Análisis de un caso concreto: Marina Cope

As previously mentioned, many authors criticise the lack of a global validation measure in PLSPM (Dijkstra and Henseler, 2015; Henseler and Sarstedt, 2013; Sharma et al., 2015). In addition to this gap, there is another topic that is driving a large production of scientific research: the assessment of predictive power in PLSPM.

Analysing historical scientific works related to PLSPM and its adoptions in business research, it is possible to see that its use resemble a descrip- tive approach where explanation and exploration are key. This usage is slightly contradictory to the PLSPM nature, which can be summarised as a non-parametric estimation procedure that is “slated” to be predictive (Hair et al., 2011). Also, Evermann and Tate(2014) note that “Herman Wold, who originally developed PLSPM, clearly and explicitly positioned it as a method for prediction (Dijkstra, 1983, 2010; Wold, 1982c)”.

Shmueli et al. (2016) stated that, so far, PLSPM literature has not made a full use of these predictive proprieties, using instead an explanatory ap- proach focussed on statistical significance and power (Becker et al.,2013).

Shmueli and Koppius (2010, 2011) reinforced the previous statements saying that quantitative research in management has been dominated by causal-explanatory statistical modelling at the expense of predictive modelling.

In the last five years the PLSPM community has shown an increasing interest in exploiting the predictive nature of PLSPM and recognising the insufficiency of considering only its theoretical validity as a statis- tical model fit; it is fundamental to assess its predictive performance

(Armstrong, 2012; Woodside, 2013).

Additionally, as stated by Gregor (2006), explanation and prediction are the two main purposes of theories and statistical methods.

In every statistical application, explanation is primarily concerned with testing the faithful representation of causal mechanisms by the statistical model and making valid inferences to population parameters. In contrast, prediction is synthesised as the ability to predict values for individual cases based on a statistical model whose parameters have been estimated from a suitable training sample (Evermann and Tate, 2016).

Shmueli and Koppius (2010, 2011) believe that emphasising predictive approaches on existing and new data sources can generate fresh insights for business practitioners and driving new theoretical hypothesis to be studied from a business and management research perspective.

When the focus is pointed at building a predictive model, the objective is to retrieve a predictive function (classification or regression, Hastie et al.

(2009)) that can be applied to new observations. With that in mind, one of the most important elements to consider is making sure that the predictive function is generalisable.

Sharma et al. (2015) identify several types of generalisations:

– Statistical Generalisation: where the model estimated from the sample generalises to the population from which the sample was drawn;

– Scientific Generalisation: where the model estimated from the sample generalises to other populations (e.g., to other contexts); – Predictive Generalisation: where the model estimated from the

sample provides sufficiently accurate predictions for new records from that population (out-of-sample prediction).

Focussing on predictive generalisation, Shmueli et al. (2016) proposed a framework based on three dimension where the prediction measures in PLSPM can be defined: (i) Construct-Level versus Item-Level; (ii) In- Sample versus Out-of-Sample; and (iii) Average Case versus Case-wise. Changing slightly the design proposed by the authors, this framework is summarised in figure 1.8.

Figure 1.8: A Prediction Framework for PLSPM Assessment Measures

From the eight available types of predictions presented in figure 1.8, only two allow for evaluating predictive performance in the sense of the aforementioned predictive generalisation: (Item-Level, Out-of-Sample, Case-wise) and (Item-Level, Out-of-Sample, Average Case).

Shmueli et al. (2016) also present a deep analysis on the existing ap- proaches highlighting their main limitations and some of the available opportunities. The authors reinforced that R2 in PLSPM allows to assess the in-sample predictability (or fit) of endogenous average case composite scores and it is not concerned with each of the other seven prediction options presented in figure 1.8. In order to assess the pre- dictive power, Becker et al. (2013) defined and used an “out-of-sample R2” which is based on case-wise, out-of-sample predictions of the en- dogenous composites scores. Shmueli et al. (2016) also commented on the Q2 and on the Operative Prediction Approach proposed by Ever- mann and Tate (2014): the first only concerns with an aggregate sense of predictability of a dataset, rather than gauging the predictability of particular cases and it is also considered, together with the q2, as ad-hoc metrics that do not provide highly interpretable results in terms of error magnitude; the second (Operative Prediction Approach) is classified as a case-wise, out-of-sample technique that produces operative predictions at item-level. Shmueli et al. (2016) find that this approach still presents several challenges to overcome before being considered as a truly useful and informative predictive evaluation for PLSPM.

Shmueli et al.(2016) presented a new procedure for evaluating predictive performance for PLSPM model with the aim of diagnosing whether the PLSPM model is overfitting the training data. The approach proposed by the authors generates item-level case-wise and average case predictions for both out-of-sample and in-sample cases. The out-of-sample allows assessing predictive performance on new data and its comparison with the in-sample results allows to assess the aforementioned issue related to

the overfitting of the training data.

The last years highlighted some insufficiency related to the assessment measures present in the PLSPM literature. These limitations open a whole new set of opportunities related to the predictive assessment of PLSPM. These steps towards prediction-driven PLSPM applications and the formalisation of a predictive assessment framework are widening the possibilities associated to the use of PLSPM and reducing the gap be- tween PLSPM and the predictive analysis world.