Method

I make use of survey data originally collected in Sevi et al. (Reference Sevi, Aviña, Péloquin-Skulski, Heisbourg, Vegas, Coulombe, Arel-Bundock, Loewen and Blais2020), which tested the effects of various graphical presentations of COVID-19 spread on public support for closures of the economy. This article uses the same data but describes public opinion instead of testing a causal effect.Footnote ¹

The key outcome variable is the answer to the question of when the respondent expects the government to allow nearly everyone back to work. The survey was conducted April 3–5, 2020, and the answers are integers ranging in increasing months from 1 to 11, where 1 = April and the numbers increase evenly to 9 = December, with 10 being “sometime in 2021” and 11 being “never.” The vast majority of answers are in the 1–9 range, and I model the outcome as a count using MRP, a method that draws on work in Gelman and Little (Reference Gelman and Little1997) and Park et al. (Reference Park, Gelman and Bafumi2004). In the graphical presentations, I treat each integer as representing the first of the associated month.

MRP has been used to estimate subnational public opinion on a wide range of issues from climate change in Canada (Mildenberger et al., Reference Mildenberger, Howe, Lachapelle, Stokes, Marlon and Gravelle2016) to same sex marriage in the United States (Warshaw and Rodden, Reference Warshaw and Rodden2012). MRP generally performs best when it makes use of geographic covariates of public opinion (Hanretty et al., Reference Hanretty, Lauderdale and Vivyan2018; Warshaw and Rodden, Reference Warshaw and Rodden2012), and even under non-ideal circumstances it tends to outperform other methods of estimating subgroup opinion such as simple disaggregation. Even more critical studies of MRP “agree that its performance exceeds that of other methods” (Buttice and Highton, Reference Buttice and Highton2013: 464).

MRP is composed of two steps, a modeling step and a poststratification step. In the modeling step, I estimate the relationship between individual and geographic covariates and the outcome of interest using a multilevel model. In the poststratification step, I take predictions from this model for each demographic-geographic subgroup and re-weight them based on their share of the population in the unit of interest.Footnote ² Combining these two steps allows me to estimate public opinion at finer levels and with less variance than is practical with even large national surveys.

I use this approach to estimate when the Canadian public expects the economy to re-open, and I do this at the level of the country, province, and federal electoral districts, and for the demographic groupings of age, gender, and education. I first model each individual's response as a function of his or her demographic characteristics and location. For individual i, with indexes j, k, l, m, for age by gender categories, level of education, federal electoral district, and region, respectively:

$$Y_i = \beta ^0 + \alpha _{\,j\lsqb i \rsqb }^{age\comma gender} + \alpha _{k\lsqb i \rsqb }^{edu} + \alpha _{l\lsqb i \rsqb }^{\,fed} + \alpha _{m\lsqb i \rsqb }^{region}$$

where the terms after the intercept are modelled as coming from a normal distribution with mean zero:

$$\alpha _j^{age,gender} \sim N\left( {0,\sigma _{age,gender}^2 } \right),{\rm \; for\; }j = 1, \ldots ,6$$

$$\alpha _k^{edu} \sim N\left( {0,\sigma _{edu}^2 } \right),{\rm \; for\; }k = 1, \ldots ,3$$

Federal electoral districts are modelled as inside regions with the following geographic covariates measured at the level of the riding: liberal vote share in the 2019 election, mean income per tax filer in 2017, Canadian childcare benefits per recipient, population, and population density. The variables are aimed at measuring political attitudes in an area, the area's economic status, and its rurality. More formally:

$$\!\!\! \! \alpha _l^{\,fed} \sim N(\alpha _{m\left[ i \right]}^{region} + \beta ^{liberal}\cdot liberal_l + \beta ^{income}\cdot income_l + \beta ^{CCB}\cdot CCB_l + \beta ^{Pop}\cdot Pop_l + $$

$$\beta ^{Density}\cdot Density_l,\sigma _{\,fed}^2 ),{\rm \; for\; }l = 1, \ldots ,335$$

Finally, regions are provinces in all cases, except that Manitoba and Saskatchewan are combined and the Maritime provinces are combined with each other and with Newfoundland. In both cases, this was done to allow pooling of information across provincial boundaries in provinces that had small numbers of observations. I do not generate predictions for the territories. Regions are modelled with only one geographic covariate, which is the total number of COVID-19 cases reported in the province as of April 3, 2020 (Dong et al., Reference Dong, Du and Gardner2020):

$$\alpha _m^{region} \sim N\left( {\beta ^{cases}\cdot cases_m,\sigma _{region}^2 } \right),{\rm \; for\; }m = 1, \ldots ,6$$

The model is fit using the stan_glmer function in the rstanarm package, which is simply a wrapper for Stan (Carpenter et al., Reference Carpenter, Gelman, Hoffman, Lee, Goodrich, Betancourt, Brubaker, Guo, Li and Riddell2017). I use the default, weakly informative priors and the Poisson family. Similar point estimates can be obtained using the glmer function in lme4.Footnote ³

The next step is poststratification, which is when predictions for each demographic-geographic type are generated and then weighted by the percentage of that type in the aggregate unit of interest. There are two gender types, three education types, three age groupings, and 335 federal electoral districts for a total of 6,030 different subgroups. To generate a prediction of public opinion at the provincial level, for example, one draws a prediction for all 6,030 subgroups and then weights each one by its share of the population within each province. Formally, I draw from the posterior predictive distribution for each subgroup c a prediction of when the economy will re-open, ϑc. Each subgroup also has a population count, Nc. I then weight each cell's prediction by its share of the total population of the relevant group, g:

$$y_{group}^{MRP} = \displaystyle{{{\rm \Sigma }_{c\in g}N_c\vartheta _c} \over {{\rm \Sigma }_{c\in g}N_c}}$$

I repeat this process 10,000 times and report either mean predictions per group or the full distribution of predictions across all 10,000 draws.