Cultural Repertoires: A Market Basket Analysis
Chris Hand1 and Alan Collins2
1. School of Marketing, Kingston University, Kingston Hill, Kingston upon
Thames, Surrey, KT2 7LB, UK
Email: c.hand@kingston.ac.uk
2. Department of Economics, University of Portsmouth, UK
Abstract
This paper investigates the effect of participation in one cultural pursuit on
participation in another. With one or two exceptions, studies of participation have
tended to focus solely on one pursuit at a time, using a standard demand function
which may include the prices of complements and substitutes.
This paper adopts an alternative, empirical approach to determining the interrelationships between cultural pursuits and employs a technique found in the
marketing and data mining literature: Market Basket Analysis. This allows us to
identify the inter-relationships between the cinema, theatre, museums / galleries,
concerts / gigs, live sport, playing sport / exercise, watching videos / DVDs and
playing computer games using a national survey from the UK.
We find three groups of pursuits which are strongly associated, where
participation in one is associated with participation in the others, as well as two
groups where participation is negatively associated.
Key words: Leisure, Participation, Market Basket Analysis
1
1. Introduction
Cultural activities have been the subject of increased attention from
Economics and Business researchers in recent years. However, attention has tended
to focus on the determinants of participation in individual leisure pursuits. For
example, Farrell and Shields (2002) investigated participation in sports in the UK
whilst Gray (2003) and Borgonovi (2004) examine attendance at performing arts in
the US. The film industry in particular has attracted attention from researchers, with
recent studies investigating the determinants of commercial success (e.g. De Vany
and Walls,1999, Collins, Hand and Snell, 2002, Walls, 2005), modelling survival
times (e.g. De Vany and Walls, 1997, Jedidi, Krider and Weinberg, 1998), release
timing for movies (Krider and Weinberg, 1998), sequential release of films across
channels, such as in movie theatres and on video (Lehmann and Weinberg, 2000) and
across markets (Elberse and Eliashberg, 2003). Studies of the theatre have addressed
similar themes. Johnson and Garbarino (2001) investigated the differences between
subscribers and non-subscribers to an off-Broadway theatre, in terms of satisfaction,
trust and commitment. Simonoff and La (2003) investigate the determinants of the
duration of a play’s run on Broadway whilst Maddison (2004) examines the
distribution of Broadway shows’ survival times. Ngobo (2005) investigates the
impact of both demographics and satisfaction on upward and downward migration
(i.e. the decision to become a subscriber and the decision to purchase tickets less
often.
It is already known that those who attend one live art frequently are likely to
attend others (Andreason and Belk, 1980). However, the relationship between
different leisure pursuits (not just live arts) and whether they are complements or
substitutes has received far less attention and has tended to focus on whether sports
2
and arts are substitutes. A second strand of the literature has investigated whether
tastes in both music and in leisure pursuits more generally have broadened over time;
whether “snobs” have become “omnivores” (e.g. Peterson and Kern, 1996, Holbrook,
Weiss and Habich, 2002).
The conventional approach in economics in defining substitutes and
complements is to examine cross-price elasticities. As Gapinski (1986) observes, the
idea that the price of substitutes are determinants of demand for the arts is far from
new. However, exactly what the substitutes for a particular leisure pursuit are is far
from clear. In models of demand for the theatre, the cinema is sometimes included as
a substitute (e.g. Touchstone, 1980). Macmillan and Smith (1999) included a proxy
for television in their model of cinema attendance, whilst Collins, Hand and Ryder
(2005) included video in their study of cinema visit frequency. Typically however,
such studies have included few substitutes and have the aim of explaining attendance
at a particular arts event, rather than determine the relationship between different
leisure pursuits. In the marketing literature, the relationship between different
channels of distribution (e.g. cinema release and release on DVD) have been studied,
but from the producer’s perspective rather than the consumers’ (for example,
Lehmann and Weinberg, 1998, considered the optimal release time for films on
video).
An alternative is to examine consumers’ behaviour over time. Over time,
consumers may change from one brand to another, to another and then back to the
original brand. As Ehrenberg (1972) has shown, in general, households are loyal to
several brands rather than being loyal to only one brand. The brands a household is
loyal to are known as the brand portfolio or brand repertoire. The effect of
participation in one activity on the likelihood of participation in another has received
3
little recent attention. Montgomery and Robinson (2005) provide a notable exception;
their study found little evidence that sports were substituted for arts, rather sports
attendance increased the likelihood of attending arts performances.
This paper takes a different approach, regarding the leisure pursuits people
engage in as forming the repertoire of pursuits they are loyal to. These “cultural
repertoires” (analogous to brand repertoires) are investigated using a market basket
analysis to determine the extent to which cinema, theatre, video / DVD, video /
computer games, concerts / gigs, galleries / museums, watching live sports and
playing sport / exercising are substitutes or complements.
2. Market Basket Analysis
Market Basket Analysis (MBA) is an exploratory technique which identifies
the strength of association between pairs of products purchased from an individual
retailer. Such analysis is usually applied to data on shopping behaviour, such as that
collected at the point of sale. If applied to grocery shopping for example, the results
of a MBA could inform a supermarket’s pricing strategy. If the supermarket knows
that bread and fruit juice tend to be purchased together, it can avoid offering price
discounts on both at the same time. In this paper, we apply the same approach to a
notional basket of leisure pursuits which we denote consumers’ leisure repertoires.
A Market Basket Analysis determines the degree to which two leisure
activities are associated and hence are likely to feature in the same “basket” of leisure
pursuits. In its simplest form, an MBA can be seen as a series of pairwise
contingency tables. With very large datasets, such contingency tables can be used to
filter out pairs of products which are not associated, allowing a more parsimonious
model to be estimated. A number of different methods have been employed in the
4
study of market baskets: pairwise comparison (e.g. Julander, 1992), association rules
(e.g. Giudici, 2003), Bayesian model search employing Markov Chain Monte Carlo
methods (Giudici and Passerone, 2002), neural network models (Decker and Monien,
2003) and the method we employ, log-linear models.
3. Data
In this study we used data from the Cinema and Video Industry Audience
Research (CAVIAR) survey. The CAVIAR survey is undertaken annually by BMRB
International on behalf of the UK’s Cinema Advertising Association. The data was
collected from a sample representative of the UK population (slightly over-sampling
younger age groups to reflect the cinema audience). Amongst other things the survey
asks which of a list of leisure pursuits each respondent enjoys participating in
(however, the survey only captures participation, data on frequency of participation is
only collected for cinema-going and watching videos / DVDs). Hence our data is
based on stated preference rather than actual consumption records.
The full CAVIAR data set contains 3106 observations; filtering out
respondents under the age of 18 reduced the sample size to 1937. Table 1 shows the
number of respondents who stated they enjoyed each leisure pursuit in each age
group.
Table 1. Age profile of Leisure Pursuits
Age
Group
Cinema Computer / Theatre Live
Concert Sport /
Gallery/ DVD /
console
Sport / gig
exercise Museum Video
games
18 – 24
474
297
113
214
213
304
98
487
25 – 34
296
178
104
121
164
182
112
330
35 – 44
259
117
120
131
140
163
119
272
45 – 54
85
31
71
45
64
56
62
97
55 – 64
34
13
53
21
27
26
37
39
65 & over
34
11
50
25
20
24
35
44
Total
1182
647
511
557
628
755
463
1269
5
Cinema-going and watching DVDs were the most popular with 1182 and 1269
respondents saying they enjoyed these activities, whilst the theatre was the least
popular. As might be expected, cinema-going, playing computer / console games and
watching DVDs / video were more popular among younger respondents, whilst
theatre-going and going to galleries and museums were more popular among older
respondents.
4. Log-Linear Model
Log-linear models can be thought of as association tests for n-way
contingency tables. Our data set contains eight leisure pursuits: cinema, theatre,
watching DVDs / videos, computer / console games, watching live sport, concerts /
gigs, sport / exercise and going to galleries or museums. We could investigate the
relationship between these activities by considering the 36 2x2 contingency tables
obtained by considering each possible pair of leisure activities. However, this would
only show marginal associations, and not conditional associations. Hence, we used a
log-linear model, rather than separate contingency tables to run the market basket
analysis.
A loglinear model predicts the log of the number of observations in each cell
of a contingency table using an estimated parameter (λ) for each value of the row and
column variables and for each combination of the row and column variables. In
general terms, for a two-way contingency table, the predicted number is obtained
from a constant (μ), two main effects coefficients which depend on the variables in
the row and column of the contingency table and an interaction term which describes
the association between the two variables. For example, in a contingency table of
6
whether cinemagoers are also theatregoers the predicted number of cases in each cell
would be as follows:
ln(m11) = μ + λ non-cinemagoer + λ non-theatregoer + λ non-cinemagoer and non-theatregoer
ln(m12) = μ + λ non-cinemagoer + λ theatregoer + λ theatregoer but non-cinemagoer
ln(m21) = μ + λ cinemagoer + λ non-theatregoer + λ cinemagoer but non-theatregoer
ln(m22) = μ + λ cinemagoer + λ theatregoer + λ cinemagoer and theatregoer
where m(ij) refers to the cell in the ith row and jth column of the table. In Market
Basket Analysis, interest is usually focussed on the interaction between purchases.
The results of log-linear models are often interpreted in terms of odds ratios.
The odds ratios are arguably easier to interpret than the log-linear coefficients. An
odds ratio of one denotes no association, less than one a negative association and
greater than one a positive association. In analyses of data sets with a large number of
variables, attention may be focused on odds ratios greater than a threshold level (e.g.
Giudici and Passerone, 2002, use an odds ratio of 5) rather than reporting all
significant associations. Market Basket Analyses are usually conducted on very large
datasets; the example presented by Giudici (2003) contains 46,727 observations.
With such large datasets inferential statistical tests can become too sensitive with very
small odds ratios being significant. Focusing on the largest odds ratios (the most
strongly associated pairs of leisure pursuits) avoids this problem. Alternatively, an
odds ratio may be regarded as significant if the lower bound of its 95% confidence
interval is greater than 1. Our dataset is sufficiently small so that the significance
tests based on Z statistics and on confidence intervals coincide.
7
5. Results
Table 2 contains the results of the log-linear model. In order to obtain the odds ratios,
we transform the estimated coefficients by exponentiating them (i.e. raising the
coefficient to the power e)1. The odds column contains the odds that each
combination of leisure pursuits is associated. Where a negative association was found
(odds less than 1), the odds against were also calculated in order to compare the
strength of the positive and negative associations. To make the table easier to read, it
is arranged with the interaction term parameters in descending order of size.
Table 2 Full log-linear model results
Parameter
Estimate
Std.
Z
Sig.
Odds
Error
Constant
4.889
0.068
Odds
against
71.451
0.000
-
-
games
-1.806
0.123 -14.720
0.000
-
-
video_DVD
-0.335
0.091
-3.693
0.000
-
-
Cinema
-0.938
0.102
-9.240
0.000
-
-
Concert_gig
-2.287
0.133 -17.204
0.000
-
-
Gallery_museum
-2.221
0.137 -16.227
0.000
-
-
live_sport
-1.834
0.123 -14.905
0.000
-
-
sport_exercise
-1.505
0.112 -13.399
0.000
-
-
Theatre
-1.912
0.128 -14.921
0.000
-
-
live_sport * sport_exercise
1.460
0.110
13.305
0.000
4.305*
-
Theatre * gallery_museum
1.388
0.121
11.504
0.000
4.005*
-
Cinema * video_DVD
1.050
0.107
9.832
0.000
2.859*
-
8
games * video_DVD
1.020
0.120
8.485
0.000
2.772*
-
Theatre * concert_gig
0.813
0.119
6.819
0.000
2.254
-
Cinema * concert_gig
0.757
0.119
6.370
0.000
2.133
-
Concert_gig * gallery_museum
0.728
0.122
5.957
0.000
2.070
-
Cinema * theatre
0.671
0.130
5.159
0.000
1.957
-
Concert_gig * video_DVD
0.546
0.122
4.485
0.000
1.726
-
sport_exercise * gallery_museum
0.485
0.124
3.902
0.000
1.624
-
games * live_sport
0.453
0.114
3.969
0.000
1.573
-
games * sport_exercise
0.389
0.109
3.563
0.000
1.475
-
Cinema * sport_exercise
0.388
0.112
3.466
0.001
1.474
-
Cinema * gallery_museum
0.379
0.133
2.844
0.004
1.461
-
live_sport * concert_gig
0.313
0.120
2.613
0.009
1.368
-
Cinema * games
0.268
0.113
2.381
0.017
1.308
-
games * concert_gig
0.202
0.113
1.783
0.075
1.223
-
Theatre * sport_exercise
0.191
0.122
1.557
0.119
1.210
-
Concert_gig * sport_exercise
0.189
0.113
1.667
0.095
1.208
-
Cinema * live_sport
0.106
0.121
0.877
0.381
1.112
-
live_sport * video_DVD
0.019
0.123
0.151
0.880
1.019
-
sport_exercise * video_DVD
-0.006
0.114
-0.053
0.958
0.994
1.006
Gallery_museum * video_DVD
-0.010
0.131
-0.075
0.940
0.990
1.010
Theatre * live_sport
-0.116
0.133
-0.875
0.382
0.890
1.123
games * gallery_museum
-0.158
0.129
-1.229
0.219
0.854
1.171
live_sport * gallery_museum
-0.286
0.137
-2.096
0.036
0.751
1.332
Theatre * video_DVD
-0.298
0.127
-2.351
0.019
0.742
1.347
9
games * theatre
-0.393
0.127
-3.092
0.002
0.675
* denotes odds ratio significantly greater than 2 (i.e. those with a lower bound of the
95% confidence interval > 2). See appendix for full results.
Of the 28 pairs of leisure activities examined, 16 show positive associations which are
significant at the 5% level; a further three show significant negative associations
(again at the 5% level). To ease interpretation, the results are summarised on
conditional independence graphs where the nodes are the leisure pursuits and an edge
is drawn between a pair of nodes if the association is between them is significant.
Figure 1 shows the conditional independence graph for all significant positive
associations.
Figure 1. Significant positive associations
live sport
playing sport /
exercise
cinema
pre-recorded
video / DVD
museum /
gallery
computer games
/ games console
theatre
concert / gig
10
1.481
All leisure pursuits are associated with between three and five other leisure pursuits;
none are pursued exclusively. Cinema and Concerts / Gigs have the most
connections, both being significantly associated with five other leisure pursuits. The
thick broken lines in figure 1 denote strong associations where the odds ratio is
significantly greater than 2. These stronger groupings are shown more clearly in
figure 2
Figure 2. Strong Positive Associations
live sport
playing sport /
exercise
cinema
pre-recorded
video / DVD
museum /
gallery
computer games
/ games console
theatre
concert / gig
Figure 2 shows three discrete groups of leisure pursuits. The groupings of activities
seem to be thematically linked with watching DVDs and going to the cinema being
linked for example. Perhaps surprisingly, in-home and out of home leisure activities
do not form separate groups. Watching live sport and playing sports / exercising form
a pair by themselves. Theatre and museums / galleries form what could be termed a
“cultured leisure” group (both are also more weakly linked to concerts / gigs). The
11
final group could be called “screen-based entertainment”. Cinema is found to be a
complement to video / DVDs, whilst watching DVDs is associated with playing
computer / video games (there is a weaker association between cinema and playing
computer / console games; the odds ratio was 1.308). The only unconnected node is
concerts / gigs. This could imply that concerts / gigs have broad appeal, or could
equally result from a broad definition so that classical concert and a rock concert are
included in the same variable.
In traditional market basket analysis attention is focused on the positive
associations. In this case however, the negative associations are perhaps of more
interest. Although no strong (odds ratio greater than two) negative associations were
found, three significant negative associations were found, as shown in figure 3.
Figure 3. Significant Negative Associations
live sport
playing sport /
exercise
cinema
pre-recorded
video / DVD
museum /
gallery
computer games
/ games console
theatre
concert / gig
Theatre-going was found to be negatively associated with watching DVDs and with
playing computer / console games. This is perhaps a reflection of the differences in
12
ages of those who participate in these leisure activities. The other significant negative
association is between going to museums / galleries and watching live sport.
6. Conclusions
The strong positive associations found are as would be expected: cinema and
DVD are associated with each other, as are theatre and museums. Watching live sport
is positively associated with playing sport or exercise and negatively associated with
the more sedentary activities of visiting museums, galleries or exhibitions. Perhaps
surprisingly, the association between watching live sport and playing sport /
exercising is the strongest of the three, with the association between cinema and
watching DVDs is the weakest. Cinema-going is not only associated with what might
be called “screen-based leisure pursuits”, but also with more “cultured” pursuits, such
as the theatre and visiting museums and art galleries. Furthermore, no leisure activity
is independent of all the others, which suggests that very few people are “loyal” to
one activity, indeed participation in one activity is associated with participation in a
number of others.
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Note
1. The way the odds ratios are obtained from the log-linear results depends on the
software used to estimate it. If SPSS is used, the odds ratio is obtained by
exponentiating the interaction coefficient (Norusis, 2005); if SAS is used, the odds
17
ratio is equal to exponentiating the interaction coefficient multiplied by four (Giudici,
2003).
Appendix: Log-linear model – Full results
Parameter
Constant
Games
Video_DVD
cinema
concert_gig
gallery_museum
live_sport
sport_exercise
theatre
live_sport * sport_exercise
theatre * gallery_museum
cinema * Video_DVD
Games * Video_DVD
theatre * concert_gig
cinema * concert_gig
concert_gig * gallery_museum
cinema * theatre
concert_gig * Video_DVD
sport_exercise * gallery_museum
Games * live_sport
Games * sport_exercise
cinema * sport_exercise
cinema * gallery_museum
live_sport * concert_gig
cinema * Games
Games * concert_gig
theatre * sport_exercise
concert_gig * sport_exercise
cinema * live_sport
live_sport * Video_DVD
sport_exercise * Video_DVD
gallery_museum * Video_DVD
theatre * live_sport
Games * gallery_museum
live_sport * gallery_museum
theatre * Video_DVD
Games * theatre
Estimate
4.889
-1.806
-0.335
-0.938
-2.287
-2.221
-1.834
-1.505
-1.912
1.460
1.388
1.050
1.020
0.813
0.757
0.728
0.671
0.546
0.485
0.453
0.389
0.388
0.379
0.313
0.268
0.202
0.191
0.189
0.106
0.019
-0.006
-0.010
-0.116
-0.158
-0.286
-0.298
-0.393
Std.
Error
0.068
0.123
0.091
0.102
0.133
0.137
0.123
0.112
0.128
0.110
0.121
0.107
0.120
0.119
0.119
0.122
0.130
0.122
0.124
0.114
0.109
0.112
0.133
0.120
0.113
0.113
0.122
0.113
0.121
0.123
0.114
0.131
0.133
0.129
0.137
0.127
0.127
Z
Sig.
71.451
-14.720
-3.693
-9.240
-17.204
-16.227
-14.905
-13.399
-14.921
13.305
11.504
9.832
8.485
6.819
6.370
5.957
5.159
4.485
3.902
3.969
3.563
3.466
2.844
2.613
2.381
1.783
1.557
1.667
0.877
0.151
-0.053
-0.075
-0.875
-1.229
-2.096
-2.351
-3.092
18
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.004
0.009
0.017
0.075
0.119
0.095
0.381
0.880
0.958
0.940
0.382
0.219
0.036
0.019
0.002
95% Confidence
Interval
Odds
Ratio
Odds
against
Lower
Bound
4.755
-2.047
-0.514
-1.137
-2.547
-2.489
-2.075
-1.726
-2.163
1.245
1.151
0.841
0.784
0.579
0.524
0.488
0.416
0.307
0.241
0.229
0.175
0.169
0.118
0.078
0.047
-0.020
-0.049
-0.033
-0.131
-0.222
-0.229
-0.267
-0.376
-0.410
-0.554
-0.547
-0.642
95%
Confidence
Interval
Upper Lower
---------4.305
4.005
2.859
2.772
2.254
2.133
2.070
1.957
1.726
1.624
1.573
1.475
1.474
1.461
1.368
1.308
1.223
1.210
1.208
1.112
1.019
0.994
0.990
0.890
0.854
0.751
0.742
0.675
---------3.472
3.162
2.319
2.190
1.784
1.689
1.629
1.516
1.360
1.273
1.258
1.191
1.184
1.125
1.081
1.049
0.980
0.952
0.967
0.877
0.801
0.795
0.765
0.686
0.663
0.574
0.579
0.526
------------------------------1.006
1.010
1.123
1.171
1.332
1.347
1.481
Upper
Bound
5.023
-1.566
-0.157
-0.739
-2.026
-1.953
-1.593
-1.285
-1.661
1.675
1.624
1.260
1.255
1.046
0.990
0.967
0.926
0.784
0.729
0.677
0.603
0.608
0.641
0.548
0.489
0.423
0.431
0.410
0.342
0.259
0.217
0.247
0.144
0.094
-0.019
-0.050
-0.144
---------5.338
5.073
3.525
3.508
2.847
2.692
2.630
2.526
2.191
2.072
1.968
1.827
1.836
1.898
1.730
1.631
1.527
1.538
1.507
1.408
1.295
1.242
1.281
1.155
1.099
0.982
0.952
0.866