two-sided linear formula object describing both the fixed-effects and random-effects parts of the model,
with the response on the left of a ~ operator. For univariate response, put variable name directly; for multivariate responses
combine variables using concatenate operator, for example, for bivariate responses, c(var1, var2). The predictor terms are separated by + operators, on the right. Random-effects terms are
distinguished by vertical bars '|' separating expressions for design matrices from grouping factors.