Functional model building process
The ranking of different bibliometric indicator subsets provides a means to identify the time series dimensions that, when combined, are most likely to provide robust out-of-sample predictions of the observed technological modes of substitution. As a result, a technology classification model is now developed using functional data analysis (see sections \ref{419943} and \ref{805423}) that is based on indicators 4 and 6 (i.e. the number of non-corporates and the number of cited references by priority year). Besides being present in all of the highest scoring sets of top ranked predictors, these particular dimensions can potentially be associated with the rate of development in technology and science respectively. This is in the sense that cited references shows a clear link to scientific production directly influencing technological development efforts, whilst the number of non-corporates by priority year (which counts the number of universities, academies, non-profit labs and technology research centres) is associated with the amount of lab work required to commercialise a technology. Considering the measure of non-corporates by priority year specifically, a large volume of lab work could indicate a lack of technological maturity, or the presence of considerable complexity in the technology being developed. By contrast, those technologies with reduced non-corporates by priority year activity may represent simpler technologies that mature more rapidly or intuitively. Non-corporates by priority year could therefore equate to a measure of technological complexity, or effort required to mature.
However, it's also worth noting that there are other indicator subset couples/triples that perform nearly as well. It is possible that these other high-performing subsets may be in some way related to the chosen indicators (i.e. perfect orthogonality can not necessarily be assumed between these metrics), and so at this point the choice has been taken to use the indicators specified as these have been seen to be the most statistically robust, whilst also being in good agreement with previous literature conclusions.
Following on from the initial introduction to functional data analysis provided in section \ref{419943}, and more detailed methods presented in \cite{Ramsay_2009}, the method outlined in Fig. \ref{529107} has been implemented in MATLAB for building a functional linear regression model for the purposes of technology classification (the MATLAB script is available in Appendix XX for further details).