Two problem in cognitive algebra are considered in this chapter. One is a problem of model diagnosis, distinguishing between two integration rule, averaging and multiplying, in causal attribution. This was the initial focus of the experiments reported here. Attempt toward model diagnosis, however, led to a further problem concerning imputations, that is, inferences about missing information. Most studies of information integration present specific pieces of information that control the judgment. In some situations, however, needed information may be missing. Judges may then impute some value to the missing information in arriving at their judgments. Imputations about missing information are inherent in all day-to-day activities; they cannot be ignored merely because they are not known. This chapter presents a systematic study of imputations about missing information, and shows that the conventional distinguishing tests between integration rules are ambiguous because of the problems connected with imputations. In a series of eight experiments, subjects received information about generosity and income of the stimulus persons and predicted size of gift by each stimulus person to a family whose house was burned down. Prediction of gift size obeyed the hypothesized multiplying rule: Gift Size = Generosity x Income. The alternative averaging rule which also specifies a similar fan pattern in the facterial plot of Generosity x Income effect was unequivocally infirmed. When judges predicted size of gift on the basis of information about generosity alone or income along of the donor, they imputed value for the missing information. Missing generosity information was imputed a constant, average value; missing income information, however, was imputed a value equal to that of the given information about generosity. Precise specification of these imputation was made possible through new distinguishing tests developed within the present research program. Application of this approach to the further study of attractiveness of consumer products, friendship formation, disciplinary judgments, and prediction of performance has been discussed.