3. Statistical model

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3.1 Estimation strategy

As data on participation levels are categorical and hierarchical, ordinary least-square and multinomial regression models provide biased estimates of the social correlates of culture participation since they all fail to utilize the ordering information of the response variable. In this context, our estimation strategy is the stereotype ordered regression (SOR) model proposed by Anderson (1984). The intuition behind the SOR model is that each interviewee (considered as a judge by Anderson) has stereotypes that characterize participation levels. Consequently, he or she analyzes each participation level and then chooses that level whose stereotype most correctly matches his or her views on the question being asked (Long and Freese, 2006).

Apart from capturing the ordinal and ordered nature of the dependent variable, the SOR model has an important advantage over alternative regression models for categorical dependent variables such as McCullagh's (1980) grouped continuous model and Fienberg's (1980) continuation-ratio model. It addresses issues such as whether two adjacent categories are essentially the same with respect to the covariates and whether an ordered relationship is appropriate (Greenwood and Farewell, 1988).

Our estimation strategy is also technically supported by two procedures of model selection. First, we tried the standard ordered logit model and applied the Brant (1990) test of parallel regression assumption. Second, we estimated the cumulative logistic model known to capture the hierarchical form of the dependent variable and we applied the score test. In results not shown, significant test statistics (i.e., Wald and score) provide evidence that the proportional odds assumption has been violated.⁸

The SOR model can be represented as:

Subject to:

where X_i denotes the vector of explanatory variables; β denotes the effect parameters for the covariates; κ is the number of cut-points for the dependent variable(Y_i);, α_q, α_s represent the constrained intercept parameters in the regression models;⁹ and Ø_q represents the scaling metric for the dependent variable.¹⁰

Condition (2.2) states that all explanatory variables other than the constant term do not necessarily have an equal effect across categories of the dependent variable. Statistically significant φs have two important implications. First, they imply that the ordering of the regression model is that suggested by the category definition. Second, they indicate that the effect of covariates upon the first odds ratio is greater than their effect on the second and so forth. Condition (2.3), which follows Anderson's (1984) recommendation, represents an additional order constraint that allows the model in (2.1) to be identifiable when using estimated values attributed to the response variable (Ananth and Kleinbaum, 1997). Under the SOR environment, a positive coefficient means that higher values for this covariate imply greater culture participation, ceteris paribus . Clearly, adults with this characteristic are more likely to report higher participation, in comparison with individuals without this characteristic, holding all other variables constant. The opposite interpretation is true with a negative coefficient.

3.2 Explanatory variables

In order to determine which socioeconomic and demographic factors are most important in explaining culture consumption in Canada, we explore a wide range of explanatory variables. First of all, we take into account variables such as household income, educational attainment and professional occupation that have been found to be statistically significant in past research (see Ateca-Amestoy, 2005; Borgonovi, 2004; Gray, 2003; Lewis and Seaman, 2004, Sturgis and Jackson, 2003). Moreover, sociologists, psychologists, marketing specialists as well as economists have all found that family background characteristics are major drivers of culture participation, whether activities take place inside or outside the home (see, for instance, Bourdieu, 1984; DiMaggio and Useem, 1978b; O'Hagan, 1996; Upright, 2004). Also, in order to capture the effect of a person's family socioeconomic situation on his or her level of culture consumption, we consider parents' schooling and conjugal partner's education.

We control for age since the regular consumption of culture commodities (such as theatre, public galleries or art museums and literature) requires the development of tastes which is a lifetime learning process (Gray, 2003; Lévy-Garboua and Montmarquette, 1996; McCain, 1995). Controlling for age also allows us to account for effects such as entrance in the labour market, ill health and lower mobility while explaining the observed heterogeneity in culture participation (Borgonovi, 2004).

Prior empirical evidence indicates that gender matters a great deal in culture participation. For instance, Gray (2003) showed that American females were more likely than their male counterparts to attend artistic events such as classical music, opera, musical theatre, theatre, ballet and museums. Likewise, in a comparative analysis on arts participation in the United States, DiMaggio and Mukhtar (2004) noted that the overrepresentation of women persists in all culture activities and even rises over time. Following this stream of literature, we control for gender.

We control for further heterogeneity underlying culture consumption by utilizing the statistical information from two variables representing the number of young children at home aged 0 to 4 and 5 to 12, respectively. As culture participation is generally time-intensive, controlling for the number of young children at home is of interest as it allows us to capture the availability of people's leisure time. We can reasonably think that young children in the household could make it more likely that individuals will be spending more time in household maintenance and family care. This in turn could lower the time available for personal leisure pursuits. Arguably therefore, we expect participation in most culture activities, and especially in those which occur outside the home, to decrease with the number of young children at home, ceteris paribus.

Similarly, four dummy variables are included to represent marital status of the respondent (i.e., married, living common-law, widowed and single, with divorced or separated serving as reference category). These variables allow us to capture the importance that living arrangements have on the behaviour of culture participants. We expect married individuals and people living common-law to be less likely than divorced or separated individuals to belong to audiences of most culture activities because the presence of a conjugal partner is likely to impose additional constraints on preferences and choice sets (Ateca-Amestoy, 2005; Upright, 2004).

In order to take into account the opportunity cost of time, we control for the labour status of the respondent during the year preceding the survey through two dummy variables: self-employment and permanent employment. All things remaining equal, we reasonably expect permanent workers to be less likely than temporary workers or students to have a high availability of leisure time.

Following past research, our analysis also includes four dummy variables representing geographic location (i.e., Atlantic Canada, Quebec, Prairies and British Columbia, with Ontario acting as reference category) and one binary variable indicating whether a person is an urban area resident or not. All these variables allow us to account for contextual factors and other omitted variables. As an example, we expect urban area residents to be more likely than rural ones to visit public galleries and art museums on a frequent basis because the existence of threshold market sizes makes it less likely that small areas will be housing major culture activities such as theatre, public galleries or art museums (Gray, 2003). The province of Quebec is one of Canada's most populous provinces and is home to a large number of non-profit performing arts organizations.¹¹ These two elements lead us to conjecture, a priori, that Quebecers will be more likely to belong to audiences of several artistic events.