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Determining heterogeneous behavior for theater attendance

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Abstract

In this paper we propose and estimate a model of theater participation using the data contained in the 2002 Survey of Public Participation in the Arts from the USA, a dataset widely used to study the determinants of cultural participation. Our contribution relies on the use of an estimation technique that respects the count data nature of the attendance variable (number of theater performances that an individual attended) and allows for heterogeneous behavior. By using a Zero Inflated Negative Binomial Model, we can characterize two distinct behaviors for the observable attendance: a group of never-goers (who never participate) and a subpopulation that has a positive probability of attending. For this latter group, we can estimate the effect of certain personal variables on the probability of highest frequency. The results suggest that the proposed model is appropriate for estimating cultural participation.

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Notes

  1. Survey data derived from the 1992 and the 2002 releases of the Survey of Public Participation in the Arts, as recorded in NEA Research Division Report #45 (NEA 2004).

  2. Data provided in the Theater Facts 2006: A Report on Practices and Performance in the American Not-for-profit Theater Based on the Annunal TCG Fiscal Survey.

  3. As we will discuss in the section that presents the estimation method, the same cannot be said of other areas such as the demand for health services or recreational services.

  4. Good examples of empirical exercises that explore the best way to estimate heterogeneity in behavior when using physician services are Jiménez-Martín et al. (2002) and Deb and Trivedi (2002). Methodological questions are covered in depth in Cameron and Trivedi (1998).

  5. The reader will find in Table 1 containing a description of the dependent variable and the explanatory variables. We have a count variable that reports on observable market behavior that takes values between 0 and 50.

  6. Categorical variables were recoded into dummy variables. Descriptive statistics and estimation results only take into account analytical weights, i.e. the inverse of the probability of being selected. Clusters and strata are not available for confidentiality reasons. For more information on geographical variables and available information, see the technical document form the U.S. Bureau of the Census (2003).

  7. As wisely suggested by a referee, the fact that supply is higher in bigger cities implies that the total price of attending to performances is smaller.

  8. We could also treat this variable as an ordered variable as Borgonovi (2004) does. When commenting our final results, we will compare them with the ones that we obtain if we estimate an ordered logit model (assuming that the paralell regression assumption is fulfilled).

  9. At each point in time, we explicitly mention the behavioral assumptions of fitting such a model. We do not consider in depth two other major approaches: hurdle models and latent class (Mullahy 1986). The use of a two-part hurdle models (TPM) would imply that all zeros are ruled by the same process; the use of a latent model (LCM) would be useful to classify types of attendees. TPM and LCM have been widely used to estimate heterogeneous individual behavior in other areas, mostly in health related choices (as diverse as health services use or consumption of unhealthy substances, e.g. tobacco demand) or in demand for recreation. From a statistical point of view, the TPM is also a finite mixture with a degenerate component. It combines zeros from a binomial density with the positives from a zero truncated density. For the implications of following the TPM approach and estimation procedures, see the outstanding contribution by Mullahy (1998). In the appendix, the reader will find the goodness of fit measures of a hurdle model. The LCM is more flexible because it permits mixing with respect to both zeros and positives (Deb and Trivedi 2002). It is not clear a priori which model would perform better empirically (see, for example, Jiménez-Martín et al. 2002).

  10. So that the process of the reshaping of the functional form to be estimated can be followed, goodness of fit tests and measures are provided in the Appendix. Those results justify the choice of the Zero Inflated Negative Binomial presented below as that which best represents individual behavior. We also provide the goodness of fit statistics of a Hurdle model (thus, a two-part model) that consider that there are two processes determining the attendance: a logit model determines the probability of going or not going and a Truncated Negative Binomial to determine the positive count outcomes. Note that this Hurdle model assumes that all the zero outcomes are generated by the same process.

  11. Caveat: as mentioned above, the parallel assumption is not met, so we cannot trust these estimations. Rather, a generalized ordered model would perform better, in the spirit of what Borgonovi herself estimates. However, we would then encounter a new problem: we would seldom be able to estimate such a model considering so many outcomes of the dependent variable. In our sample, there are a great many values of the dependent variable with very few observations. One possible way to overcome this problem is to regroup under an arbitrary criterion. Another way is to estimate a latent class model.

  12. We would like to remark that very few variables are statistically significant in Borgonovi’s specification for “drama” participations in Table 5 and 6. Sometimes the statistically significant coefficients are small in size (odds ratio around 1).

  13. With the exception of those studies that determine spouses’ joint participation.

  14. In what follows, when talking about the Negative Binomial Model, we will refer to the Negative Binomial II Model, in terms of Cameron and Trivedi (1998).

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Acknowledgments

I would like to thank the guidance of Antonio Morales-Siles, who was my thesis advisor, as well as helpful comments by the Editor and two anonimous referees. This paper also benefited from comments recieved on the 14th Cultural Economics International Conference, especially from the discussion of Bruce Seaman. All errors are solely mine. I would also like to thank the financial support of SGAE-Fundacion Autor, the Spanish Ministry of Education (SEJ 2005/06099) and the Basque Government (BFI-05.225 and IT-241-07).

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Authors and Affiliations

  1. Universidad del País Vasco and Instituto de Estudios Sociales Avanzados (IESA-CSIC), Cordoba, Spain

    Victoria Ateca-Amestoy

  2. Department of Economic Analysis II, University of the Basque Country, Avda. Lehendakari Aguirre, 83, 48015, Bilbao, Spain

    Victoria Ateca-Amestoy

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  1. Victoria Ateca-Amestoy
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Correspondence to Victoria Ateca-Amestoy.

Appendix

Appendix

1.1 Model selection criteria

At every stage of the estimation of the count model, we have performed several contrasts and goodness of fit tests to select the most suitable model. We show the path followed to select the ZINB Model as the sample data-generating process (Long and Freese 2006).

The less sophisticated model is the Poisson Regression Model; it has to fulfill the condition of equal conditional mean and variance (equidispersion). Since the goodness of fit test rejects the hypothesis of equidispersion (the conditional variance would be higher than the conditional mean), we estimate a Negative Binomial II Model (Cameron and Trivedi 1998), Footnote 14 which parameterize the conditional variance so it can accommodate the overdispersion. Thus, we estimate a zero inflated model that would accommodate simultaneously the binary fact of participation as well as the count model. For the binary participation decision, we estimate a logit regression model, whereas for the count we face a double alternative: Poisson or negative binomial distribution. In this way, we have two models, the ZIP and the ZINB, being the second model a particular case of the first one. We also estimate a Hurdle model (logit for the binary outcome and Negative Binomial II for the count).

Goodness of fit statistics for the estimated models

 

BIC

AIC

Loglik

Poisson

2.453e+12

1.472e+08

−1.226e+12

NB (Negative Binomial II)

1.908e+12

1.146e+08

−9.542e+11

ZIP

1.950e+12

1.171e+08

−9.752e+11

ZINB

1.806e+12

1.084e+08

−9.032e+11

Hurdle

NA

1.08e+08

−9.036e+11

Goodness of fit tests for the estimated modelsa

 

Statistic

Test

Poisson

χ2 = 1.84e+12

P > χ2 (16,656) = 0.0000

Poisson versus NB

LR = −2 *  (llp − llnb) = 5.4e+11

with P ≥ 0.000

ZIP versus ZINB

LR = −2 *  (llzip − llzinb) = 1.4e+11

with P ≥ 0.000

  1. aWe could not estimate Vuong tests to discard Poisson versus ZIP and NB versus ZINB since we used probability weights to estimate our models. Voung test cannot be computed in stata with pweight option

As seen in the tables above, standard information criteria provide strong evidence to support the suitability of the ZINB. Finally, we present the graphic that represents how well each of the models have performed (Fig. 1).

Fig. 1
figure 1

Difference between observed and predicted values (truncated at 9 for this graphic). Note: Positive deviations show underpredictions

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Ateca-Amestoy, V. Determining heterogeneous behavior for theater attendance. J Cult Econ 32, 127–151 (2008). https://doi.org/10.1007/s10824-008-9065-z

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