Analytical model: Generalised linear mixed model

Once I had decided how to code the video material and how to document the data, I approached a statistician and statistically adept researchers to get advice regarding the statistical analysis that would be most suited to my research questions and my data set. The analysis of music therapy session videos was supposed to answer my research subquestions 2-4, as outlined in the introductory chapter, which are:

- Do music therapy sessions increase behaviours indicative of resilience in young children with ASD?

- Does different treatment intensity result in different increase or decrease in behaviours indicative of resilience?

- Does verbal ability of children influence increase or decrease in behaviours indicative of resilience?

Therefore, the statistical analysis needed to provide answers to the following three questions:

1) Does the relative frequency of each target behaviour change over the course of the 20-week therapy?

2) Does the relative frequency of each target behaviour differ between children receiving low- and high-intensity therapy?

3) Does the relative frequency of each target behaviour differ between verbal and non- verbal children?

I decided to use a generalised linear mixed model (GLMM; McCullagh & Nelder, 1989). GLMMs are extensions of the more traditional statistical techniques, such as ANOVA or regression, and provide more flexibility regarding the data and designs that can be studied. GLMMs ‘enhance our options to gain insight into what our data reveal’ (Mundry, 2017). As far as I have been able to find out, GLMMs have not been used by music therapists. However, in other research fields relevant to music therapy, such as medicine (e.g. Yarkiner, Hunter, O’Neil, & de Lusignan, 2013), psychology (e.g. Andersen et al., 2016), and occupational therapy (e.g. Piek et al., 2015), GLMMs are already used more routinely. GLMMs are especially suited to analyse longitudinal data and ‘this methodological approach is a useful and appropriate mechanism for investigating dynamic relationships within health- related data’ (Yarkiner et al., 2013, p. 1). I chose GLMM because it allowed me to investigate all three questions in a single analysis. This was very important, because the ability to model all three effects at the same time meant that I could use the entire data set. There was no need to split the data set, which would have caused loss of information and power. A GLMM enabled me to combine the continuous and categorical predictor variables into one analysis. Furthermore, the model provided the possibility to model non-linear effects.

Linear models in general model a single response as a function of predictor variables. The response variables in this study are the pre-determined target behaviours. Each behaviour was expressed as a proportion of observations in which the behaviour was present relative to the session-excerpt length. Table 4 lists the eleven different response variables (target behaviours), specifies the individual coding variables that comprise each response variable, and names the protective factors which the response variables represent. The relative frequency of behaviour was modelled as a function of three predictor variables that were determined by the three questions listed above. The predictor variables were:

1) Session number 2) Therapy intensity 3) Verbal ability

Session number is a continuous, quantitative predictor variable which was coded from one to 20. It is unlikely that the responses to session number are always linear. Children do not usually respond to more therapy sessions with a linear improvement in a specific behaviour. They often develop in a more irregular way with sudden improvements, slow progress, and plateaus in their developments all being observable at different times with different children. To account for this in the model, I also included ‘session number2_{’ as a predictor variable.}

Anticipated effects of the predictor variable ‘session number’ on each response variable, and explanations for the anticipated effects, can be found in Table 4. Both ‘therapy intensity’ and ‘verbal ability’ are categorical predictor variables, with the factor low/high and the factor yes/no, respectively. No separate tables were designed for the predictor variables ‘therapy intensity’ and ‘verbal ability’ because the anticipated effect of these categorical predictors on all response variables was likely to differ and thus determined ‘not consistent’.

Table 4: Anticipated effects of predictor ‘session number’ on response variables Response variable Composed of codes Representing protective factors Anticipated effect Explanation

Play total Play, Asst- Play Ability to express emotions Goal-directed behaviour Self-efficacy Not consistent

Different aims for children. While some children were encouraged to play more, others who might have masked anxiety by frantic playing were helped to relax and listen. Vocal Vocal Ability to

express emotions Goal-directed behaviour Self-efficacy

Positive Children were encouraged to use their voice more often to express themselves and to communicate.

Move Move Ability to

express emotions Goal-directed behaviour Self-efficacy Not

consistent Different aims for children. While some children were encouraged to move more, others who might have been hyperactive were helped to relax and control their movements. Expression Play, Asst-

Play, Talk, Vocal, Move, Object Ability to express emotions Goal-directed behaviour Self-efficacy

Positive Children were encouraged to express themselves.

Response variable Composed of codes Representing protective factors Anticipated effect Explanation

Smile Smile Ability to express emotions Reaching out to others

Positive I hypothesised that children developed a positive relationship with the therapist and enjoyed music making and

interacting more. Look total Look, Look-

TA

Awareness of others

Reaching out to others

Positive I hypothesised that children developed a greater interest in the therapist and TA and in communicating with them. Initiate Initiate Goal-directed

behaviour Self-efficacy Reaching out to others

Positive I hypothesised that children gained

confidence and initiated new ideas more often.

Respond Respond Awareness of others

Reaching out to others

Positive I hypothesised that children developed more awareness of the therapist and were more likely to respond to her.

Engaged Engaged Goal-directed behaviour

Positive I hypothesised that children developed more interest in mutual activities and were more able to focus in interactions for longer.

Contact total Contact, Contact-TA Ability to regulate emotions Reaching out to others Not consistent

Different reasons for initiating physical contact. While some children expressed their trust or affection with hugs or taking the therapist’s hand, others sought physical closeness when they were anxious. Difficulty Fidget, Anxiety Ability to regulate emotions Impulse control

Negative Children were helped to channel repetitive behaviour into more expressive and

communicative behaviour, and to find more

appropriate ways to regulate emotions. I hypothesised that children felt more comfortable and less anxious.

For each of the eleven target behaviours I fitted a separate GLMM with the proportion of the target behaviour as a response. Depending on the characteristics of the variable, Gaussian error distribution with identity link function or beta probability distribution were used (see 5.2.2.1 for a detailed description of this process). I included the three predictors ‘session number’, ‘therapy type’, and ‘verbal ability’ as test predictors (Mundry, 2014) into the model. With a GLMM I was able to control for the fact that there are differences between individuals. Children are likely to differ in their response to the therapy and to account for this in the research model, I needed to include child-ID as a random effect. Specifically, I modelled individual differences by including random intercept and random slope:

1) Children are likely to start at different levels, for example the proportion of playing instruments or the proportion of initiating interactions at baseline varies from child to child. To account for this in the research model, I needed to include a random intercept for each child.

2) Children are likely to differ in how they respond to the treatment, for example some might show strong and others weak changes, or they might show an increase or a decrease in the display of certain behaviours. To account for this in the GLMM, I needed to include a random slope for ‘session number’ and for ‘session number2_{’ in}

child-ID (Barr, Levy, Scheepers, & Tily, 2013; Schielzeth & Forstmeier, 2009). I included individual child-ID as a random effect, consisting of random intercept and random slope. Thereby I controlled for the non-independence of data points from each child. As my data set included repeated observations of the same children (longitudinal data), it was obligatory to account for this. Including child-ID as a random effect meant that I looked at changes and progress made by individual children and related that back to their starting point rather than expecting all children to reach a certain developmental outcome. My research question focuses on the within-subjects predictor. The random effect controls for variation between children with regard to their average response. Ignoring this effect may lead to power loss and erroneously non-significant findings (Mundry, 2017). The model included random intercepts (difference of individual starting points), random slopes (difference in individual response to music therapy treatment), and the interaction between both. The full model was:

Proportion of behaviour ~ session number + session number2 _{+ therapy intensity + verbal}

ability + (1 + session number + session number2 _{| child-ID).}

All the analyses were implemented in R version 3.5.0 (R Core Team, 2018). Although most quantitative research studies in music therapy have used SPSS, I chose R because it allows the researcher to process, analyse and plot the data using only one software programme. R is free and open-source, which means that its functions are transparent, and that researchers are able to always use R independently of what their institutions might provide.

To learn and use R, I received guidance from a team of statisticians and researchers based at the Max Planck Institute for Evolutionary Anthropology in Leipzig, as they have ample experience with R. The full R script including codes for data cleansing, model implementation and data plotting is added to this thesis (Appendix 4.7.1.3). All models were fitted with the R function ‘lmer’ of the R package ‘lme4’ version 1.1-11 (Bates, Mächler, Bolker, & Walker, 2015). I carried out all the tests needed in rigorous quantitative research. To test the significance of the fixed effects as a whole, I compared the fit of the full model with that of a null model lacking all test predictors but comprising the same random-effects structure as the full model (Forstmeier & Schielzeth, 2011) using a likelihood ratio test (Dobson & Barnett, 2008). Model stability was assessed by comparing the estimates of the model based on all the data, compared to models based on data excluding children one at a time. The model was stable regarding the effects of all significant predictors.