Preguntes obertes i tancades de Berganza i Ruiz (2005: 191)

The process of model calibration seeks to set model parameters in such a way that the model is able to reproduce existing consumer behaviour to an acceptable level of accuracy. If observed behaviour can be consistently replicated by the calibrated model, the model can be used in a predictive capacity; for example to consider the impact of new store openings with confidence. To calibrate, some form of observed flow data is required and this can be used to assign values to parameters such that the model outputs minimise the difference between observed and predicted flows. In practice calibration involves setting model parameters to optimize one or more conditions that are thought to be representative of flow patterns, in this case average trip distance (ATD) outlined in section 6.5.2. Since the model is non-linear in nature, application of ‘standard’ techniques, such as regression, to estimate model parameters is not possible (Wilson, 1971). Measures of goodness-of-fit (GOF) are then used to validate and test the degree of statistical fit between the observed and predicted data. This section first considers the required data for calibration and validation (see Fotheringham and Knudsen, 1987; Knudsen and Fotheringham, 1986; and Openshaw, 1975 for more detail).

6.5.1 Data for calibration

Effective calibration is dependent upon the availability of sufficient observed customer flow data. Obtaining observed flow data can be tricky and inevitably involves generalising from a sample of customers which, at best, tends to represent one retailer’s clients rather than the entire market. This thesis greatly benefits from access to data derived from Sainsbury’s Nectar loyalty card, which is a useful tool for model calibration. The calibration data has been derived from individual transaction level records for all transactions involving a loyalty card in the four study stores of interest (see Chapter 4 for more detail on the loyalty card dataset). Sainsbury’s own in house analysis, based on their knowledge of market penetration and Nectar card uptake, has generalised these recorded Nectar flows which are used to estimate their store revenue derived from each OA. This data effectively represents the flow of consumer expenditure from each OA to each store. It is these flows that have been used as observed flows for model calibration (aggregated to LSOA level to reduce the effect of very low flows from some OAs), and it is from these flows that observed ATD has been calculated.

The great benefit that this consumer level data brings to the thesis, and in particular for calibration, has been noted throughout. It should be recognised, however, that there may be some bias introduced by assuming that all flows in the model, including flows to other retailers, can be calibrated with reference to data from one retailer. As noted in section 6.3, it is recognised that flows will be driven by the relative attractiveness of different brands,

which is not captured within the Sainsbury’s data. The use of the alpha parameter here, which has been set entirely independently with reference to consumers’ stated behaviour in the Acxiom ROP, should go some way to account for this brand preference.

Since this study does not have access to any form of reliable surveyed data for consumer brand preference in Cornwall, attempts have not been made to calibrate the model through variation within the alpha parameter (although some experimentation was undertaken in order to determine the appropriate magnitude for the alpha value). Any attempt to fit the alpha values to the Cornwall flow data (which is limited to one retailer and four stores) would represent too much of an attempt to fit the model to the observed data, which Birkin et al. (2010a) term ‘over-paramatization’. It would be all-to-easy to artificially alter the alpha values such that the model exactly replicated the observed Sainsbury’s flows for the study stores, but with absolutely no regard for actual consumer behaviour. Nonetheless, the impact of incorporating brand attractiveness has been assessed and is addressed in section 6.5.2. Calibration of will take place with reference to the average trip distance and validated using selected GOF statistics. The model’s overall performance will then be considered in terms of its ability to replicate observed store revenue (section 6.7).

6.5.2 Model calibration using average trip distance (ATD)

The distance deterrence parameter ( ) allows predicted consumer flows to be controlled, determining the importance of distance/travel ‘cost’ in consumer decision making behaviour. Birkin et al. (2010a) identify that calibration of is traditionally undertaken by comparing observed and predicted ATD. Batty and Mackie (1972) assert that this is the most appropriate calibration statistic to use for a SIM which employs an exponential distance function. The premise is simple: if the model can replicate observed consumer trip making characteristics (such as the average distance travelled or other travel ‘cost’) then it is likely to estimate the spatial patterns of trade (or store catchment area) effectively. Assuming that demand estimates are reasonable, and that the model has an appropriate representation of store attractiveness, actual expenditure flows to stores, and thus individual store revenue should then represent reality as closely as possible. Equation 6.10 outlines the calculation used to minimise the difference between observed and predicted ATD:

(6.10) Where: ∑ ∑ (6.11) ∑ ̂ ∑ ̂ (6.12)

The spreadsheet based model, developed by the author, iterates through a series of values, recording the associated ATD, with a view to minimising the difference between _{. Since the model operates using road travel time in place of distance, ATD can be} thought of as the average trip ‘cost’, and reflects the average travel time (in minutes) (Table 6.5). The observed ATD or cost has been calculated using Sainsbury’s transaction level data, linked to consumers’ loyalty cards, reported at an OA level. Comparison of ATD based on road travel time in Table 6.5 identifies a close correspondence between predicted and observed ATD, with a trade-off between the slight over-estimation at Newquay and under-estimation at Truro, which, due to its size and location on the major road network, is able to draw consumers from a wider trade area.

Since the Nectar card dataset is characterised by a number of OAs with very low flows (often representing only a handful of customers), the Sainsbury’s data (and corresponding model flows) have also been aggregated to LSOA level (to reduce the impact of very low flows) for use in calibration and validation. Since road travel time data is not available at the LSOA level, the ATD at the LSOA level reflects actual (straight line) distance, calculated using centroid co-ordinates from each LSOA, and co-ordinates derived from individual store postcodes. Table 6.5 shows also the observed and predicted ATD based on LSOA travel time on a store-by-store basis, demonstrating a close association between _{and ,} and again highlighting the trade-off between Newquay and Truro.

The ability of the model to predict ATD such that it closely resembles observed ATD suggests that the model parameters set are appropriate. In particular, ATD can be used to identify the effectiveness of incorporating alpha as a parameter. As identified in section 6.3.2, alpha is intended to control the relative attractiveness of different brands to different household types, based on income. Following the introduction of alpha as a model parameter it is expected that higher end retailers, such as M&S, Waitrose and Sainsbury’s will be more attractive to high income households and less attractive to low income households, whilst discount retailers (such as Lidl, Aldi, Iceland and, to an extent, ASDA) will be relatively more appealing to low income households. Therefore high income consumers should be willing to travel further to visit higher end retailers, and low income consumers are expected to exhibit a willingness to travel further to reach a discount retailer, notwithstanding the fact that has been set to increase the impedance of distance for low income consumers. In order to identify the impact of alpha on consumer flows (as measured by ATD), Table 6.6 shows the average predicted travel time for low and high income consumers under two scenarios: one where alpha is equal to one (as such it has no impact on modelled flows); and secondly where alpha varies based on the store and household income combination.

Table ‎6.5 - Observed and predicted ATD (travel time and straight line distance) for Cornish study stores.

Based on 52 week flows.

ATD Road Travel Time (Minutes) – OA Level

Straight line distance (km) – LSOA Level Newquay 9.91 8.84 1.12 2.73 2.30 1.19 Bude 10.70 10.27 1.04 3.76 3.34 1.13 Bodmin 12.16 11.70 1.04 5.99 5.36 1.12 Truro 25.80 27.34 0.94 6.81 7.20 0.95 Average 14.64 14.54 1.04 4.87 4.55 1.11

Table 6.6 clearly demonstrates that the incorporation of alpha values (from Table 6.3) improves the ability of the model to replicate the type of consumer behaviour anticipated. Considering low income consumers, the use of alpha values (that vary by consumer income and brand type) increase these consumers’ average travel time to an ASDA store by over 9 minutes (compared to = 1), suggesting that the model can now account for the fact that these consumers are willing to travel further to reach ASDA stores, which become relatively more attractive, by-passing stores that are geographically proximate in order to do so. Similarly, high income consumers exhibit increasing willingness to experience longer average travel times (increasing by around 50%) to shop at M&S, and considerably reduced average journey times for visits to ASDA, for example.

Table 6.7 considers individual brands/retailers’ countywide market shares, shown before and after incorporation of the alpha parameter. In common with Table 6.6, market share analysis identifies that the inclusion of relative brand attractiveness by income group generates market shares in line with expectations. For example, discount retailers such as Aldi and Lidl, and those more focussed on price (e.g. ASDA) exhibit higher market shares among OAs classified as low income following the introduction of the alpha parameter. Table 6.5 to Table 6.7 suggest that the model can replicate observed ATD, accounting for expected behavioural characteristics associated with household income and brand attractiveness. Section 6.6 seeks to assess model performance more broadly using GOF statistics.

Table ‎6.6 - Impact of alpha parameter on ATD for low and high income consumer groups

Retailer Low income consumers High income consumers

= 1 varies by k and n = 1 varies by k and n Aldi 6.80 6.69 6.90 5.17 ASDA 21.83 30.86 25.21 15.83 Lidl 11.39 11.61 9.65 7.00 M&S 4.88 4.02 3.73 6.83 Morrisons 20.65 24.97 16.46 18.40 Sainsbury’s 23.03 15.91 19.79 26.62 Tesco 29.89 25.50 22.64 29.31

Table ‎6.7 - Impact of alpha parameter on retailer market shares

Retailer Low income consumers High income consumers

= 1 varies by k and n = 1 varies by k and n Aldi 3.3 3.0 4.3 3.0 ASDA 14.0 21.7 22.3 13.8 Lidl 10.3 10.5 9.2 6.3 M&S 1.3 0.7 1.5 3.2 Morrisons 14.8 19.7 10.5 11.3 Sainsbury’s 14.3 8.1 15.8 23.8 Tesco 27.1 20.4 22.3 28.6