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.