1 Introduction
I first met Harvey on what was probably an important day for him for very different reasons. For me, it was the exciting trip of my first visit to the Royal Statistical Society headquarters at Errol Street on the 15th November 1995 as I had just started on my PhD studies with David Draper in Bath. The main event was of course the reading of Harvey and David Spiegelhalter's seminal paper on League Tables (Goldstein and Spiegelhalter, 1996). The whole day was really inspirational for me as a young student, meeting two superstar statisticians who would influence my career and seeing how statistics can make a difference to the world in general. In fact at the time, I knew more of the work of David Speigelhalter than Harvey having used his team's BUGS software in my Masters project. However, David Draper introduced me to Harvey and as Harvey was beginning to see uses for Monte Carlo Markov chain (MCMC) methods, it was agreed that we would all work together developing software as a side project to my PhD. I was supplied with a 200 MHz PC for my office in Bath (complete with security cage to prevent the theft of the processor) and the start of a 25-year working relationship began.
2 Harvey’s Inspirational Work
At this stage, I discovered how important Harvey's work was already to the field of multilevel modelling (a term I suspect he invented) as I began my literature review for my thesis. Harvey's initial forays into modelling realistically complex data structures began with his work at ICH on longitudinal growth curve models for child growth. Harvey's interest in models that captured aspects of child development, however, extended beyond the physical measures of growth to academic development, and in 1977, he moved to the Institute of Education (IoE) in London as a Professor of Statistical Methods. This was an important career move for Harvey as he was then to work at the Institute until his (first) retirement in 2005.
It was at the Institute that he began to work more on social statistics with a particular focus on educational assessment and school effectiveness and this in turn led to his interest in multilevel modelling. When considering educational data, there exist natural hierarchies to the data, for example students are nested within classrooms within schools and therefore as such the data is collected at multiple levels. These hierarchies remove the independence of the data which is a key assumption for regression type models and Harvey's seminal work would be in developing classical statistical methods to fit models that thus controlled for the complex data structure. He first developed the iterative generalised least squares or IGLS algorithm in 1986 (Goldstein, 1986) and then extended it to a restricted form (RIGLS) that removed biases in variance estimation (Goldstein, 1989).
3 The Centre for Multilevel Modelling (CMM) Team in London
One of Harvey's key strengths as an academic was that he realised that writing academic papers (of which he wrote more than 370) was only part of the story and particular within methodology research it was really important to not only devise the methods but also get them to the applied researchers who would use them. Harvey was always interested in programming and software development as is evidenced by his later work on the REALCOM package that he coded himself. A key academic partnership developed in the late 1980s when Jon Rasbash joined Harvey at the IoE. Jon had been working with Michael Healy at the London School of Hygiene and Tropical Medicine and was an excellent programmer. Between them Jon and Harvey developed a series of (at the time DOS-based) computer programs to fit more and more advanced multilevel models. ML2 was developed in 1988 and fitted 2 level models, followed by ML3 in 1990 for 3 level models and then finally MLN in 1995 in the same year as the RSS meeting mentioned in the introduction.
It was about this time that Windows-based software became much more prevalent and so the MLwiN software package was developed and first appeared in 1998 (Rasbash et al., 1998). Harvey's methodological work with a little help from Jon's programming was now available to a large user base and it would be hard to imagine at the time that today MLwiN would end up with thousands of users worldwide but sadly would out live both Jon and Harvey.
Back in the late 1990s, however, through his research grant capture skills Harvey had built an excellent research team of Jon Rasbash, Min Yang and Huiqi Pan, with administrative support for the software sales from Amy Burch and Lisa, that I was fortunate to join in 1998. In the wider IoE group were Fiona Steele, Ian Plewis, Geoff Woodhouse and Sally Thomas, and Chris Charlton who ultimately took over the programming of MLwiN worked as a summer student.
For me, this was a hugely formative time as a young researcher. Harvey was a hugely supportive boss, an excellent sounding board for ideas and there was almost a family atmosphere to the team which extended to an impressive group of CMM fellows (including Alastair Leyland, Nigel Rice, Tony Fielding, Toby Lewis, Dougal Hutchinson, James Carpenter and Ian Langford) who would come to London for monthly meetings and our annual summer croquet away day (see Figure 1). It was a testament to the breadth of Harvey's work that each of these fellows was working on a project alongside Harvey so that Harvey's influence stretched to topics such as spatial modelling, endogeneity, measurement error adjustment and dealing with missing data.
Photo of the Centre for Multilevel Modelling team from the annual summer croquet game. As was often the case, Harvey was the photographer and so is not in the photo.
The centre had begun in the late 1980s and Harvey and Jon had made many further methodology advances including key papers that elegantly extended the IGLS algorithm to fit more complex data structures (Rasbash & Goldstein, 1994) and different types of response variable (Goldstein & Rasbash, 1996). Harvey worked with Min Yang on multilevel extensions to meta-analysis (Goldstein, Yang, et al., 2000; Turner et al., 2000) and repeated binary outcomes (Yang et al., 2000) among other topics and with Huiqi Pan on longitudinal growth models (Pan & Goldstein, 1997).
Having met Harvey in 1995, I continued on my PhD in Bath doing work that involved comparing the classical approaches Harvey developed with Bayesian MCMC approaches using BUGS. We latterly incorporated an MCMC engine that I had written into the MLwiN software for its release in 1998 via a few very intensive visits to London to work with Jon Rasbash to plumb in the code and this was my route to become a postdoc in the centre from 1998. In fact my first work with Harvey (and Jon and David Draper) was in fact from my PhD thesis looking at MCMC algorithms for dealing with complex level 1 variation, that is when the amount of variability within clusters depends on predictor variables (Browne et al., 2002).
Harvey was a kind and encouraging collaborator and a much more prolific writer than me and so I was fortunate to work with him on many extensions to multilevel models particularly in using MCMC methods. These included extensions to dynamic household structures with a group of collaborators from Belgium (Goldstein, Rasbash, et al., 2000). We looked at adjusting for measurement errors (Browne, Goldstein, Woodhouse et al., 2001) which Harvey had tackled using classical methods with Geoff Woodhouse (Woodhouse et al., 1996). Following Harvey's work with Jon Rasbash on multiple membership models, we extended this to a general framework that we named multiple membership multiple classification models (Browne, Goldstein, Rasbash, 2001). We also considered multilevel models use with medical data (Goldstein et al., 2002a) and to multivariate responses and exam results (Yang et al., 2002).
Along with Jon Rasbash we developed the concept of the variance partition coefficient or VPC (Goldstein et al., 2002b) that showed which level in the data had the most influence on a response for both continuous and binary responses. This work was later extended to cases of models with overdispersion (Browne et al., 2005) and to count data (Leckie et al., 2020). Harvey worked more widely applying multilevel modelling to other application areas with colleagues at the IoE including with Fiona Steele on extensions to event history models (Steele et al., 2004) and Peter Blatchford on class size effects (Blatchford et al., 2002).
Alongside his multilevel modelling methodological work, Harvey continued to produce lots of more applied work in education. Towards the end of my time in London Harvey was also becoming interested in the challenges that working with real ‘messy’ data presented. He began work on missing data with collaborations with Mike Kenward, James Carpenter and others, and on how different data sources can be linked together with Katie Harron and other collaborators at both the ICH and Bristol.
4 Reunited in Bristol
I left London in 2003 to move to Nottingham but continued to work with Harvey and Jon. Harvey then retired (for the first time) from the IoE in 2005 and at the time Jon Rasbash moved along with the centre to the University of Bristol. Fiona Steele followed soon after and CMM was re-established as a research power house within Bristol with researchers spanning several faculties including Kelvyn Jones in Geography and myself in Vet Science at the time. Harvey continued to work 1 week a month in Bristol establishing new collaborations with Liz Washbrook, Richard Parker, Daphne Kounali, Rebecca Pullinger, Edmond Ng, Lucy Prior, Kate Tilling, Andy Boyd and Paul Burton. He did not slow down and had written close to a further 100 journal articles between his retirement from the Institute and his death.
For me, the pull of the chance to work more closely again with Harvey was a major factor in my own move to Bristol in 2007 and I was fortunate to continue our collaboration during his monthly visits. We extended our joint writing to MCMC work on dealing with scenarios where there is non-independence of residuals in a multilevel model both within and between clusters (Browne & Goldstein, 2010), missing data modelling with James Carpenter for many different response types (Goldstein et al., 2014), misclassification errors in models fitted to higher education data (Goldstein, Browne, et al., 2018) and applications of extensions of multilevel models to aspects of growth curve modelling (Goldstein, Leckie, et al., 2018).
Harvey was always so easy to discuss research ideas with and I miss our lively methodological debates tremendously. Outside of work we were also great friends and Harvey was always so kind to me and my family. The fact that Harvey came to Bristol for a week at a time meant that there were many opportunities for him to come out for dinner with the family in Wrington where we are based. I have fond memories of Harvey tutoring my eldest daughter on her flute or playing whatever games my daughters had dreamt up. Equally I will always be grateful for the hospitality that Harvey and Barbara supplied when I visited London and needed somewhere to stay. Harvey has a huge legacy which his many younger collaborators will hopefully build on for years to come. We were so lucky that a meeting was arranged for Harvey's 80th birthday celebrations in 2019 as it was so much better to be able to let him know how great we all thought he and his work was but hopefully in writing these words in a journal article we will bring the huge breadth of his work to a wider audience.
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