Generalised Linear mixed models

Standard statistical analysis methods, such as analysis of variance (ANOVA) and multiple regression do not take into account repeated measurements from the same sta- tistical units which is a characteristic in most of the datasets of this thesis. In addition, linear regression analyses can deal with large data sets but do not allow the construction of a model that specifies interactions between the fixed and random effects.

To address this, several Generalised Linear Mixed Model (GLMM) analyses were performed on the collected aggregated datasets to analyse relationships between audience responses in different parts of the performance, differences in their hand behaviour as well as to compare survey responses with aggregated time series data. For each case the distribution that was appropriate to the data was used.

Numerous studies have adopted GLMMs for the analysis of continuous and subjective human measurements (Solberg et al.; Katevas et al., 2015). GLMMs estimate the rela- tionship between a dependent variable and associated covariates by taking into account both fixed and random effects. They also allow for missing data points for subjects, which was the case with some of the data-sets in this study. They are used to model the combined random effects, categorical and interval fixed effects and repeated measures involved in the audience responses obtained.

In this thesis, we illustrate mixed-effects modelling with R using the lme4 package (Bates et al., 2015; Bates, 2007) that offers fast and reliable algorithms for parameter estimation. However, the lme4 package provides many ways for evaluating the signifi- cance of fixed effects of the GLMM (Luke, 2017). The reason for this is that in linear mixed models applied in an unbalanced dataset it is not obvious what the appropriate denominator degrees of freedom to use are. In this thesis a likelihood ratio test (LRT) was used to compare two different models to determine if one is a better fit to the data than the other. In a GLMM, LRTs are used to decide if a particular fixed or random effect should be retained in the model by evaluating whether that effect improves the fit of the model. According to Luke (2017) among other methods LRT is one of the most common methods used for evaluating significance.

3.7

Summary

Overall, this chapter presented some example studies that explore audience be- havioural responses during live events. Most of these studies explore audiences in non- naturalistic environments or using post-performance methods while only a few of them manage to record audience responses using both a naturalistic method and a satisfied sample size. As a result, many basic questions about audience engagement, the dynamics of collective and individual responses during a live event and the ways in which these responses are captured and transmitted remain unanswered. In addition a summary of the methods used for data collection is presented as well as a brief description of the statistical analysis techniques we followed to analyse the data. In the following chap- ters, we show how this methodological approach was adopted to study the audience and dancers responses in three empirical studies (Chapter 4, 5, and 6). Chapter 7 provides a detailed assessment and discussion of the results of those three studies.

Chapter 4

Audience responses part I:

Recognising audience overt

responses

4.1

Introduction

This chapter presents the first exploratory study of this thesis, which was designed to investigate the behavioural responses of a live audience during a contemporary dance performance. Exploratory studies provide means of revealing previously unimagined connections and causal mechanisms; and are well suited to cases where little is known about the area of interest (Reiter, 2013).

The study took place at the Theatre Royal in Glasgow, where the contemporary dance performance "Frames" made its world premier. "Frames" was one of the three dance performances that the Rambert Company presented in Glasgow, over a period of 3 days, on the 5th, 6th and 7th of March 2015. Informed by the methods and techniques discussed in the previous chapter, continuous quantitative measures were extracted from recordings of the audiences and the dancers during the three days of the performances. In this chapter, the data collected during the first performance, on the 5th of March was analysed. A detailed description of the methodological approach, as well as a broad analysis of the data are undertaken here, and the findings are reported below.

4.2

"Frames" - A contemporary dance performance by

Alexander Whitley

"Frames" (see figure 4.1) is a contemporary dance performance that presents the Rambert dance company in a choreography directed by Alexander Whitley in collabo- ration with the artists Revital Cohen and Tuur Van Balen and with music made by the

composer Daniel Bjarnason. It is 37 minutes in duration and has a cast of 12 dancers. The piece incorporates movement, visual setting elements (lighting, set-design etc) and aural elements (live music). The concept of the piece is broadly related to the notion of production, focusing on the manufacturing of objects as well as the manufacturing of experiences in the context of the theatre and how people - in this case dancers - can organise such processes (Whitley, 2015). "Frames" explores these ideas by using the theatre as a microcosm for these processes to unfold. In his interview at the DanceTabs magazine Whitley said

"I’ve been interested for a long time in the connection between choreogra- phy and industrial manufacturing in terms of how people’s movements are coordinated and synchronised, and to a large extent habituated by repetitive processes. I was fascinated to learn, for example, that Rudolf Laban worked with industrialists in the mid-20th _{Century to try and improve efficiency in}

factories by applying his principles of movement from dance" (DanceTabs, 2015).

On stage, dancers construct different shapes using metal structures (frames) and portable light objects. As the choreography and the metal structures emerge, different images come to life that create a stage within a stage.

The performance begins with a short section in which one of the dancers organises the stage by placing the metal structures and the light objects in various locations to be ready for the dancers to pick them up during the performance. For the sake of the data analysis, this section will be called "pre-performance". The performance starts with a solo accompanied by music. At the end of the solo, the other 11 dancers come on stage and with some choreographed movements start to arrange the metal frames around the stage. During the performance, the dancers use the frames to build up different shapes controlling them with their bodies and in collaboration with the other dancers. The performance ends with the frames hanging from the ceiling and the dancers performing a final choreography accompanied by intense music.

"Frames" had its world premiere at the Theatre Royal Glasgow on the 5th of March 2015, followed by presentations in Inverness and Brighton, with a final performance at Sadler’s Wells in London.

The Theatre Royal (see figure 4.2) is the oldest theatre in Glasgow, it opened in 1867, and it is considered the home of the Scottish opera and ballet. Today, it is operated by the Ambassador Theatre Group. It has an old style architectural character with a big stage and can accommodate up to 3000 people.

Figure 4.1: "Frames", a contemporary dance performance directed by Alexander Whitley