| Statistical analyzes are used in a variety of areas in order to better understand a system, how it changes or evolves over time, and the effects of factors and interventions such as a preventive maintenance plan or a new training program for operators on its performance. When performing the analysis on these types of systems, we find that data are often affected by problems of incompleteness; i.e., data missing during collection, lost through manipulation or even missing by design. Naive methods to deal with these problems are based on simply deleting cases with missing values. In most circumstances, especially with longitudinal data, these methods might render a large percentage of the data set unusable. Other methods, including expectation-maximization, regression and multiple imputations also have disadvantages; e.g., they may provide biased mean estimations or underestimated variances; they may have difficulties imputing integer values; or they may rely heavily on assumed data models.; The object of this research is to develop a method to deal with different problems of missing ordinal or categorical values in longitudinal data sets. Furthermore, the proposed method does not assume an underlying data model. It can be used when more than one variable has missing values, and it preserves the integer nature of the imputed data as well as its range.; A fuzzy adaptive resonance theory (ART) neural network was modified to allow clustering of incomplete data and provide a probabilistic classification. The proposed method to deal with missing data, designated “fuzzy ART multiple imputations (FAM),” uses a modified fuzzy ART network to classify incomplete cases and to select a cluster of complete cases sufficiently similar to the incomplete one. Then, the missing values are imputed with elements obtained from similar complete cases.; Simulated and real data were used to validate the method. It was observed that FAM provided mean estimations as good as that of the most popular methods and sometimes better estimates of variance, without the need to assume an underlying data model. |
