Multiple outcome recurrent event data are typical in social sciences, where several outcomes on an individual are collected. In situations where aggregated counts of events over a long observation period are recorded, rounding is common, leading to counts being heaped at rounded values. We consider situations where multiple outcome recurrent event data are recorded as binary responses indicating presence/absence of events between periodic assessments. By analyzing these jointly through linkage via random effects, we show that a joint outcome analysis of the presence/absence data, that are less prone to recall errors, provides high relative efficiency, compared to the analysis of true counts. Motivated by a study of criminal behavior, we demonstrate the utility of such joint analyses, including that the analysis of longitudinal presence/absence data eliminates the bias arising from the analysis of heaped count data, and hence incorrect conclusions concerning possible risk factors.