Nominal

Nominal variables (other than dichotomous) must be treated quite differently than ordinal variables. Any multinomial variables in the data set (such as religion coded 1 for Catholic, 2 for Jewish, and 3 for Protestant) must be specified to ${\mathfrak{A}melia}$ using the _AMnoms global. Setting _AMnoms to ``2 5'' for example will tell ${\mathfrak{A}melia}$ to treat the second and fifth variables in the dataset as multinomial.

For a $p$-category multinomial variable, ${\mathfrak{A}melia}$ will find $p$ (as long as your data contain at least one value in each category), and substitute $p-1$ binary variables to specify each possible category. These new $p-1$ variables will be treated as the other variables in the multivariate normal imputation method chosen, and receive continuous imputations. These continuously valued imputations will then be appropriately scaled into probabilities for each of the $p$ possible categories, and one of these categories will be drawn, where upon the original $p$-category multinomial variable will be reconstructed and returned to the user. Thus all imputations will be appropriately multinomial.

Since ${\mathfrak{A}melia}$ properly treats a $p$-category multinomial variable as $p-1$ variables, one should understand the number of parameters that are quickly accumulating if many multinomial variables are being used. If the square of the number of real and constructed variables is large relative to the number of observations, the user is recommended to implement a ridge prior distribution on the parameter space (see Section 7.1). (Note: The global option _AMempri=-3 does not currently work if multinomial variables are identified to ${\mathfrak{A}melia}$, and _AMstart can only be set to 1, its default, or 2.)