For statistical significance it is necessary that the observed test statistic is found in the tail of the distribution generated. As such, in this stage of the analysis the high and low-dimensional models perform best as the observed F-statistics are furthest along each distribution's right tail in relative terms in comparison to the other distributions generated for the constant and monomial based models. These distributions also suggest that a similar level of statistical significance is observed between the high and low-dimensional models, although as this permutation testing was only based on 1,000 permutations, the distributions could still evolve further with a greater number of permutations. However, the constant basis system model is more clearly seen here not to perform as well, with the observed F-statistic closest to the main body of the distribution. This, in combination with the other 'goodness-of-fit' measures, would therefore suggest that the high-dimensional functional linear regression model provides the best basis for a technology substitution classification model from those tested in this analysis.

Conclusions from statistical ranking and functional data analysis

Expanding on previous historical accounts of technological substitutions this study has examined the premise that two principal modes are often observed when considering transitions between successive commercially prevalent technologies: reactive and presumptive technological substitutions. These two modes are believed to correspond to significantly different technology adoption characteristics (not discussed in this paper), with scientific foresight believed to play a crucial role in the identification of presumptive innovations, and performance stagnation leading to reactive transitions. In both cases, technological anomalies are believed to arise, either as a result of scientific or technological crisis, that subsequently trigger the eventual shift to the next technological paradigm. As such, this paper has considered 23 example technologies where literature evidence of performance development trends has been found in order to test the ability to correctly identify associated adoption modes using bibliometric, pattern recognition, and statistical analysis techniques. The results obtained from this analysis suggest that statistical analysis of patent indicator time series, segmented based on identified Technology Life Cycle features, provides a possible means for classification of technological substitutions. Specifically, for the datasets considered measures of the number of cited references and the involvement of non-corporate entities by year during the emergence phase were found to provide a good indication of the expected mode of substitution when used as a basis for functional linear regression (correctly classifying 19 out of 20 technologies included in this stage), and performed consistently well in statistical ranking of predictive capability. These selected patent data dimensions can be associated with perceptions of scientific and technological production respectively, consistent with the basic prerequisites listed in section \ref{585124} for a classification scheme that can identify presumptive technological substitutions. Whilst these two patent dimensions occur in all of the most robust predictor subsets (i.e. in terms of out-of-sample reliability) when basing analysis on the emergence stage, this does not prove that these are the only indicators capable of predicting modes of technological substitution. As discussed in section \ref{311620}, the possibility of orthogonality has not been ruled out with regards to the other patent indicators shown in Table \ref{table:bibliometric_indicators}. However, these two dimensions are in good agreement with the technological anomaly arguments put forward by Constant in sections \ref{646617} and \ref{585124}, and so were felt to be reasonable for forming the basis of the technology classification model that has been developed using functional linear regression. In particular, a regression fit made up of beta coefficient functions with many B-spline elements was found to provide a viable means of correctly matching the mode of substitution to the technology profile being evaluated when considering multiple 'goodness of fit' measures. Permutation testing of the derived technology classification model further suggests that the regression fit is sensitive to the ordering of the expected mode labels relative to the technology time series being considered, so this relationship would appear to be based on the specifics of the individual technology curves considered, and does not appear to be occurring by chance. This implies that it is possible to predict modes of substitution from limited bibliometric data during the earliest stages of technology development, providing some evaluation of the progress through the early stages of Technology Life Cycle is made (this can be obtained using a nearest neighbour matching process, not discussed in this paper). Equally this shows that the functional data approach employed corroborates well the earlier statistical rankings produced using Dynamic Time Warping, K-Medoids clustering, and leave-one-out cross-validation of the selected patent indicators, suggesting that these two methods are compatible for this type of analysis.
It is also important to remember the potential limitations of this study that would need to be addressed for further confidence in the methodology used. Firstly, only a relatively small number of technologies have been evaluated in this study due to the time-consuming process required for data extraction, preparation, and identification of supporting evidence from literature for the assignment of expected classification labels. Consequently, whilst precautions have been taken to minimise the risk of model over-fitting, the cross-validation procedures employed would benefit from further verification with a more diverse spread of technologies to ensure that out-of-sample errors are accurately captured here. Regression models based on small sample sizes can be very fickle to the datasets they are calibrated to, so it cannot be ruled out that the results presented here are a better fit to the industries included in this analysis, rather than a model that can be necessarily generalised to all technologies. However, perhaps the most important note of caution regarding this work relates to the quantitative approaches used here. Whilst statistical approaches are well-suited to detecting underlying correlations in historical and experimental datasets, this on it's own does not provide a detailed understanding of the causation behind associated events, particularly in this case when considering the breadth of reasons for technological stagnations, 'failures', or presumptive leaps to occur. Equally, statistical methods are not generally well suited to predicting disruptive events and complex interactions, with other simulation techniques such as System Dynamics and Agent Based Modelling performing better in these areas. Accordingly, to identify causation effects and test the sensitivity of technological substitution patterns to variability arising from real-world socio-technical behaviours not captured in simple bibliometric indicators (such as the influence of competition, organisational, and economic effects), the fitted regression model presented here also needs to be evaluated in a causal environment. Similarly, in order to demonstrate practical applicability the mode of substitutions considered here need to be related to observed adoption characteristics (not discussed in this paper). Consequently, a System Dynamics model built on the regression functions identified in this study is proposed (although not discussed here) in order to calibrate these extracted technology profiles and mode predictions to empirical adoption data. This aims to more thoroughly explore the causal mechanisms relating early indicators of technological substitution to the eventual adoption patterns observed and provide a means of applying greater reasoning to the relationships identified here.