Sample Size Determination to Evaluate the Impact of Highway Improvements

This paper was prepared for the Department of Transport, as a support document to a main report on the feasibility of measuring responses to highway improvements. The paper discusses the statistical issues involved, particularly as regards the determination of suitable sample sizes. Worked examples are provided, using such data on ambient variability and adjustment factors as were available to us. Some of the data is included as an appendix where it was felt to be otherwise not easily available. The note asks two sort of questions. Firstly, what is the minimum sample size to take to be a certain percent confident that a given quantity lies in a range of a given width. Secondly, what sample sizes should be taken in Before and After studies so as to be a certain percent confident that a change in a quantity by a given amount will be detected as a statistically significant difference at some chosen significance level. Three sorts of quantities are discussed: - total flows past a point, which may be counted by loops, tubes or manually; - partial flows, such as a particular 0-D flow, which require roadside interviews; - journey times over particular links

Outlier Detection and Missing Value Estimation in Time Series Traffic Count Data: Final Report of SERC Project GR/G23180.

A serious problem in analysing traffic count data is what to do when missing or extreme values occur, perhaps as a result of a breakdown in automatic counting equipment. The objectives of this current work were to attempt to look at ways of solving this problem by: 1)establishing the applicability of time series and influence function techniques for estimating missing values and detecting outliers in time series traffic data; 2)making a comparative assessment of new techniques with those used by traffic engineers in practice for local, regional or national traffic count systems Two alternative approaches were identified as being potentially useful and these were evaluated and compared with methods currently employed for `cleaning' traffic count series. These were based on evaluating the effect of individual or groups of observations on the estimate of the auto-correlation structure and events influencing a parametric model (ARIMA). These were compared with the existing methods which included visual inspection and smoothing techniques such as the exponentially weighted moving average in which means and variances are updated using observations from the same time and day of week. The results showed advantages and disadvantages for each of the methods. The exponentially weighted moving average method tended to detect unreasonable outliers and also suggested replacements which were consistently larger than could reasonably be expected. Methods based on the autocorrelation structure were reasonably successful in detecting events but the replacement values were suspect particularly when there were groups of values needing replacement. The methods also had problems in the presence of non-stationarity, often detecting outliers which were really a result of the changing level of the data rather than extreme values. In the presence of other events, such as a change in level or seasonality, both the influence function and change in autocorrelation present problems of interpretation since there is no way of distinguishing these events from outliers. It is clear that the outlier problem cannot be separated from that of identifying structural changes as many of the statistics used to identify outliers also respond to structural changes. The ARIMA (1,0,0)(0,1,1)7 was found to describe the vast majority of traffic count series which means that the problem of identifying a starting model can largely be avoided with a high degree of assurance. Unfortunately it is clear that a black-box approach to data validation is prone to error but methods such as those described above lend themselves to an interactive graphics data-validation technique in which outliers and other events are highlighted requiring acceptance or otherwise manually. An adaptive approach to fitting the model may result in something which can be more automatic and this would allow for changes in the underlying model to be accommodated. In conclusion it was found that methods based on the autocorrelation structure are the most computationally efficient but lead to problems of interpretation both between different types of event and in the presence of non-stationarity. Using the residuals from a fitted ARIMA model is the most successful method at finding outliers and distinguishing them from other events, being less expensive than case deletion. The replacement values derived from the ARIMA model were found to be the most accurate

Setar Modelling of Traffic Count Data.

As part of a SERC funded project investigating outlier detection and replacement with transport data, univariate Box-Jenkins (1976) models have already been successfully applied to traffic count series (see Redfern et al, 1992). However, the underlying assumption of normality for ARIMA models implies they are not ideally suited for time series exhibiting certain behavioural characteristics. The limitations of ARIMA models are discussed in some detail by Tong (1983), including problems with time irreversibility, non-normality, cyclicity and asymmetry. Data with irregularly spaced extreme values are unlikely to be modelled well by ARIMA models, which are better suited to data where the probability of a very high value is small. Tong (1983) argues that one way of modelling such non-normal behaviour might be to retain the general ARIMA framework and allow the white noise element to be non-gaussian. As an alternative he proposes abandoning the linearity assumption and defines a group of non linear structures, one of which is the Self-Exciting Threshold Autoregressive (SETAR) model. The model form is described in more detail below but basically consists of two (or more) piecewise linear models, with the time series "tripping" between each model according to its value with respect to a threshold point. The model is called "Self-Exciting" because the indicator variable determining the appropriate linear model for each piece of data is itself a function of the data series. Intuitively this means the mechanism driving the alternation between each model form is not an external input such as a related time series (other models can be defined where this exists), but is actually contained within the series itself. The series is thus Self-Exciting. The three concepts embedded within the SETAR model structure are those of the threshold, limit cycle and time delay, each of which can be illustrated by the diverse applications such models can take. The threshold can be defined as some point beyond which, if the data falls, the series structure changes inherently and so an alternative linear model form would be appropriate. In hydrology this is seen as the non-linearity of soil infiltration, where at the soil saturation point (threshold) a new model for infiltration would become appropriate. Limit cycles describe the stable cyclical phenomena which we sometimes observe within time series. The cyclical behaviour is stationary, ie consists of regular, sustained oscillations and is an intrinsic property of the data. The limit cycle phenomena is physically observable in the field of radio-engineering where a triode valve is used to generate oscillations (see Tong, 1983 for a full description). Essentially the triode value produces self-sustaining oscillations between emitting and collecting electrons, according to the voltage value of a grid placed between the anode and cathode (thereby acting as the threshold indicator). The third essential concept within the SETAR structure is that of the time delay and is perhaps intuitively the easiest to grasp. It can be seen within the field of population biology where many types of non-linear model may apply. For example within the cyclical oscillations of blowfly population data there is an inbuilt "feedback" mechanism given by the hatching period for eggs, which would give rise to a time delay parameter within the model. For some processes this inherent delay may be so small as to be virtually instantaneous and so the delay parameter could be omitted. In general time series Tong (1983) found the SETAR model well suited to the cyclical nature of the Canadian Lynx trapping series and for modelling riverflow systems (Tong, Thanoon & Gudmundsson, 1984). Here we investigate their applicability with time series traffic counts, some of which have exhibited the type of non-linear and cyclical characteristics which could undermine a straightforward linear modelling process

Neutron Path Length Correction of a 3He Spin Filter

Abstract3He neutron spin filters (NSF) have been widely used for polarized neutron instrumentation for worldwide neutron facilities. Here we report characterization of the two-dimensional neutron path variation of a 3He NSF when a large divergent, scattered neutron beam passes through the end windows of a cylindrical 3He cell. Path length variations of the transmission of the unpolarized neutrons through a 3He NSF and neutron polarization produced from a 3He NSF are characterized. We present a ray-tracing model to explain the path length variation and corresponding neutron transmission and neutron polarization variations, and compare the measured variations to those calculated from the model. Although the path length effect is not large, it should be corrected in the polarization efficiency correction software when a 3He NSF is used for SANS polarization analysis. The path length variation effect can be adopted to other types of neutron scattering spectrometers when using 3He NSFs

An Influence Method for Outliers Detection Applied to Time Series Traffic Data

The applicability of an outlier detection statistic developed for standard time series is assessed in estimating missing values and detecting outliers in traffic count data. The work of Chernick, Downing and Pike (1982) is extended to form a quantitive outlier detection statistic for use with time series data. The statistic is formed from the squared elements of the Influence Function Matrix, where each element of the matrix gives the influence on pk, of a pair of observations at time lag k. Approximate first four moments for the statistic are derived and by fitting Johnson curves to those theoretical moments, critical points are also produced. The statistic is also used to form the basis of an adjustment procedure to treat outliers or estimate missing values in the time series. Chernick et al's (1982) nuclear power data and the Department of Transport's traffic count data are used for practical illustration

Experiences of maternity care in New South Wales among women with mental health conditions

Background: High quality maternity care is increasingly understood to represent a continuum of care. As well as ensuring a positive experience for mothers and families, integrated maternity care is responsive to mental health needs of mothers. The aim of this paper is to summarize differences in women's experiences of maternity care between women with and without a self-reported mental health condition. Methods: Secondary analyses of a randomized, stratified sample patient experience survey of 4787 women who gave birth in a New South Wales public hospital in 2017. We focused on 64 measures of experiences of antenatal care, hospital care during and following birth and follow up at home. Experiences covered eight dimensions: overall impressions, emotional support, respect for preferences, information, involvement, physical comfort and continuity. Multivariable logistic regression was used to compare experiences of women with and without a self-reported longstanding mental health condition. Results: Compared to women without a condition, women with a longstanding mental health condition (n = 353) reported significantly less positive experiences by eight percentage points on average, with significant differences on 41 out of 64 measures after adjusting for age, education, language, parity, type of birth and region. Disparities were pronounced for key measures of emotional support (discussion of worries and fears, trust in providers), physical comfort (assistance, pain management) and overall impressions of care. Most women with mental health conditions (75% or more) reported positive experiences for measures related to guidelines for maternity care for women with mental illness (discussion of emotional health, healthy behaviours, weight gain). Their experiences were not significantly different from those of women with no reported conditions. Conclusions: Women with a mental health condition had significantly less positive experiences of maternity care across all stages of care compared to women with no condition. However, for some measures, including those related to guidelines for maternity care for women with mental illness, there were highly positive ratings and no significant differences between groups. This suggests disparities in experiences of care for women with mental health conditions are not inevitable. More can be done to improve experiences of maternity care for women with mental health conditions

Detection of Outliers in Time Series.

As part of a SERC funded project this study aims to summarise the most relevant and recent literature with respect to outlier detection for time series and missing value estimation in traffic count data. Many types of transport data are collected over time and are potentlally suited to the application of time series analysis techniques. including accident data, ticket sales and traffic counts. Missing data or outliers in traffic counts can cause problems when analysing the data, for example in order to produce forecasts. At present it seems that little work has been undertaken to assess the merits of alternative methods to treat such data or develop a more analytic approach. Here we intend to review current practices in the transport field and summarise more general time series techniques for handling outlying or missing data. The literature study forms the fist stage of a research project aiming to establish the applicability of time series and other techniques in estimating missing values and outlier detection/replacement in a variety of transport data. Missing data and outliers can occur for a variety of reasons, for example the breakdown of automatic counters. Initial enquiries suggest that methods for patching such data can be crude. Local authorities are to be approached individually usinga short questionnaire enquiry form in order to attempt to ascertain their current practices. Having reviewed current practices the project aims to transfer recently developed methods for dealing with outliers in general time series into a transport context. It is anticipated that comparisons between possible methods could highlight an alternative and more analytical approach to current practices. A description of the main methods ior detecting outliers in time series is given within the first section. In the second section practical applications of Box-Jenkins methods within a transport context are given. current practices for dealing with outlying and missing data within transport are discussed in section three. Recommendations for methods to be used in our current research are followed by the appendices containing most of the mathematical detail

Development of an Influence Statistic for Outlier Detection With Time Series Traffic Data.

As part of a SERC funded project investigating the detection and treatment of outlying time series transport data, the practical applicability of the Influence Statistic described by Watson et al(1991) is assessed here. Missing or outlying data occur in a variety of transport time series such as traflic counts or journey times for many reasons including broken machinery and recording errors. In practice such data is patched largely by subjective opinion or using simple aggregate methods. In the analysis of non-transport time series several methods have been recently developed to both detect and treat outliers, including work by Kohn and Ansley (1986), Hau and Tong (1984) and Bruce and Martin (1989). These methods use either an intervention modelling approach (where the outlier is modelled as part of an ARIMA structure) or look at the influence an observation exerts on a particular parameter associated with the model. An alternative is the Influence Statistic proposed by Watson (1987) and Watson et al (1992) which examines the influence of an observation on the sample autocorrelation function. Initial research showed the statistic has practical application in a transport context, and a replacement procedure based on the method was found to be effective in treating maverick data. Here we report the results from a wider application of the statistic using traffic count data fmm. the Department of Transport. Further developments are suggested and investigated for the replacement procedure and a comparison is made between possible variations in the method

Modelling Outliers and Missing Values in traffic Count Data Using the ARIMA Model.

This paper considers the application of the methodology to traffic count time series in which both missing values and outliers are present. Intervention analysis and detection using large residuals are shown to he reasonably effective but possible problems that result from non- stationarity in the data are identified. It is shown that despite considerable variabilty in the types of series the model selected from the ARIMA family is surprisingly homogeneous

A regional water quality model designed for a range of users and for retrofit and re-use

We discuss the motivations for, and software design concepts underpinning, the development of a regional water quality model. The Environmental Management Support System (EMSS) was developed to predict daily fluxes of runoff, total suspended sediment, total nitrogen and total phosphorous through a large-scale river network. It was built using a custom environmental modelling framework called Tarsier, founded on the Borland C++ Builder rapid application development environment. Three autonomous models are integrated within the EMSS, but are loosely coupled so that alternative models could be retrofitted into the system if desired. The three models share common data handling and visualisation routines resident in the Tarsier modelling environment and used in other modelling applications. The EMSS was designed for use by a range of stakeholders with varying levels of computer and technical proficiency. To satisfy their varying needs, we built three different interfaces, suited to ‘expert’, ‘intermediate’ and ‘basic’ users. The interfaces for the latter two groups were developed using interface prototyping methods, resulting in software that suited the user requirements. The object-oriented design employed in the coding of the EMSS has enhanced the extendibility and re-useability of the software. The EMSS development was part of a larger hydrologic modelling initiative aimed at reducing duplication in model building and standardising approaches to model design and delivery. The lessons learned during development of the EMSS have informed our future model development strategy