5.2 Univariate models
After deploying our GUI (see Figure 5.1), the user should select Univariate Models from the top panel. Then, Figure 5.2 is displayed, showing a radio button on the left-hand side that lists the specific models within this category. In particular, users can see that the normal model is selected from the univariate models class.
Figure 5.2: Univariate models: Specification.
Then, the right-hand panel displays a widget for uploading the input dataset, which must be a csv file with headers in the first row. Users must also select the separator type used in the input file: comma, semicolon, or tab (use the DataSim and DataApp folders for input file templates). Once the dataset is uploaded, users can preview the data. Range sliders allow users to set the number of iterations for the Markov Chain Monte Carlo algorithm, specify the burn-in period, and adjust the thinning parameter (see the following chapters in this section for technical details).
Next, users must specify the equation. This can be done using the formula builder, where they select the dependent variable and independent variables, then click on the Build Formula tab. The equation appears in the Main Equation space, formatted according to R syntax (see the main equation box in Figure 5.2, e.g., y∼x1+x2+x3). Users can modify this as needed, including higher-order terms, interaction effects, or other transformations. These modifications must follow the standard formula syntax.26
By default, univariate models include an intercept, except for ordered probit models, where the specification must explicitly exclude it due to identification constraints (see details below).27 Thus, users should specify this explicitly as follows: y∼x1+x2+x3−1.
Finally, users must define the prior hyperparameters. For example, in the normal-inverse gamma model, these include the mean vector, covariance matrix, shape parameter, and scale parameter (see Figure 5.3). However, our GUI uses non-informative hyperparameters by default across all modeling frameworks, so this step is optional.
Figure 5.3: Univariate models: Results.
After completing the specification process, users should click the Go! button to initiate the estimation. Once the process is finished, our GUI displays the summary statistics and convergence diagnostics (see Figure 5.3). Additionally, widgets allow users to download the posterior chains (csv file) and graphs (pdf and eps files). Note that in the results—summary, posterior chains, and graphs—the coefficients are ordered with location parameters appearing first, followed by scale parameters.
For multinomial models (probit and logit), the dataset must be structured as follows: the first column should contain the dependent variable, followed by alternative-specific regressors (e.g., alternatives’ prices), and finally, non-alternative-specific regressors (e.g., income). The formula builder allows users to specify the dependent variable as well as both types of independent variables (see technical details in the next chapter). Additionally, users must define the base category, the number of alternatives (which is also required for ordered probit), the number of alternative-specific regressors, and the number of non-alternative-specific regressors (see Figure 5.4).
For multinomial logit models, users can also specify a tuning parameter—the degrees of freedom for the Metropolis–Hastings algorithm (see technical details in the next chapter). This tuning option is available in our GUI when estimation relies on the Metropolis–Hastings algorithm.
In the results of these models, coefficients are ordered as follows:
Figure 5.4: Univariate models: Multinomial.
Note that the non-alternative-specific regressors associated with the base category are set to zero and do not appear in the results. Additionally, due to identification constraints in multinomial and multivariate probit models, some coefficients in the main diagonal of the covariance matrix remain constant.
Figure 5.5: Univariate models: Bootstrap.
For the negative binomial model, users must specify a dispersion parameter (see the next chapter for details). Similarly, for Tobit and quantile models, users need to define the censorship points and quantiles, respectively.
The Bayesian bootstrap method only requires uploading a dataset, specifying the number of MCMC iterations, setting the resampling size, and defining the equation (see Figure 5.5). The input file should follow the same structure as the one used for the univariate normal model.
See https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/formula↩︎
An identification issue arises when multiple sets of model parameters yield the same likelihood function value.↩︎