Ordinal

In much statistical research, researchers treat independent ordinal (including dichotomous) variables as if they were really continuous. If the analysis model to be employed is of this type, then nothing extra is required of the of the imputation model. Users are advised to allow ${\mathfrak{A}melia}$ to impute non-integer values for any missing data, and to use these non-integer values in their analysis. Sometimes this makes sense, and sometimes this defies intuition. One particular imputation of 2.35 for a missing value on a seven point scale carries the intuition that the respondent is between a 2 and a 3 and most probably would have responded 2 had the data been observed. This is easier to accept than an imputation of 0.79 for a dichotomous variable where a zero represents a male and a one represents a female respondent. However, in both cases the non-integer imputations carry more information about the underlying distribution than would be carried if we were to force the imputations to be integers. Thus whenever the analysis model permits, missing ordinal observations should be allowed to take on continuously valued imputations.

Often, however, analysis models require some variables to be strictly ordinal, as for example the dependent variable must be in a logistical regression. Such variables should be specified to ${\mathfrak{A}melia}$ using the _AMords global. Setting _AMords to ``2 5'' for example will tell ${\mathfrak{A}melia}$ to make the second and fifth variables in the dataset ordinal, and integer imputations will be created for those variables. These imputations are created by taking the continuously valued imputation and using an appropriately scaled version of this as the probability of success in a binomial distribution. The draw from this binomial distribution is then translated back into one of the ordinal categories.