the above modeling approach for banks in the EU countries. Actually, European financial integration is seen as a stepping stone for the development of a competitive single EU market that promotes efficiency and increases consumer welfare, changing the risk profile of the European banks. Particularly, financial integration allows more risk diversification and permits banks to use more advanced risk management instruments and systems, however it has at the same time increased the probability of systematic risks. Financial integration has increased the risk of contagion and changed its nature and scope. Consequently the bank’s risk seems to be an important issue to be investigated.

Semiparametric smooth-coefficient stoachastic frontier model

This paper proposes a semiparametric smooth-coefficient stochastic production frontier model where all the coefficients are expressed as some unknown functions of environmental factors. The inefficiency term is multiplicatively decomposed into a scaling function of the environmental factors and a standard truncated normal random variable. A testing procedure is suggested for the relevance of the environmental factors. Monte Carlo study shows plausible ¯nite sample behavior of our proposed estimation and inference procedure. An empirical example is given, where both the semiparametric and standard parametric models are estimated and results are compared.